Control Algorithm Design of the Active Pneumatic ... - Science Direct

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ScienceDirect Procedia Engineering 176 (2017) 653 – 660

Dynamics and Vibroacoustics of Machines (DVM2016)

Control algorithm design of the active pneumatic vibration isolator Peter V. Kosenkov*, Georgy M. Makaryants Samara National Research University, Moskovskoe shosse, 34, Samara, 443086, Russian Federation

Abstract The background for the proposed vibration isolation method is based on the principle of active pressure control, minimizing the cyclic load transmitted to the system base through elastic pneumatic element. The paper presents a research on effectiveness of PID-control algorithm with back-calculation of integrator part. Pressure pulsation inside the pneumatic element of the vibration isolator is studied in the frequency range that includes its sub-resonant and resonant frequencies. Spectral analysis is conducted in order to analyze the harmonic excitation response of an active pneumatic isolation system and a passive one, with disabled valves control. The minimal bore size and response rate of the control valve are defined to achieve at least a double advantage of the active system over the passive one in the frequency range including the vibration isolator resonant frequency. As expected, the proposed control algorithm demonstrated a decent decrease of pressure pulsation amplitude at a low frequency range of a Hertzlevel excitation signal. The calculation data analysis shows that PID-control algorithm with back-calculation of integrator part can be effectively used for active pneumatic vibration isolator, if the control valve parameters are within specified ranges. © 2017 2016The TheAuthors. Authors. Published by Elsevier Ltd. is an open access article under the CC BY-NC-ND license © Published by Elsevier Ltd. This Peer-review under responsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2016). (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the international conference on Dynamics and Vibroacoustics of Machines Keywords: Vibration isolator, active system, control valve, pressure pulsations.

1. Introduction The operation of most technical objects is inevitably tied to cyclic loads. Systems with rotary engines and shafts [1], including construction equipment [2, 3] and precision tools [4, 5] are all subject to vibration. The most common solution to this problem is to install several passive vibration isolation elements in order to protect the key mechanism parts. The articles [6-10] thoroughly describe the various details and possible implementation issues of passive vibration isolation systems. However, any passive system relies on elements which exhibit fixed

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1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the international conference on Dynamics and Vibroacoustics of Machines

doi:10.1016/j.proeng.2017.02.309

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Peter V. Kosenkov and Georgy M. Makaryants / Procedia Engineering 176 (2017) 653 – 660

characteristics: modal frequency, general stiffness, damping parameters. In some cases it turns the solution into a complex engineering problem. The overall tightening of vibration level regulations has forced the evolution of active and semi-active vibration isolation systems. The key part of these systems is an elastic member, whose parameters can be tuned during operation for the maximum efficiency. Pneumatic bellows, for example, may be tuned by adjusting the chamber pressure, changing the object modal frequency, and providing the necessary offset from excitation frequencies. For these purposes researchers from the University of Castille-La Manche (UCLM) have developed a control algorithm [1, 11] which changes the resonant frequency of pneumatic systems through switching between two connector tubes of various diameters, and the length between the bellows and additional gas vessel with rigid walls. At Korea Advanced Institute of Science and Technology (KAIST), another group of researchers used the algorithm of air supply control into the pneumatic element following a reference model with the required modal parameters [5, 12]. Two teams – the integrated one of the University of Ulsan (Korea) and Novosibirsk State Technical University [3], and another one from Newport Corporation [13] developed a control algorithm of pneumatic vibroinsulator stiffness minimization. However, all of these systems are united with one drawback: the system modal frequency cannot be lowered indefinitely due to construction parameters and vibration sensors’ limitations. An occasional shift of the disturbing force frequency would cause another system resonance. As a result, the studies of alternate vibration control methods remain important. An alternate solution to the isolator modal frequency control is an active counteraction to the disturbing force. In order to implement it, Maciejewski et al. [2, 14] used the proportional control algorithm with vibration, relative vibration speed and relative vibration displacement as regulated parameters. This article is a further development of our research [16] on single-coordinate vibration isolation. In this case, a PID-regulator with back-calculation of integrator part, controls the instant value of gas pressure in the pneumatic bellow. The choice of regulated parameter is evident since the reduction in amplitude of pressure pulsations within the bellows would cause a proportional decrease in the load transmitted to the protected unit. The article pays special attention to valve models and thoroughly defines their parameters. 2. The mathematical model The design diagram on Fig.1 provides the general outline for the mathematical model. In our case the theoretical study was conducted using a single coordinate vibration isolation model that included a pneumatic element, a control valve assembly model and a control algorithm block. For the study purposes the complex behavior of a pneumatic diaphragm was simplified to a piston chamber coupled with an elastic body. Hence, the equation (1) represents the displacement x of an object with mass m, attached to the top of pneumatic piston chamber, coupled with a spring, which is described by the specified stiffness k and damping coefficient c. The system is oscillated by the applied excitation force Fin , described by sine law (2): d 2x dt 2

m  Fin  mg  Sef P  P0   kx  c

dx dt

Fin  A sin t

(1) (2)

The following assumptions were drawn in order to derive the continuity equation for the variable volume piston chamber:  the working fluid (air) behaves as a homogenous ideal gas  the gas compression is considered to be a quick process; hence, the adiabatic laws are applied  the piston chamber effective area Sef remains constant Based on the above, the following continuity Equation (3) was implemented:

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dP hmean  x dx P Sef  Gin  Gout  Sef dt kRT dt RT

(3)

where Gin and Gout are the gas flows at the system inlet and outlet, hmean is a pneumatic bellows height with no disturbance.

Fig. 1. Pneumatic system model: I – pneumatic bellows; 2 – pneumatic system inlet; 3 – pneumatic system outlet; 4 – mass load.

The control valves assembly was represented by two presets: a pair of cutoff valves, located at the system inlet and outlet, and a single proportional servo valve. In both cases the variable area pneumatic orifice model incorporated the Saint-Venant formula (4):  2k 1    G  Api k  1 RT    

2 k 1  p2  k  p 2  k       p1    p1   

(4)

where G is mass flow rate, μ is discharge coefficient, A is orifice cross-sectional area, p1 and p2 are the absolute pressures at the orifice inlet and outlet, k is a polytrope coefficient, R – specific gas constant and T - gas temperature. In our case the temperature was considered constant (T=295ºK). At the critical ratio   0,55 the choked flow occurred, after which the flow rate depended on the inlet pressure only (5): k 1

k G  Api RT

 p2  k    p1 

(5)

In case of very small pressure difference, the square root relationship had an infinite gradient. In order to prevent calculation difficulties the flow was set to zero for pressure differences, defined by p2 / p1  0,999 . The valve assemblies were modeled with account to their respective throttling characteristics, presented in figures 2a and 2b [15]:

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a)

b) Fig. 2. Throttling characteristics of the different valve types: a – servo valve (LRWA); b – spool valve (AP)

These graphs depict the correlation between the valve opening area and the input control signal. The servo valve was controlled by the analog electric signal, whereas the AP valves were regulated by the PWM signal. In order to obtain the maximum available gas flow, the following valve models were taken in consideration: Table 1. Pneumatic valve parameters. Control valve model

Bore diameter, mm

response time, s

Camozzi AP 7211-NR2-0711

2.4

0.3

Camozzi LRWA2-34-3-A-00

6

0.27

The “response time” was defined empirically as a time of the full valve opening, controlled by the staircase signal. It is worth noting, that LRWA valve was operated with analog electric signal, whereas the AP valves were controlled using PWM signal in order to represent the real valve operation. The realisation of a PID-controller in MathLab Simulink is presented on figure 3. It includes the basic proportional and integral parts, the differential part is presented by the real differentiator unit with adjustable gain coefficient and characteristic time. The back-calculation of integral part was implemented in order to provide further operation stability: the integrator part would be discharged when the subsystem in question exceeded the saturation limits.

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Fig. 3.PID-controller algorithm with back-calculation of integral part.

The calculation procedure was comprised of series of repetitive system runs, where the cyclic sine load frequency varied from 1 to 30Hz and the applied load amplitude remained constant (40N for instance). A single test run took 5s to perform in average. The oscillogram of pressure pulsation within the pneumatic bellows was recorded. Then, the FFT analysis was performed in order to point out the main frequencies of recorded signal and their corresponding amplitudes. After that, recordings of «active» and «passive» systems were compared. The overall efficiency was measured using two parameters. The first one was defined by the correlation between the tone components at the same frequency of disturbing force in both systems: Et 

Ap pas Apact

,

(6)

f  fin

where Appas is a tone component of the passive system pressure pulsation amplitude, Apact is a tone component of the active system pressure pulsation amplitude, fin is a disturbing force frequency. 3. Adjustment of the PID-controller coefficients and result analysis The PID coefficients were empirically defined in order to achieve best performance for both valve assemblies. Figure 4 represents the initial step of the adjustment. The simulink model was brought to a stable self-oscillatory state in order to define the maximum value of proportional coefficient. Then, the differential and integral coefficients were tuned in order to achieve required setting time and eliminate any possible over-control.

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Fig. 4. system time response for a single disturbing impulse with different proportional coefficients: 1 – Kp = 0,2; 2 – Kp = 0,25; 3 – Kp = 0,3;

The careful consideration of these facts brought up the following coefficient ranges: Table 2. PID controller empiric coefficient ranges for different valve assemblies. Control valve operating model

KP

KI

KD

τD

Camozzi AP 7211-NR2-0711

0.54…0.75

0.11…0.14

0.012

1.07

Camozzi LRWA2-34-3-A-00

0.2…0.24

0.07…0.10

0.012

1.08

(a)

(b) Fig. 5. System efficiency of the various valve assemblies: a – servo valve (LRWA); b – direct proportional valve (AP)

Obviously, the servovalve achieved much greater efficiency due to its larger bore diameter and slightly higher response rate. The figure 6 illustrates the transmissibility factor comparison between the passive vibroisolator and the active one, fitted with servo valve assembly:


Fig. 6. Comparison of pressure pulsation levels in active and passive systems.

4. Conclusion We have suggested an algorithm for achieving reasonable pressure drops between pressure feed system, pneumatic bellows and outer space. The developed algorithm gives the possibility to distribute the total pressure difference, so that base-transmitted load is minimized. This is achieved by means of an active pressure control using the PID-algorithm with integral closed loop. We have provided computational dependencies for the detailed mathematical representation of the active pneumatic vibroisolation system, taking into account the derived PID coefficients. The vibration isolation system efficiency depends on the size of the orifice area and response time of the pressure control valve. In our case, the servo type valve was chosen for its optimal correlation between bore diameter value and response time. The practical efficiency of the proportional control algorithm with dynamic pressure control output in terms of active pneumatic vibration isolator was found. The active system effectively dampened the resonant peak of the passive isolator, allowing a decrease in the transmitted load by 1.65 times. The system operation frequency range spanned from 5Hz to 30Hz. Acknowledgements The research has been done with funding from Ministry of Education and Science of the Russian Federation. References [1] Nieto, A.J., Morales, A.L., Chicharro, J.M. and Pintado, P. Unbalanced machinery vibration isolation with a semi-active pneumatic suspension, Journal of sound and vibration, 329, 3–12, (2010) [2] Maciejewski, I., Meyer, L. and Krzyzynski, T. The vibration damping effectiveness of an active seat suspension system and its robustness to varying mass loading, Journal of sound and vibration, 329, 38987–3914, (2010) [3] Lee, C.-M., Bogatchenkov, A.H., Goverdovskiy, V.N., Shynkarenko, Y.V. and Temnikov, A.I. Position control of seat suspension with minimum stiffness, Journal of sound and vibration, 292, 435–442, (2006). [4] Abakumov, A.M. and Miatov. G.N. Control algorithms for active vibration isolation systems subject to random disturbances, Journal of sound and vibration, 289, 889–907, (2006)

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