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Using Recurrent Procedures in Adaptive Control System for Identify the Model Parameters of the Moving Vessel on the Cross Slipway Hanna Rudakova, Oksana Polyvoda and Anton Omelchuk * Engineering Cybernetics Department, Kherson National Technical University, Kherson 73008, Ukraine; [email protected] (H.R.); [email protected] (O.P.) * Correspondence: [email protected]; Tel.: +380-500317468 Received: 4 November 2018; Accepted: 4 December 2018; Published: 7 December 2018







Abstract: The article analyses the problems connected with ensuring the coordinated operation of slipway drives that arise during the launch of a ship. The dynamic model of load of the electric drive of the ship’s cart is obtained taking into account the peculiarities of the construction of the ship-lifting complex, which allows us to analyse the influence of external factors and random influences during the entire process of launching the ship. A linearized mathematical model of the dynamics of a complex vessel movement in the process of descent in the space of states is developed, which allows us to identify the mode of operation of the multi-drive system, taking into account its structure. The analysis of application efficiency of recurrent methods for identification (stochastic approximation and least squares) of the linearized model parameters in the space of states is carried out. A decision support system has been developed in the automated system of operational control by the module for estimating the situation and the control synthesis to ensure a coherent motion of a complex ship-carts object in a two-phase environment. Keywords: the slipway; the adaptive control system; the least squares method; the periodic procedure; the parameters estimation; a large-sized object; a recurrent algorithm; the identification procedure

1. Introduction Shipbuilding and ship repairing are the most important sectors of the economy in countries with access to the sea or which have large river systems. Depending on the technology of the construction of vessels, as well as their size and purpose, different facilities for moving ships to and from the water are used [1–3]. The slipways make up about 30% of all existing boat launch systems and apply to 60% of shipbuilding facilities. Most slipways, for example in the CIS countries, were built in the 60s and 80s of the twentieth century. The main problems of these facilities are the use of outdated control systems on the one hand and their considerable deterioration on the other, these facts a number of difficulties during the operation of the launching facilities. The ship-lifting facilities are complex electromechanical systems. For the operational control it is advisable to use the means of automated systems. The type of slipway complex is presented in Figure 1. For descent or ascent using a slipway, the vessel is mounted on special carts, which moves along rail tracks is located on an inclined plane at an angle α of 6–10◦ . Each cart is driven by a single electric drive using a steel cable. Carts have the ability to independently move down along the rails down (up), while the main task, during the descent (lifting) of the vessel, is the coordinated movement of carts, in which the vessel should move uniformly at a given speed without distortions.

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Figure 1. Cross slipway: 1—carts; 2—rail tracks; 3—electric drives; 4—cables; 5—vessel. Figure 1. 1. Cross slipway: 1—carts; drives; 4—cables; 4—cables; 5—vessel. 5—vessel. Figure Cross slipway: 1—carts; 2—rail 2—rail tracks; tracks; 3—electric 3—electric drives;

The process of launching the ship can be divided into several stages (Figure 2): The process of launching the ship ship can can be be divided divided into into several several stages stages (Figure (Figure 2): 2): 1. The movement of the cart with acceleration to the necessary constant mode speed of descent, 1. The movement of the cart with acceleration to the necessary necessary constant constant mode mode speed speed of of descent, descent, 𝑙 ∈ [0, 𝑙1 ]. 𝑙0 —the distance from the starting point of the cart to the point of the cable stop. l𝑙 ∈ [0, distance from the starting point of cart of stop. [0, 𝑙l11 ]].. l𝑙00—the distance from the point ofthe the cartto tothe thepoint point ofthe thecable cable 2. The—the movement of the cart atstarting a constant speed before entering the water, 𝑙 ∈ [𝑙1stop. , 𝑙2 ]. 𝑙3 − 𝑙2 = 2. The movement movement of of the the cart cart at at a constant constant speed speed before before entering entering the the water, water, l𝑙 ∈ [𝑙 [l11 , 𝑙l22]. ]. l𝑙33 − − l𝑙22 = = 𝑙 𝑇 —appropriate cart width. l𝑙T𝑇 —appropriate cart width. 3. Transfer of the cart from the slipway surface to the underwater part, 𝑙 ∈ [𝑙2 , 𝑙3 ]. 𝑙𝑤 —distance 3. Transfer Transfer of the cart from the slipway surface to the underwater part, l ∈ [l2[𝑙, 2l3, ]𝑙.3 ]. lw —distance to 𝑙𝑤 —distance to water line. of the cart from the slipway surface to the underwater part, 𝑙 ∈ water line. to water line.submersion carts under water, 𝑙 ∈ [𝑙3 , 𝑙4 ]. 4. Full 4.5.Full l𝑙∈∈speed l33, ,l𝑙44]in . the water before the vessel ascends, 𝑙 ∈ [𝑙 , 𝑙 ]. [[𝑙 ]. carts under Thesubmersion movement of the cart at awater, constant 4 5 5.6.The of the cart at a constant speed inthe the before vesselascends, ascends, 𝑙l ∈∈ [𝑙[l44,,𝑙l55].]. movement of the cart at a constant speed [𝑙vessel The ascent of the ship and the braking of the in cart towater awater full before stop, 𝑙 the ∈the 5 , 𝑙6 ]. 6.Control The ascent ofmotion the shipparameters and the braking of the cart to a full stop, l𝑙∈ l5throughout . ∈ [[𝑙 of the of the trigger car must be carried out the journey. 5, ,l𝑙66]]. Control of the motion parameters of the trigger car must be carried out throughout the journey.

Figure2. 2. Stages Stages of of launching launching the Figure the vessel vessel using usingaaslipway. slipway. Figure 2. Stages of launching the vessel using a slipway.

Despiteofthe of the regulatory forcar themust technical operation of ship-lifting Control theexistence motion parameters of therules trigger be carried out throughout thefacilities, journey. it isDespite necessary describe the step by step the sequence of actions during the preparation and vessel the existence of the regulatory rules for the technical operation of ship-lifting facilities, Despite the existence of the regulatory rules for the technical operation of ship-lifting facilities, launching, the emergency situations occurred periodically. The main reason for this is the uneven it it is is necessary necessary describe describe the the step step by by step step the the sequence sequence of of actions actions during during the the preparation preparation and and vessel vessel load on the electric drives, and, accordingly, the overload of electric motors andthis cables. launching, the emergency situations occurred periodically. The main reason for is the uneven load launching, the emergency situations occurred periodically. The main reason for this is the uneven The overhaul of and, the ship-building facilities implies substantial financial costs, while the cost of on the electric drives, accordingly, the overload of electric motors and cables. load on the electric drives, and, accordingly, the overload of electric motors and cables. modernizing the control system is several times lower. The financial costs, costs, while while the The overhaul overhaul of of the the ship-building ship-building facilities facilities implies implies substantial substantial financial the cost cost of of The bulky objects motion isisperformed withlower. help of the cooperative work of electric motors and modernizing the control system several times modernizing the control system is several times lower. mechanisms complex.motion Movement processes happen in non-stationary conditions when exposed to The of electric electric motors and The bulky bulky objects objects motion is is performed performed with with help help of of the the cooperative cooperative work work of motors and external effects that vary extensively in all points of movement, which frequently could create the mechanisms Movement processes processes happen happen in in non-stationary when exposed mechanisms complex. complex. Movement non-stationary conditions conditions when exposed to to nonstandard situations. The reliable in operation of of mentioned complexes could be done only with external effects that vary extensively all points movement, which frequently could external effects that vary extensively in all points of movement, which frequently could create create the the application of adaptive control systems taking in of account the stochastically inner nonstandard The reliable reliable operation mentioned complexes changing could be beouter doneand only with nonstandard situations. situations. The operation of mentioned complexes could done only with factors. In the synthesis of rational management of the work of the components of electromechanical application of adaptive control systems taking in account the stochastically changing outer and inner application of adaptive control systems taking in account the stochastically changing outer and inner complexes, there periodically take place problems of identifying the parameters of the model of the factors. In the the synthesis synthesis of of rational rational management management of of the the work work of of the the components components of of electromechanical electromechanical factors. In motion process. complexes, there periodically take place place problems problems of identifying the parameters parameters of of the the model model of of the complexes, periodically take identifying the the Lately,there the artificial intelligence methods oftenofused to execute the process identification, such motion process. motion process. as fuzzy logic, neural networks and so forth. Lately, the process identification, such as Lately, the the artificial artificialintelligence intelligencemethods methodsoften oftenused usedtotoexecute execute the process identification, such fuzzy logic, neural networks andand so forth. as fuzzy logic, neural networks so forth.

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But to make use the neural network technology possible, it is required to employ a large amount learning set for a teaching of the artificial intelligent system, which is not always possible, due to the lack of a data set for training or limited training time [4,5]. [4,5]. While fuzzy systems application the design problem of base rules set and membership functions could occur connected with the heavy conditions caused by the rapid changing factors which have impact on the process. 2. Model Description Description 2. Model For of the carts, as as well well as as in in the For aa uniform uniform movement movement of the launching launching carts, the areas areas of of its its acceleration acceleration and and deceleration, it is necessary to constantly provide the appropriate cable tension. The main forces acting deceleration, it is necessary to constantly provide the appropriate cable tension. The main forces to the cart during the descent are shown in Figure 3. acting to the cart during the descent are shown in Figure 3.

Figure 3. Forces that acting to the cart during the launch of the vessel.

Using the second law of Newton, we will create a system of equations for a cart with a ship mounted on it, taking into account all the forces acting on the cart along the entire path (both by land and in water):

+𝑇m+C𝑚 sin⋅(α𝑠𝑖𝑛( ) −𝛼) T ·cos − α)ϕ−−FT𝛼)−−FC𝐹𝑇·cos (αС )⋅ − FA𝛼) ·sin−(α𝐹𝐴) = ) g𝐶·)𝑔 (m T𝛼)+ mC ) a, ∑ F∑ 𝐹𝑥(m = T(𝑚 − 𝑇(φ⋅ 𝑐𝑜𝑠( −𝐹 𝑐𝑜𝑠( ⋅ 𝑠𝑖𝑛( x = (1) T ·sin(φ − α) + FA ·cos(α) − mg·cos(α) − FC ·sin(α) = 0, ∑ Fy = N=+(𝑚 𝑇 + 𝑚𝐶 )𝑎, FT = µ· N, (1) ∑ 𝐹𝑦 = 𝑁 + 𝑇 ⋅ 𝑠𝑖𝑛( ϕ − 𝛼) + 𝐹𝐴 ⋅ 𝑐𝑜𝑠( 𝛼) − 𝑚𝑔 ⋅ 𝑐𝑜𝑠( 𝛼) − 𝐹𝐶 ⋅ 𝑠𝑖𝑛( 𝛼) = 0, where m T is the mass of the cart, mC is the mass of the ship section, α is the slope angle of the slip; 𝜇 ⋅ 𝑁, T—cable tension, φ—the deflection of𝐹the 𝑇 =cable; FT —friction force, FC —water resistance force, FA —Archimedes force; where 𝑚 𝑇 is the mass of the cart, 𝑚𝐶 is the mass of the ship section, 𝛼 is the slope angle of the slip; a—cart acceleration, µ is the coefficient of rolling friction between the wheels of the cart and the 𝑇—cable tension, ϕ—the deflection of the cable; rails, N is the reaction force of the support. 𝐹𝑇 —friction force, 𝐹𝐶 —water resistance force, 𝐹𝐴 —Archimedes force; Thus, from system (1) it is possible to express the tension of the cable T in the following form 𝑎—cart acceleration, 𝜇 is the coefficient of rolling friction between the wheels of the cart and the rails, 𝑁 is the reaction of the support. ((mforce T + mC ) g − FA )·(sin( α ) − µ ·cos( α )) − FC ( µ ·sin( α ) + cos( α )) = . (2) Thus, fromTsystem (1) it is possibleµto express tension ·sin (φ − α)the − cos (φ − of α)the cable 𝑇 in the following form ((𝑚 𝑇 + 𝑚𝐶 )𝑔 − 𝐹𝐴 ) ⋅ (𝑠𝑖𝑛( 𝛼) − 𝜇 ⋅ 𝑐𝑜𝑠( 𝛼)) − 𝐹𝐶 (𝜇 ⋅ 𝑠𝑖𝑛( 𝛼) + 𝑐𝑜𝑠( 𝛼)) The forces 𝑇 = acting on the cart when moving in water (Archimedes force FA and the. resistance force (2) 𝜇 ⋅ defined 𝑠𝑖𝑛( 𝜙 −by 𝛼)the − 𝑐𝑜𝑠( 𝜙 − 𝛼)relations: from the water side FC ) have the form following The forces acting on the cart when moving in water (Archimedes force 𝐹𝐴 and the resistance ρv2 force from the water side 𝐹𝐶 ) have the formFdefined by the following relations: = k S , (3) c C 2

𝐹𝐴 = 𝜌𝑔𝑉𝐴 ,

(4)

where 𝑘𝑐 is the coefficient of resistance of the vessel and the cart (for the central sections of the vessel, can be taken ≈ 1); 𝑆 = 𝑆𝐶 + 𝑆𝑇 is the characteristic surface area of the vessel and cart, 𝑣—cart speed, 𝜌 is the density Data 2018, 3,of60water; 4 of 21 𝑉𝐴 = 𝑉𝐶 + 𝑉𝑇 is the volume of the vessel and the cart submerged in water. Consider the dependence of all changing factors on the distance travelled 𝑙. In Figure 4 shows = ρgVA , length. (4) A height the geometry of the object (slip), the ratio of F its and The change in the height of the slip is relative to its length and can be described by the where k c is the coefficient of resistance −𝜆𝑙 of the vessel and the cart (for the central sections of the vessel, exponential dependence ℎ(𝑙) = 𝐻 ⋅ 𝑒 or, taking into account a small change in the angle of can be taken ≈ 1); inclination—𝛼 ≈ 4° from the slip geometry can be found as S = SC + ST is the characteristic surface area of the vessel and cart, v—cart speed, ρ is the density (5) ℎ(𝑙) = 𝐻 − 𝑙 ∙ 𝑠𝑖𝑛(𝛼), of water; VA = + Vheight of the vessel and the cart submerged in water. T is the where 𝐻V isCthe ofvolume the slipway. Consider the dependence of all changing on ϕ theduring distance l. In Figure 4 shows the Figure 4 shows the angle of inclination offactors the cable thetravelled descent process without taking geometry of the object (slip), the ratio of its height and length. into account the extension of the cable.

Figure 4. 4. Graph of the angle Figure angle of of inclination inclinationofofthe thecable cableϕ. φ.

The change in the relationships, height of the slip is relative its lengthrelation and can be described by the exponential From geometric we can get thetofollowing − λl dependence h(l ) = H ·e or, taking into account a small change in the angle of inclination—α ≈ 4◦ (𝐻−ℎ)+(ℎ 0 −ℎ𝑇 ) ϕ = 𝑎𝑟𝑐𝑡𝑔 ( ), (6) 𝑙+𝑙0 from the slip geometry can be found as where ℎ0 is the height of the block; ℎ 𝑇 is the height of the cart; ℎ—the current height of the cart. h(l )object = H− l ·sin(α), (5) To take into account the impact on the of Archimedes force, it is necessary to consider the change in the vessel and the vessel submerged in water 𝑉𝐴 , since, according to (4), 𝐹𝐴 = 𝑓(𝑉п ). Due where H is the height of the slipway. to the design features of the slipway, first, the cart will be submerged in water, which has a very small Figure 4 shows the angle of inclination of the cable φ during the descent process without taking volume compared to the ship hull, then the lower, narrower part of the vessel enters the water; after into account the extension of the cable. that the volume 𝑉𝐴 will increase nonlinearly. Figure 5 shows the cart and section of the vessel when From geometric relationships, we can get the following relation submerged under water and the dependence of the total submerged volume 𝑉𝐴 on 𝑙, where 1 is the  2 are the submerged  parts of the cart and vessel, surface part of the vessel and zones 3 and ( H − h ) + ( h0 − h T ) φ = arctg , (6) respectively. l + l0 Figures 6–8 shows the different diagrams of submerged volume of the cart 𝑉𝑇 and the vessel section in dependencies from the path of𝑙. the cart; h—the current height of the cart. where h0 𝑉 is𝐶 ,the height of the block; h T traveled is the height To take into account the impact on the object of Archimedes force, it is necessary to consider
the change in the vessel and the vessel submerged in water VA , since, according to (4), FA = f V∏ . Due to the design features of the slipway, first, the cart will be submerged in water, which has a very small volume compared to the ship hull, then the lower, narrower part of the vessel enters the water; after that the volume VA will increase nonlinearly. Figure 5 shows the cart and section of the vessel when submerged under water and the dependence of the total submerged volume VA on l, where 1 is the surface part of the vessel and zones 3 and 2 are the submerged parts of the cart and vessel, respectively. Figures 6–8 shows the different diagrams of submerged volume of the cart VT and the vessel section VC , in dependencies from the traveled path l.

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Figure5.5.Visual Visualcart cartand andvessel section submerged volume change. Figure cart and vessel sectionsubmerged submergedvolume volumechange. change. vesselsection Figure

submergedvolume Figure6.6.Diagram Diagramof ofcart volume 𝑉ТТТTchange change cartsubmerged Figure Diagram of cart submerged volume𝑉V change. Figure

Figure7. 7.Diagram Diagramof oftypical typicalvessel vesselsection sectionsubmerged submerged volume change Figure 7. Diagram Figure typical vessel section submergedvolume volume𝑉𝑉 V change. СССCchange

.. Figure8. 8.Diagram Diagramof ofcart cartand andvessel vesselsection section submerged volume change. Figure 8. Figure of cart and vessel sectionsubmerged submergedvolume volumechange. change.

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Thus, can be predicted predicted with withthe theknown knownlaw lawofofvolume volumechange. change. Thus,the theimpact impactof ofthe thebuoyancy buoyancy force force can can be be Thus, the impact of the buoyancy force predicted with the known law of volume change. Due to the fact that the volume of the launch of the submerged carriage is extremely small and the Due to to the the fact fact that that the the volume volume of of the the launch launch of of the the submerged submerged carriage carriage is is extremely extremely small small and and the the Due same volume of thevessel vesselsection sectionin Cartesiancoordinates coordinatessystem system samefor forall allcarts, carts,itit itcan canbe beneglected. neglected. The of the the vessel section ininCartesian Cartesian coordinates system same for all carts, can be neglected. The volume can be calculated using the triple integral [6]. can be calculated using the triple integral [6]. can be calculated using the triple integral [6]. The vessel is is the area which is is perpendicular to to thethe flow of of water. In this Thecharacteristic characteristicarea areaofof ofthe the vessel is the area which is perpendicular perpendicular to the flow of water. water. In The characteristic area the vessel the area which flow In case, for the central part of the vessel, the characteristic area of the vessel is equal to the area of the this case, for the central part of the vessel, the characteristic area of the vessel is equal to the area of this case, for the central part of the vessel, the characteristic area of the vessel is equal to the area of the rectangle formed by the length of section 𝑑 and the height of the vessel ℎ . If to neglect the rectangle formed by the length of section d and the height of the vessel h . If to neglect the characteristic v vessel ℎvv. If to neglect the the rectangle formed by the length of section 𝑑 and the height of the characteristic area of the the cart cart 𝑆𝑆ТТ area of the cart area ST of characteristic hv ·d. = Sℎ ℎvv=⋅⋅ 𝑑. 𝑑. (7) (7) 𝑆𝑆 = (7) The resistance and andititbecomes becomesgreater greaterasas Thecharacteristic characteristicarea areaS𝑆𝑆has hasan aneffect effecton onthe theforce force of of water water resistance resistance The characteristic area has an effect on the force of water and it becomes greater as the ship sinks deeper into the water, therefore, it depends on l. Figure 9 shows the dependence the ship ship sinks sinks deeper deeper into into the the water, water, therefore, therefore, it it depends depends on on 𝑙. 𝑙. Figure Figure 99 shows shows the the dependence dependenceofof ofS 𝑆𝑆on the the l. 𝑙. onslip the length slip length length on the slip 𝑙.

Figure9.9. 9.Changing Changingthe the characteristic characteristic area area of of the the vessel vessel and carts while diving. Figure vessel and andcarts cartswhile whilediving. diving. Figure Changing the characteristic

The ofof friction µ when driving over landland or water has constant values. However, when Thecoefficient coefficient of friction when driving over land or water water has constant constant values. However, The coefficient friction 𝜇𝜇 when driving over or has values. However, a when cart enters the water (zone 3), it smoothly changes (Figure 10). when aa cart cart enters enters the the water water (zone (zone 3), 3), it it smoothly smoothly changes changes (Figure (Figure 10). 10).

Figure 10. 10. The The change change of of the the coefficient coefficient of of rolling friction friction during immersion. immersion. Figure Figure 10. The change of the coefficient of rolling rolling frictionduring during immersion.

Todescribe describethe thedependence dependence of of µ𝜇𝜇 on on the the path path traveled, traveled, you you can use z-shaped membership describe the dependence of on the path traveled, ToTo you can can use use z-shaped z-shapedmembership membership functions [7], which leads to the expression functions [7], which leads to the expression functions [7], which leads to the expression 𝜇 −𝜇 −𝜇2 2 , 𝜇(𝑙) = = 𝜇𝜇22 + + 𝜇11𝛿⋅(𝑙−𝑙 (8) 𝜇(𝑙) (8) 1+𝑒𝛿⋅(𝑙−𝑙 )), µ2 µ1 вв− 1+𝑒 µ ( l ) = µ2 + , (8) B ) the cart and the rails on land and in where 𝜇𝜇11,, 𝜇𝜇22—coefficients —coefficients of of friction friction between between the the1 wheels wheels of + eδ·(l −lof where the cart and the rails on land and in water, respectively; respectively; 𝛿𝛿 is is the the coefficient coefficient of of steepness. steepness. water, where µ1 , µ2 —coefficients of friction between the wheels of the cart and the rails on land and in water, The coefficient of slope 𝛿 is as follows The coefficient of slope 𝛿 is as follows respectively; δ is the coefficient of steepness. 4 1 = 4 ⋅⋅ 𝑙𝑛 𝑙𝑛 ((1 − − 1), 1), The coefficient of slope δ is as follows (9) 𝛿𝛿 = (9) 𝑙 𝜀 𝑇 𝑙𝑇

where 𝜀𝜀 is is the the admissible admissible error. error. where

𝜀

  4 1 δ = ·ln −1 , lT ε

(9)

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where ε is the admissible error. Since the motion parameters in different zones are distinguished by the presence and magnitude of some forces and factors, for modelling it is necessary to set them accordingly, as shown above. Possible values of the parameters considered by zones are shown in Table 1. Table 1. Movement parameters at various stages of descent. Zones Parameters

1

2

3

4

5

6

Cart weight, m T

m1

m1

m1

m1

m1

m1

Ship section weight, mC

m2

m2

m2

m2

m2

0

Acceleration, a

a1 = const, a1 > 0

0

0

0

0

a2 = const, a2 < 0

µ2

µ2

µ2

ST

ST

0 ÷ SC

0

VT

VT

Slipway slope angle, α

α(l )

Cable deflection angle, φ

φ(l ) µ1 ÷ µ2

Coefficient of friction, µ

µ1

µ1

Cart area, ST

0

0

Ship section area, SC

0

0

Cart volume, VT

0

0

Ship section volume, VC

0

0

0

0

0 ÷ VC

0

Speed, v

0 ÷ vd

vd

vd

vd

vd

vd ÷ 0

0 ÷ ST 0

0 0 ÷ VT

Given specific values of the parameters, it is possible to obtain for them analytical dependencies based on relations (2)–(9) and to analyse the changes in the loads (forces) and parameters of interest when the trigger car moves along the entire length of the slipway. When analysing the movement of the trigger carriage, it is necessary to take into account the change of parameters that affect the process of descent at all stages—from the beginning of movement to the end. The dependences and relations obtained allow us to determine the cable tension T depending on the given mode of motion (speed vd , acceleration a1 and deceleration a2 ) throughout the entire route. This makes it possible to estimate the load on the electric drive during the descent process. To optimize (match) the drive control of a complex electromechanical system for launching a ship into the “slipway” type, it is advisable to develop a dynamic model of the engine of the launching carriage in the state space based on Equation (2). The bulky object motion on a plane can be described in form of sums of translational and rotational motions, which are presented by expressions relatively to the centre of mass [7]: -

for translational motion m

-

dv = dt

dl

∑ F, dt

= v,

(10)

for rotational motion J

dω = dt

∑ M,

dφ = ω, dt

(11)

where m is the mass of the object, v is the translational motion speed, l is the motion length, t is the time, ∑ F is the total value of all external forces applied to the object, J is the object inertia moment relative to the rotation axis, ω is the object angular velocity, φ is the object rotation angle, ∑ M is the total rotational moment of all forces relatively to rotation axis of the mass centre of a bulky object. A diagram for determining the parameters of motion for two points of measurement is shown in Figure 11.

While synthesis of optimal control actions, the methods of modern control theory the linearized model of system usually are used, presented in the state space [9]. To identify the parameters of the motion of a large object, which must be taken into account Data 2018, 3, 60 8 of 21 when controlling the mode of operation of the slipway and the synthesis of drive control, it is possible to measure the distance of some points of the object when moved from their original position.

Figure 11. Scheme for the determining of the parameters of motion. Figure 11. Scheme for the determining of the parameters of motion.

One of the obvious solutions to the problem of ensuring a consistent movement of the launch The system of relations (10),the (11) can be of written as expressions in the state(Figure space of12). theIndeed, fourth trucks is to provide control over position the stern  and bow of the vessel T orderof [8]the with state vector of the object being moved = on , where x2 = v, x1thextrack most problems arising from the launching of axship the have axdirect 1 = S, impact 2 x3of x 4 slip on the position of the ship. Due to the design of the slip, the misalignment of the movement of the v = dS/dt x3 = φ, x4 = ω = dφ/dt; control actions vector u and output vector y describe the carts (their position is not in an “even row”) leadssuch to asystems change in the position of the hull, its distortion construction of the monitoring system. Usually, model has non-linear relations. and displacement. While synthesis of optimal control actions, the methods of modern control theory the linearized Under slip operation the most acceptable technical characteristics are the use of model of system usually areconditions, used, presented in the state space [9]. optical since it of requires measurement the open in the of 1–100 m ±when 0.01. Tolocation identify means, the parameters the motion of a large in object, whichairmust be range taken into account Given the shape of the hull of the vessel (Figure 13), it seems convenient to measure the distance controlling the mode of operation of the slipway and the synthesis of drive control, it is possible to the hull using laser range finders. measure the distance of some points of the object when moved from their original position. One of the obvious solutions to the problem of ensuring a consistent movement of the launch trucks is to provide control over the position of the stern and bow of the vessel (Figure 12). Indeed, most of the problems arising from the launching of a ship on the track of the slip have a direct impact on the position of the ship. Due to the design of the slip, the misalignment of the movement of the carts (their position is not in an “even row”) leads to a change in the position of the hull, its distortion and displacement. Under slip operation conditions, the most acceptable technical characteristics are the use of optical location means, since it requires measurement in the open air in the range of 1–100 m ± 0.01. Given the shape of the hull of the vessel (Figure 13), it seems convenient to measure the distance to the hull using laser range finders.

Data 2018, 3, x FOR PEER REVIEW Data 2018, 3, 60

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Figure 12. Control of the ship movement with a range finder—general view. Figure range finder—general finder—generalview. view. Figure 12. 12. Control Control of of the the ship ship movement movement with with aaarange range finder—general view.

Figure 13. Control of ship movement with a range finder—side view. Figure movement with aaarange finder—side view. Figure13. 13. Control of ofaship ship movement with rangeof finder—side view. on a slipway. The Consider the process of Control moving bulky object by example a ship’s descent Figure 13. Control of ship movement with range finder—side view. impacting forces on moving “ship-cart” distributed objects in time of a controlled downhill motion Consider the process object by example of descent on slipway. The Considerin the process of moving object byby example of aaofship’s ship’s descent onaaon slipway. The Consider process ofmoving movingaa bulky abulky bulky object example a ship’s descent a slipway. are presented Figure 14.of impacting forces on moving “ship-cart” distributed objects in time of aaacontrolled downhill motion impacting forces on moving “ship-cart” distributed objects in time of controlled downhill motion The impacting forces on moving “ship-cart” distributed objects in time of controlled motion The ship motion model on a slipway, designed in the states space, which considers all the are in Figure are presented presented in influences, Figure 14. 14. is nonlinear [10]. important outer The The ship ship motion motion model model on on aa slipway, slipway, designed designed in in the the states states space, space, which which considers considers all all the the important important outer outer influences, influences, is is nonlinear nonlinear [10]. [10].

Figure 14. The structure of forces acting on the “ship-carts” object. Figure 14. The structure of acting the “ship-carts” object. Figure 14.the The of forces acting on thestates “ship-carts” object. The ship motion model onequations astructure slipway, designed inon the space, which considers the Based on the analysis of offorces motion, the equations of state of the model of theallshipimportant outer influences, is nonlinear [10]. cart object are formulated in the state space in the form Based Based on onthe the analysis analysisof of the the equations equationsof of motion, motion, the the equations equationsof of state state of of the the model model of of the the shipshipcart object are formulated in the state space in the form cart object are formulated in the state space in the form

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Based on the analysis of the equations of motion, the equations of state of the model of the ship-cart object are formulated in the state space in the form .

x 1 = x2 , N 1 x2 = m ∑i=1 Fxi ( x1 ) − Tmm ∑iN=1 ui , . x 3 = x4 , . x4 = 1J ∑iN=1 ( Tm ui − Fxi ( x1 ))·[(k − i )∆z + dz]· cos x3 , .

(12)

where x1 = l is the displacement of the center of mass of the vessel along the x axis; x2 = ν is the rate of translational motion of the center of mass along the x axis; x3 = φ—the angle of rotation of the vessel; x4 = ω—vessel rotation speed;  T u = u1 u2 . . . u N is the control vector, ui = Ti /Tm , i = 1, N; Ti is the tension force of the cable of the i-th cart; Tm —maximum allowable cable tension; Fxi (li )—the load on the i-th drive, due to the forces affecting the cart at the point of the movement path li ; m = mc + N ·m T is the mass of the vessel-carts object, mc is the mass of the vessel, N is the number of carts, m T is the mass of the cart; J is the moment of inertia of the vessel; ∆z is the distance between the centers of neighboring carts; dz is the distance from the rotation point (RP) (centre of mass of the object) to the centre of the k-th cart. The output equations of the model are y j = x1 − [(k − j)∆z + dz]sinx3 , j = 1, r,

(13)

where r is the number of outputs needed to identify the motion parameters of a complex object. The following mathematical model was gained in the states space in the vector-matrix form in the result of linearization . ^ ^ xˆ = Ax + Bu, → → y = C· x

(14)

The matrices A, B and C have a constant structure but a change depending on the operating conditions of the system and have the form    A=     B= 

0 K1 0 q 1 K2

C=

0 a21 0 a41

1 0 0 0

0 a23 0 a43 0 ··· K1 ··· 0 ··· q 2 K2 · · · 1 0 q1 1 0 qN

0 0 1 0

0 0

    

0 K1 0 q! N K2

    

(15)

The elements of the matrix A are defined as a21 = f 21 ( x1s , x3s ), a23 = f 23 ( x1s ), a41 = f 41 ( x1s , x3s ), a43 = f 43 ( x1s ),

(16)

where x1s , x3s are the elements of the stable state vector of the object xs = ( x1s , . . . , x4s ) T in a bounded neighborhood;

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K1 = − Tm /m, K2 = Tm /J are scale coefficients; qi = (k − i )∆z + dz, i = 1, N is distance of the i-th force application point from the rotation point (the bulky object mass centre). Data 2018, 3, x FOR PEER REVIEW 11 of 21 The elements of the matrix C correspond to the structure of the measurement system. The diagram of of the the adaptive adaptive control control system system of of complex complex object object with with observer observer and andregulator, regulator, The block block diagram is is shown shown in in Figure Figure 15. 15.

Figure 15. 15. Block of adaptive adaptive control control system. system. Figure Block diagram diagram of

as “PEM,” “PEM,” which which implements implements the The Parameter Estimation Module is marked at Figure 15 as thethe linearized model control object (LMCO). The recurrent algorithm algorithm for formatrix matrixidentification identification𝐀 Aofof linearized model control object (LMCO). values changes of the matrix 𝐀 components lead to to the The values changes of the matrix A components lead theneed needtotosearch searchaanew new values values of observer andregulator regulatorcoefficients coefficientsF Fand, and, accordingly, solve Riccati equation [11]. matrix KK and accordingly, to to solve of of Riccati equation [11]. elements of of the the matrices matricesA, 𝐀,B𝐁and and can change time object motion process relying The elements C,С, can change in in time thethe object motion process relying on on the conditions of the system operation, saving matrices structure. the conditions of the system operation, saving matrices structure. The elements of the matrices, which depend on the outer and inner operating conditions of the ofof thethe model parameters to keep its system, may change, change, which whichcauses causesthe theneed needofoftuning tuningthe thevalues values model parameters to keep adequacy. AsAs a result, with the its adequacy. a result, with thetuning tuningofofthe themotion motiontrajectory trajectoryparameters parametersaccording according to to the outer conditions, it is need to start at intervals an an operation operation for for identifying identifying model model parameters. parameters. To perform performthe themotion motion process model parameters identification real ittime, it is suitable to To process model parameters identification in realintime, is suitable to involve involve recurrent procedures which allow the modelif parameters if new recurrent procedures which allow getting an getting estimatean of estimate the modelofparameters new measurement measurement results come up formula [11]. Thedescribes next formula describesevaluation the recurrent evaluation procedures results come up [11]. The next the recurrent procedures (17) 𝐏[𝑘 + 1] = 𝐏[𝑘] + 𝛾[𝑘 + 1] ⋅ 𝑓(𝐏[𝑘], 𝐲[𝑘 + 1], 𝐮[𝑘 + 1]) P[k + 1] = P[k] + γ[k + 1]· f (P[k], y[k + 1], u[k + 1]) (17) where 𝐏[𝑘] is the current evaluation of the parameter; 𝛄[𝑘]—the weight coefficient; 𝑓 is special where P[kthat current evaluation of the parameter; γ[k ]—the coefficient; is special function ] is the function relies on the current value 𝐏[𝑘] and defines theweight size and trend of fthe following step; that relies on the value P[k] and definesand theinput) size and of the step; y[k + 1] and 𝐲[𝑘 + 1] and 𝐮[𝑘current + 1] are the signals (output thattrend go after thefollowing current value. u[k +The 1] are the signals (output andmethod input) that current value. stochastic approximation and go theafter leastthe square method are the most known recurrent The stochastic approximation method and the least square method are the most known recurrent procedures [12]. Because the accuracy of the stochastic approximation method could only be gained procedures Because in theReference accuracy of the so stochastic approximation method could only be gained for 𝑡 → ∞, [12]. as described [11], it cannot be implemented while performing model parameters identification for solving problems of controlling the bulky object motion in real time. Let us consider identification procedures using the methods of recurrent stochastic approximation and least squares to determine the parameters of the model for the process of moving a ship on a slipway, represented in the form (17). While getting new measuring data on the control object at discrete moments of time, it is convenient to implement models in form of the state space as following

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for t → ∞ , as described in Reference [11], so it cannot be implemented while performing model parameters identification for solving problems of controlling the bulky object motion in real time. Let us consider identification procedures using the methods of recurrent stochastic approximation and least squares to determine the parameters of the model for the process of moving a ship on a slipway, represented in the form (17). While getting new measuring data on the control object at discrete moments of time, it is convenient to implement models in form of the state space as following xm [k ] = A[k − 1]·xm [k − 1] + B·u[k − 1].

(18)

The deviation values based on analysis of the state variables obtained from the model xm [k ] and as a result of measurements xo [k ] let evaluate the adequacy of the model to object, that is, by the value of the error e [ k ] = xo [ k ] − xm [ k ]. (19) The algorithm for setting parameters has the form T A[k] = A[k − 1] + Γ[k ]·e[k]·xm [ k ],

(20)

where Γ[k ]—is the matrix obtained on h i the basis of real values of the state vector measured over the entire observation interval t ∈ t0 , t f , which can be determined recurrently by different ways. In the case of the method of stochastic approximation as:

where

Γ[k] = Γ[k − 1] − Γ[k − 1]·xo [k]·γ[k − 1]·xoT [k]·Γ[k − 1],

(21)

h i −1 γ[k − 1] = 1 + xoT [k ]·Γ[k − 1]·xo [k ]

(22)

In the case of the least squares method the matrix Γ[k] as: γ Γ[k ] = In · , γ > 0, k

(23)

To implement the both methods, it is necessary to specify the initial values of the state vector components of the model xm [0] = xo [0] and also the matrix components initial values A[0], for the known dynamics of the control vectors u[k] and the state of the object xo [k] for k = 1, 2, 3, . . . N. The initial values of the matrix Γ[0] are chosen as Γ[0] = I·(1/α), where α is a numerical coefficient whose value influence the convergence of the identification algorithm. The identification phase ends when tiny deviations of the matrix A components values occur for all i and j, that is, the following conditions is satisfied: aij [k ] − aij [k − 1] < δ

(24)

Let us consider identification procedures using the recurrent methods of stochastic approximation and least squares to determine the parameters of the model of the process of moving a ship on a slip. In the process of calculations using the recurrent method of stochastic approximation, the best results were obtained using the algorithm tuning coefficient γ = 0.5 and ∆t = 1, for the initial values h iT of the model state vector xm [0] = 0 0.05 0 0 . The initial and final values of the components of the matrix A are as follows

Data 2018, 3, 60

   A[0] =  

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1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1





    , A[300] =   

−0.651 0.356 −0.081 2.57·10−4

1.061 0.012 0.087 −2.03·10−5

2.016·10−3 4.78·10−4 2.4·10−4 0.5

0.064 −9.77·10−4 0.51 1.7·10−6

   . 

(25)

The change in the values of the matrix A components in the calculation process is shown in Figure 16. of the resulting matrices (25) is significantly different from the structure Data 2018, 3, xThe FORstructure PEER REVIEW 13 of of 21 the matrix, resulting from the linearization of the nonlinear motion model. The finite time of the It is advisable analyse effectiveness of more accurate identification methods in s, the control identification phasetousing thethe recurrent stochastic approximation method was t > 350 which is system, whichlarge allow you the to maintain the structure matrixes of the linearized model of of the unacceptably when vessel is moving, since of thethe external conditions for the movement a process of moving vessel the slipway, for example, the least squares method [15,16]. large object change the with new on objects and the definition of new matrix A values is required. a11

1.4

a12

0.2 0

100 1

a13

0.15

200

300

-3

2 10

400

0.1

-3

1.510

- 0.2

-3

0.8

1 10

- 0.4

0.05 -4

0.6 0.4

a14

-3

2.510

t[s]

1.2

t[s] 0

100

200

300

t[s] - 0.8

400

a21

0.08

5 10

- 0.6

0

a22

0.55

100

200

300

a23

0.01

t[s] 0

400

100

200

300

100

200

300

400

a24

-4

5 10

-4

4 10

0.06

0.5

-3

510 0.04

-4

3 10

0.45

0.02

0

0.4

t[s] 0

100

200

300

0.35

400

a31

0.15

t[s] 0

100

200

300

400

-4

t[s]

2 10

400

1 10

-4

t[s]

-3

- 510

a33

0.515

400

a34

-4

310

t[s]

0 100 0.1

300

0

a32

0.02

100

200

300

400

-4

0.51

210

0.505

110

- 0.02 - 0.04

0.05

- 0.06

t[s] 0

100

200

300

a41 0

100

200

300

-4

- 0.08

t[s] 0.5

400

- 0.1

t[s]

3 10

-4

a42

0

-6

510

100

200

300

a43

100

200

300

100

200

300

400

a44

0.5

t[s]

-4

2 10

0

-5

-4

t[s] 0 -4

300

400

- 510

- 1 10

- 1 10

200

-6

-4

1 10

-4

0

400

- 5 10

- 1.510

t[s]

400

100

200

300

-5

- 110

400 -5

- 1.510

t[s] 0.49 0

400

Figure 16. 16. Dynamics of the adjustment of the values of the matrix A 𝐀 components components obtained obtained by by using using Figure stochastic approximation approximation method. method

According to the theory the accuracy of the stochastic methodmethod can be The identification process[13,14], was modelled with application of the approximation recurrent least squares considered only with t → ∞ [9], therefore it is not advisable to use it when identifying model with the initial values of the object state vector and the initial values of the components of the matrix parameters to solve problems of controlling the movement of a large object in real time. 𝐀 of the form It is advisable to analyse the effectiveness of more accurate identification methods in the control 0 0 1 0 0 system, which allow you to maintain the structure of 1the0matrixes 0.05 1 0 of the linearized model of the [0] 𝐱 = [ ] , 𝐀[0] = [ ]. (26) 𝑜 process of moving the vessel on the slipway, for example, 0 0 the 0 least 0 1squares method [15,16]. The identification process was modelled with application 0 1 0 1of the 0 recurrent least squares method with the initial values of the object state vector and the initial values of the components of the in matrix A The change in the values of the matrix Acomponents during the calculations is shown Figure of 17.the form As a result of the calculations, a matrix 𝐀 of the following form obtained 0.98 1.02 -0.12 -0.03 𝐀[350] = [ 0.15 2.95 ⋅ 10−3 -0.13 -0.03

0.14 5.63 ⋅ 10−5 0.85 -6.75 ⋅ 10−5 ]. 0.02 1 0.85 -7.22 ⋅ 10−5

Taking into account the permissible error of 5%, the resulting matrix 𝐀 can be written as

(27)

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   xo [0 ] =  

0 0.05 0 0





0 1 0 1

    , A[0] =   

1 0 0 0

0 1 0 1

0 0 1 0

   . 

(26)

DataThe 2018,change 3, x FOR in PEER 14 of 2117. theREVIEW values of the matrix A components during the calculations is shown in Figure

a11

a13

a12

0.8

0.1

1

0.05

0

1

0.6 0.4

a14

0.2 0

100

200

t[s]

300

0

a21

1

100

200

300

t[s]

0

a22

100

200

200

300

300 t[s]

300

t[s]

100

200

300

t[s]

200

300

t[s]

200

300

t[s]

a24 1

0.9 100

200

300 t[s]

0.95

0 0

200

a23

1

1

0.5

100

100

0

t[s] 0.85 0

a31

a32

0.15

100

200

a33

1

300 t[s]

a34 1

1

0.1 0

0.05 0 1

100

200

300

100

200

300

0

t[s]

100

1 1

0.5

t[s] 200

t[s] 0

a42

100

300

t[s]

a41

0

200

0

1

0.95 0.9 100

200

300

0

t[s]

300

100

a44

a43

100

0.85 0

100

200

300

t[s]

Figure17. 17.Dynamics Dynamics of of adjusting adjusting the values Figure valuesof ofmatrix matrix 𝐀A components componentsobtained obtainedby byusing usingleast leastsquares squares method. method.

Setting values = 150 and aΔ𝑡matrix = 1s A gives thefollowing best results using the algorithm. Using As a result of the𝛾calculations, of the formby obtained recurrent stochastic approximation method gives the time of identification phase 𝑡 = 100 s, which is   0.98 1.02 0.14 of the 5.63bulky ·10−5 object motion changes and acceptable, because only with 𝑡 > 300 s the outer conditions  −0.12 −0.03 0.85 −6.75·10−5  the calculation of new matrix 𝐀 values is need.   A[350] =  (27) .  components 0.15 2.95dynamics ·10−3 0.02 1 (line 1) and the model (line 2) The graphs of the state vector of the object −0.13 −0.03 0.85 −7.22·10−5 are shown in Figure 18.

Taking into account the permissible error of 5%, the resulting matrix A can be written as x1 [m] x2 [m/s]   0.98 1 0.14 0 15  −0.12 02 0.85 0    2 ∗ A =  . 10   0.15 0 0 1 1 1 0.85 0 − 0.13 0 5

(28)

1

2

Setting values γ = 150 and ∆t = 1 s gives the best results by using the algorithm. Using recurrent 0 100 200 300 100 200 300 t [s] t [s] 0 stochastic approximation method gives the time of identification phase t = 100 s, which is acceptable, [deg] x4 [deg/s] because only with t > 300 sx3the outer conditions of the bulky object motion changes and the calculation of new matrix A values is need. 2

2 1

1

2

1 1

2

0

100

200

300

t [s]

0

100

200

300

t [s]

Figure 17. Dynamics of adjusting the values of matrix 𝐀 components obtained by using least squares method.

Setting values 𝛾 = 150 and Δ𝑡 = 1 s gives the best results by using the algorithm. Using recurrent stochastic approximation method gives the time of identification phase 𝑡 = 100 s, which is Data 2018, 3, 60 15 of 21 acceptable, because only with 𝑡 > 300 s the outer conditions of the bulky object motion changes and the calculation of new matrix 𝐀 values is need. The graphs graphs of of the the state state vector vector components components dynamics dynamics of of the the object object (line (line 1) 1) and and the the model model (line (line 2) 2) The are shown shown in in Figure Figure 18. 18. are

x1 [m]

x2 [m/s]

15 2

2

10 1

1

5

1 2

0

100

200

300

t [s]

0

x3 [deg]

100

2 1

200

300

t [s]

2

1 1

2

0

300

x4 [deg/s]

2

1

200

100

200

300

t [s]

0

100

t [s]

Data 2018, 3, x FOR PEER REVIEW Figure 18. 18. Graphs of dynamics of the states vector components. components. Figure

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error dependence dependence ∆x 𝛥𝑥i 𝑖((𝑡) areshown shownininFigure Figure19. 19. Graphs of the error t) == x𝑥o𝑜((𝑡) t) −−x𝑥m𝑚((𝑡) t) are

Δx1 [m]

Δx2 [m/s] 2

1

1

0.5

0 -1 0

100

200

300

100

200

300

t [s]

300

t [s]

t [s]

Δx3 [deg]

Δx4 [deg/s] 2

0.2

1 0

0.1

100

200

-1 0

100

200

300

t [s]

error. Figure 19. The graphs of the dynamics error.

When When changing changing the the external external conditions conditions for for aa large-sized large-sized object object moving, moving, it it is is necessary necessary to to re-start re-start the identification process. The start clause of the identification phase is the identification process. The start clause of the identification phase is |𝑥𝑜| x(𝑡) − 𝑥 (𝑡)| > 𝜀. o ( t ) −𝑚xm ( t )| > ε.

(29) (29)

When the outer conditions of bulky object motion change, it is needed to re-start the When the outer conditions of bulky object motion change, it is needed to re-start the identification identification process. The condition for the activation phase identification process. The condition for the activation phase identification |𝑦𝑜 (𝑡) − 𝑦𝑚 (𝑡)| > 𝜀. (30) (30) |yo (t) − ym (t)| > ε. The study of the effectiveness of the procedure for identifying the parameters of a ship moving model on a slip by the recurrent method of stochastic approximation confirmed the adjustment problems of the algorithm associated with the choice of initial design values and weights that affect both its convergence and error and also revealed that the allowable time allotted on the evaluation of model parameters. When identifying model parameters for adaptive real-time control of the process

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The study of the effectiveness of the procedure for identifying the parameters of a ship moving model on a slip by the recurrent method of stochastic approximation confirmed the adjustment problems of the algorithm associated with the choice of initial design values and weights that affect both its convergence and error and also revealed that the allowable time allotted on the evaluation of model parameters. When identifying model parameters for adaptive real-time control of the process of moving a large object, it is advisable to use the least squares method [17]. 3. Methods Computerized control systems are often introduced to manage complex technical complexes. A characteristic feature of such systems is the presence of several levels of control. To control the slip-raising complex, it is advisable to use a two-level control system. The first (lower) level is used for direct control of individual slip actuators, while the second, the upper level of the system, serves to implement a specific strategy for launching or lifting a vessel [18]. Before the start of the salvaging works, an obligatory check of all units and mechanisms of the slip is performed. At the next stage, the operator sets the slip operation mode (descent/ascent) through the appropriate SCADA window and selects the type of vessel to be prepared for installation on the slip carts (if the required type of vessel is not in the database, the operator manually enters the information). After entering the data, the system processes them using the available models and displays the corresponding recommendations on the display. After installation of the vessel on carts and the beginning of their movement along the rail tracks, the control system continuously monitors the main parameters of the operating ship-lifting complex using the monitoring subsystem. The obtained data is used by local control systems. Operating parameters of the local control unit (LCU) are sent to decision support system, which serves the operator’s workstation. The central control unit (CCU) determines the presence of deviations that are corrected by the LCU under the visual control of the operator. The launching or lifting of the vessel can be stopped at any time in the case of an emergency or as a result of a successful completion of work. The algorithm of functioning of the computerized process control system for launching/lifting the vessel is shown in Figure 20. The lower control level consists of the number of modules, the exact number of which depends on the number of slip carts. The slip trolley is driven by its electric drive, as a result, for the synthesis of control in the local system of the lower level, it is necessary to use information about the load (cable tension) and the operating parameters of the electric motor. Each of the lower-level control modules is a microprocessor system; however, due to the use of different electric motors on the slipways, they may have a different device. The upper level of the control system is implemented using a controller, a set of appropriate input/output modules that form the central control unit (CCU), whose task is to coordinate the work of local lower level systems in order to stabilize the rotational movements of the vessel on the slip and maintain it uniform translational motion. Effective operation of the central control unit is possible subject to the availability of an appropriate algorithm, a special database adequate to the mathematical model of the process of moving the vessel on the slip and timely information from the monitoring subsystem about the position of the trucks, their speed, the tension of the cable of each truck, the value of current in the electric motor circuits skewing of the vessel and from the control modules of the lower level. To form the structure of information and measuring system, it is advisable to divide the factors that have a different disturbing effect on the work of a slipway, into four groups according to a functional feature, as shown in Figure 21.

decision support system, which serves the operator’s workstation. The central control unit (CCU) determines the presence of deviations that are corrected by the LCU under the visual control of the operator. The launching or lifting of the vessel can be stopped at any time in the case of an emergency or as a result of a successful completion of work. Data 2018, 3, 60algorithm of functioning of the computerized process control system for launching/lifting 17 of 21 The the vessel is shown in Figure 20.

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To form the structure of information and measuring system, it is advisable to divide the factors that have a different disturbing effect on the work of a slipway, into four groups according to a Figure20. 20. The algorithm of the the control control system functional feature, asFigure shown inThe Figure 21. of algorithm systemwork workwith withthe theslip. slip. The lower control level consists of the number of modules, the exact number of which depends on the number of slip carts. The slip trolley is driven by its electric drive, as a result, for the synthesis of control in the local system of the lower level, it is necessary to use information about the load (cable tension) and the operating parameters of the electric motor. Each of the lower-level control modules is a microprocessor system; however, due to the use of different electric motors on the slipways, they may have a different device. The upper level of the control system is implemented using a controller, a set of appropriate input/output modules that form the central control unit (CCU), whose task is to coordinate the work of local lower level systems in order to stabilize the rotational movements of the vessel on the slip and maintain it uniform translational motion. Effective operation of the central control unit is possible subject to the availability of an appropriate algorithm, a special database adequate to the mathematical model of the process of moving the vessel on the slip and timely information from the monitoring subsystem about the position of the trucks, their speed, the tension of the cable of each truck, the value of current in the electric motor circuits skewing of the vessel and from the control modules of the lower level.

Figure 21. Analysis of factors affecting the work of slipway. slipway.

Before starting the procedure of launching the vessel, it is required to collect preliminary information about the object and the external conditions. Information on the type of vessel, its weight and size characteristics and the distribution of weight loads should be set into the control system. The position of the carts should also be checked.

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Before starting the procedure of launching the vessel, it is required to collect preliminary information about the object and the external conditions. Information on the type of vessel, its weight and size characteristics and the distribution of weight loads should be set into the control system. The position of the carts should also be checked. Console ship-lifting complex should be provided with hardware and software automated workplace (AW). Continuous monitoring and control of the process parameters by the operator allows us to implement the SCADA-system. The developed models, theoretical and methodological approaches and recommendations can be used for the decision support system development as a part of the control system. Decision Support Systems (DSS) includes the following components: a database (DB), a modelling subsystem, a problem solving subsystem, an interactive subsystem, a data transfer subsystem and an information processing subsystem. Data on the type of vessel, dock drawing of the vessel, that can be developed by the technical department of the enterprise. The database should store information on the largest possible number of vessels that can be serviced by the shipyard, since the expected distribution of load between carts plays an important role and the coordinates of the centre of gravity of vessels, due to their construction, are different. The availability and development of such a database allows us not only to automate the slipway but also to reduce the time of preparation for ship-lifting or launch operations. Information on weather conditions and their impact on the work of the slip should also be stored in the database. The ship should be lowered under favourable weather conditions. However, due to the limitations imposed by the time of construction/repair and delivery of the vessel to the customer, as well as due to the reduction of equipment downtime, it can be problematic to delay ship-lifting work; therefore it is necessary to control the weather factors in order to be able to launch the vessel under satisfactory weather conditions. The modelling subsystem should contain the developed models of the main units of the slip and model the operation of the ship-lifting complex based on the use of data entered by the operator or obtained from the database, helping the operator to evaluate the progress of work and decide on the management of the ship-lifting complex using the task-solving subsystem. The data transfer subsystem connects the DSS with the information measuring subsystem and the lower level LCU. The interactive subsystem at the present stage is usually implemented by means of SCADA-system. The structure of the DSS is shown in Figure 22. The structural scheme of the computerized control system is presented in Figure 23. A set of sensors is installed on each electric drive of the slip cart: torque, cable tension and current and for extreme drives, in addition, range-finder sensors. The information collected by the sensors enters the pre-processing information units (IPPU). The sets of sensors and pre-processing blocks of the information form the monitoring subsystem. From each IPPU, information is transmitted to the appropriate local control system, as well as to the central control unit. A separate LCU consists of an information processing unit (IPU), which serves to receive and process data from the monitoring subsystem, an engine control unit (ECU) used to control the electric motor and a control module (CM) which controls the operation of the LCS, as well as the CCU, receiving commands from it and transmitting information about the functioning of the LCS. Local control systems form the lower level of control. The upper control level is represented by the central control unit and the automated workplace of the decision maker. The CCU is developed on the basis of one of the modern controllers that have proven themselves to be reliable and have qualified technical support, for example, on the basis of the Siemens SIMATIC S7-300 universal modular controller. The controller of the CCU, on the basis of the collected information from all IPPU and all LCS, performs basic calculations in the system and then adjusts the work of the control modules. Using a SCADA system, the results of the CCU operation are visualized on the display screen of the operator. As a SCADA system for an automated workplace, it is possible, respectively, to use a multifunctional an d universal SIMATIC WinCC system.

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obtained from the database, helping the operator to evaluate the progress of work and decide on the management of the ship-lifting complex using the task-solving subsystem. The data transfer subsystem connects the DSS with the information measuring subsystem and the lower level LCU. Data 2018, 3, 60 The interactive subsystem at the present stage is usually implemented by means of SCADA-system. The structure of the DSS is shown in Figure 22.

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that have proven themselves to be reliable and have qualified technical support, for example, on the basis of the Siemens SIMATIC S7-300 universal modular controller. The controller of the CCU, on the basis of the collected information from all IPPU and all LCS, performs basic calculations in the system and then adjusts the work of the control modules. Using a SCADA system, the results of the CCU operation are visualized on the display screen of the operator. As a SCADA system for an automated workplace, it is possible, respectively, to use a multifunctional 22. The structure of the DSS for the slip control system. FigureFigure 22. The structure and universal SIMATIC WinCC system. of the DSS for the slip control system. The structural scheme of the computerized control system is presented in Figure 23. A set of sensors is installed on each electric drive of the slip cart: torque, cable tension and current and for extreme drives, in addition, range-finder sensors. The information collected by the sensors enters the pre-processing information units (IPPU). The sets of sensors and pre-processing blocks of the information form the monitoring subsystem. From each IPPU, information is transmitted to the appropriate local control system, as well as to the central control unit. A separate LCU consists of an information processing unit (IPU), which serves to receive and process data from the monitoring subsystem, an engine control unit (ECU) used to control the electric motor and a control module (CM) which controls the operation of the LCS, as well as the CCU, receiving commands from it and transmitting information about the functioning of the LCS. Local control systems form the lower level of control. The upper control level is represented by the central control unit and the automated workplace of the decision maker. The CCU is developed on the basis of one of the modern controllers

Block diagram of the computerized control system of the slip: 1—measuring the distance Figure 23.Figure Block23. diagram of the computerized control system of the slip: 1—measuring the distance to to the vessel, 2—sensors for measuring the tension force of the cable, 3—measuring the moment on the vessel,the 2—sensors for measuring the tension force of the cable, 3—measuring the moment on the shaft, 4—sensors for measuring current, 5—electric drives, 6—ship-carrying carts, 7—rail tracks. shaft, 4—sensors for measuring current, 5—electric drives, 6—ship-carrying carts, 7—rail tracks.

The considered computerized system will allow us to increase the reliability of the slip operation and to ensure increased safety during the execution of lifting operations under uncertainty about external and internal factors of a random nature. 4. Conclusions Analysis of the process of moving the ship on the slipway revealed the following problems: the

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The considered computerized system will allow us to increase the reliability of the slip operation and to ensure increased safety during the execution of lifting operations under uncertainty about external and internal factors of a random nature. 4. Conclusions Analysis of the process of moving the ship on the slipway revealed the following problems: the need for coordinated management of a group of electric drives, the frequent occurrence of emergency situations, the impact of external and internal factors of random nature. Ensuring safety and improving the reliability of the operation of the ship-lifting complex is possible through the introduction of an information management system and the use of adaptive management methods for the process of moving a ship on a slipway. To analyse the operation of individual electric drives throughout the process of moving the vessel, a dynamic model of motor load based on the analysis of the forces acting on the ship’s trolley was proposed. It allows estimating the cable tension at any point along the way depending on the design parameters of the system and external factors. To obtain an analytical description of the spatially changing system parameters, the apparatus of the theory of fuzzy sets was used. A linearized model of the dynamics of the complex movement of the vessel in the process of moving on an inclined surface, taking into account the joint translational and rotational movements, as well as the structure of the multi-drive system, has been developed. The model, obtained takes into account the influence of external factors and changes in the parameters of the ship-lifting complex, allows us to ensure operational control and timely identifying the occurrence of critical situations during the operation of the ship-lifting complex. The procedures for identifying the parameters of a ship moving model on a slipway by recurrent methods of stochastic approximation and least squares for use in an adaptive control system, that preserve the structure of the matrixes of the linearized model of the process of moving the ship on the slipway, are investigated. The issues related to the implementation of the proposed models and methods for the operational control of the ship-lifting complex based on the use of modern microcontroller controls are considered. The ways of further improvement of the decision support system in the automated system of operational management of the situation assessment module have been identified to ensure the coordinated operation of the multi-drive system, which allows us for the maximum automation of the operational management process of the ship-lifting slipway-type complex. Author Contributions: H.R. and O.P. designed the model and the computational framework and analysed the data and carried out the implementation. A.O. performed the approbations. O.P. wrote the manuscript with materials from all authors. A.O. contributed to the final version of the manuscript. H.R. supervised of project. Conflicts of Interest: The authors declare no conflict of interest.

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