Vector Control of a Hydraulic Crane

Vector Control of a Hydraulic Crane Petter Krus

Jan-Ove Palmberg

Division of Fluid Power Technology

Department of Mechanical Engineering

Linkoping University, S-58183 Linkoping, Sweden

ABSTRACT Mobile hydraulic equipment are today operated manu­ ally to a very large extent. There are, however, some ap­ plications where substantial benefits would be obtaind if some kind of feedback and more sophisticated con­ trol was used. One such application is the control of a crane. Usually the operator controlls the flow to each of the pistons so that the crane tip is moved in the de­ sired direction (Fig. 1). Since many mobile hydraulic valves packages have electronic input and there exists built in position transducers for the pistons, it seems to be rather straightforward to introduce vector control of the crane tip directly. That is, the operator commands controlls the direction and speed of the crane tip. Here, a control algorithm is described that allows the use of mobile electrohydraulic proportional valves while still having accurate vector control of the crane tip.

to solve this is to introduce more sophisticated control algorithms and using valves with more ideal character­ istics. On the other hand, an experienced operator can make excellent vector control even with valves with rel­ atively poor control characteristics. The approach here, is to remove some of the feedback that is introduced with a straigthforward implementation of vector control. In this way stability and response is improved while a high degree of directional accuracy is maintained Figure 2 shows definitions of the different coordinates in the crane.

z x

Figure 1: Vector control of crane

INTRODUCTION Attempts to use a straightforward implementation of vector control is difficult with electrohydraulic propor­ tional valves. In order to obtain accuracy, speed feed­ back is inadequate. Some kind of integration of the con­ trol (speed) error is necessary which in effect yields a position control loop. The non ideal characteristics of mobile hydraulic valves and the complex dynamics of the mechanical strucure makes it difficult to have gains that gives acceptable response, see Romer [3]. One approach

Figure 2: Hydraulic crane

CONTROL ALGORITHM Figure 3 shows the principles of the control algorithm. XL, ZL is the actual load position. A reference point xr,n+l, Zr,n+l is calculated that is situated on the refer­ ence line r and at a distance R from the actual loadpo­ sition. R is here refered to as the tolerance radius. The

the reference load position X r, Zr and in the same way the load position XL, Z L can be transformed into the pis­ ton positions X p1,x p2' The input signals to the valves are then calculated as

Figure 3: Principles of the control algorithm

reference line is defined by the previous reference point Xr,n, Zr,n and the direction given by the input signals. The commands from the operator U x and U z repre­ sents speeds in the x and Z directions respectively. Polar transformation is used to obtain the reference vector a r and the magnitude a. Ux Uz

= Ju x2 + uz2

Zr,n+1

= XL + Rcoe o; =

ZL

(3) (4)

+ Rsina c

here (5)

where a2

. (R = arcsm R

e

.

Xp1)

(10)

U tl 2

=

X p2)

(11)

ak 2(x p2,r -

Here the factors k 1 and k 2 should be chosen so that a certain error in piston positions gives approximatly the same piston speed in both actuators. If this is achieved the reference vector and the correcting vector will be close to aligned in steady state. The control law have some interesting properties. The fact that the reference position for the load, and the actual position are kept separate with the distance R means that the magnitude of the valve signals are con­ trolled by the magnitude of the input signals a.' This means that the response from input signals to move­ ment of the load are very similar to the response when no controller is used. The controller only handles the distribution between the two valve signals. Since there is a feedback present there is also the risk of instability. The control law is nonlinear with variable gains gl and g2.

(2)

The case of zero inputs must be treated separatly since eq. 1 is not defined then. This is, however, trivial. The new reference point X r , z; can be calculated as Xr,n+1

= ak1(xp1,r -

(1)

a r = arctan- ­ a

Utl1

sin a1

)

gl

= ak ,

(12)

g2

= ak 2

(13)

The highest gain is then of course with maximum input signal. In a hydraulic valve, however, damping is also proportional to the input signal. This means that the gain is high where also the damping is high. In pressure compensated valves, however, the damping do not follow such a simple relationship. Idealy pressure compensated valves do not contribute to damping at all. See Krus [1] an d Krus et al [2]. Saturation is handled in the following way. If one of the signals are saturated a factor !.at is calculated.

(6) !.at

= u.at/utI,max

(14)

here (7)

The angle a e can be calculated as

ae

= arctan ,

(Zrn -

zL)

xr,n -

XL

('

)

(8)

The function arctan- is just like arctan except that it can give angles in all four quadrants depending on the signs of the dominator and numerator in the argument. The distance R; can be calculated as

Using invers kinematics the corresponding reference po­ sitions Xp1,r, X p2,r, for the pistons can be calculated from

where utI,max is the input signal with maximum value and U.at is the level where it gets saturated. The input signals are then recalculated as: Utl1

=

!.atak1(Xp1,r -

Xp1)

(15)

U tl2

=

!.atak2(Xp2,r -

X p2)

(16)

The resulting controller can be described by the block diagram in Fig. 4. In the block diagram there are two feedbacks of the piston positions (or load position). The feedback to the block that generates the reference point partly can­ cels the other feedback, thereby improving the stability properties of the controller. Another advantage of this algorithm is that even if the system do get unstable,

.94

ZLp,Zr(m)

XLp(m) 3.50

.92 .90 ~

~~

~~. ~

~.~

3.00

.88

Figure 4: Block diagram of vector controller

_._~

\._... .84

it can be stopped by making zero input signals to the system, since this will nullify the gain. The case where the load position is at a greater dis­ tance from the reference line than the tolerance radius R, must also be handled since this may occur during "- transients. In this case the reference point is placed at the reference line as close as possible to the load posi­ tion. So far we have considered the tolerance radius R to be constant. It is, however, suitable to allow it to be small for very small input signals.

5.0

. ._ 2.50

x Lp

10.0 Time (sec)

Figure 5: vertical position as afunction of time

Z

and horizontal position x

The trace of the cranetip is drawn to scale together with the crane in Fig 6.

EXPERIMENTAL RESULTS The control algorithm was implemented on a real lorry crane. It was equipped with Vickers CMX electrohy­ draulic proportional valves. The CMX valves can be equipped with a pressure feedback pin to improve damp­ ing. In the, experiments, however, this was not used in order to obtain more general results. The results for a horisontal translation is shown in Fig 5. The input signal is a soft positive and then negative step of the horizontal speed. Here the position XLp, ZLp represents the load position calculated from the piston positions. Consequently deformations in the mechanical structure are not included. z; is the horizontal compo­ nent of the reference line. Figure 6: Trace of the cranetip drawn in scale together with the crane

CONCLUSIONS An algorithm for vector control of loads controlled by two actuators is described in this paper. The advan­ tage of this algorithm is that it allows accurate vector control to be performed with standard mobile electrohy­ draulic valves. The algorithm is very robust since feed­ back not contributing to the vector control (but never­ theless introduced in a straigthforward implementation) is removed. The algorithm presented here represents a very basic implementation. There are, however, some obvious improvments that can be introduced i.e. iden­ tification of the gain between input signal to a valve and speed of the actuator. This can be performed us­ ing some recursive parameter identification on line. In this way the factors k1 and k 2 can be adjusted so that the correcting vector can be moved to be almost aligned with the reference vector and consequently the tolerance radius can be increased to further improve stability (for the same accuracy). Furthermore, the tolerance radius can be variable and dependent on the position of the load, since some locations are closer to instability than .'-.- others (especially near singularities). The algorithm seems very well suited for application where vector control is desired. It can also be used in applications with position control. The algorithm can then be used to give a linear translation from one refer­ ence point to another. REFERENCES [1J P. Krus.

On Load Sensing Fluid Power Systems, With Special Reference to Dynamic Properties and Control Aspects. PhD thesis, Linkoping University,

S-58183 Linkoping, 1988. [2J P. Krus, J .-0. Palmberg, and T. Persson. Dynamic properties of load sensing systems with complex me­ chanicalloads. In NCFP88, Chicago, USA, 1988. [3] D. Romer. Programmentwicklung einer Mikroprozessorgesteurten Regelung eines Mo­ bilkranes, LiTH-IKP-EX-668. Linkoping University, Linkoping, Sweden, 1987.