Time Variable Speed Control of Pump Controlled Hydraulic Motor Using Natural Tracking Control

Copyright © IFAC Control of Industrial Systems. Belfort. France. 1997

TIME VARIABLE SPEED CONTROL OF PUMP CONTROLLED HYDRAULIC MOTOR USING NATURAL TRACKING CONTROL

Novak N. Nedic and Dragan H. Prsic

University ofKragujevac, Faculty ofMechanical Engineering Kraljevo, Serbia, Yugoslavia

Abstract: A pump controlled hydraulic motor meets problems with speed and accuracy. These problems become very significant with time varying motion. One way to overcome these problems is to develop some kind of control algorithm. Having in mind the task of these systems, a control algorithm based on the trackability concept seems logical. The special kind of control algorithm based on this concept has been investigated on time variable speed control of pump controlled hydraulic motor. Experimental and simulation results are shown. Keywords: hydraulic motor, speed control, tracking applications

Resume: En cas de commande par pompe de moteur hydro, on rencontre le probleme de vitesse et de precision. Ces problemes sont presents surtout au mouvement variable temporel. Un des moyens de depassement de ces problemes est le developpement d'un type d'algorithme de commande. Compte tenant du devoir de ces systemes, l'algorithme de commande, fonde sur l'accompagnement, semble tres logique. Une categorie speciale d'algorithme de commande, fondee sur ce principe, est examinee sur la commande de moteur commande par pompe avec la vitesse variable par rapport au temps. Les recherches sont confirmees par I'experiment et la simulation dont les resultats figurent dans cet oeuvre. Mots clefs: moteur hydro, commande de vitesse, application de l'accompagnemenl

1. INTRODUCTION

losses. However, they are very fast and accurate. A pump controlled hydraulic motor offers much bette" energy efficiency. On the other hend, it meets problems with speed and accuracy (Backe' and Murrenhoff, 1994). Moreover, these problems become very significant with time varying motion Regarding this, pump controlled hydraulic motor performance need to have some modification.

Improvement of the flexibility and efficiency of hydraulic control systems becomes the imperative of today. The real motion of hydraulic motors should track its desired motion regardless of whether the desired motion is either complex time varying or time invariant and even in the presence of loads. Furthermore, the power efficiency and energy efficiency are necessary to be very high (mobile, aircraft and industrial systems). Hydraulic motors with valve controls are frequently connected to a constant pressure. They exhibit very high throttling

In order to satisfy these requirements a designer meets different kinds of problems. The following problems are typIcal and they are given as follows: (1) complex internal dynamics, (2) time varying

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parameters and (3) complex loads. Ifwe consider all these elements, it becomes quite clear that the corresponding mathematical models turn out to be very complex and consequently do not allow us to accomplish the control synthesis. The special kind of control algorithm has been developed recently (Grujic, 1985; Grujic and Mounfield, 1991; Mounfield and Grujic, 1992). This control algorithm is based on the trackability concept without using any information about a mathematical description of the internal dynamics of the object and about a variable inaccessible for measurement and is known as the natural trackability concept. The authors of this paper successfully investigated the applicability of this control algorithm to pneumatic position control (Nedic and Prsic, 1994).

Fig.I. The hydroelectric closed loop speed control system with the load simulator F

Here, the applicability of this control algorithm to time variable speed control of pump controlled hydraulic motor has been investigated using the natural tracking control. The first part of this paper deals with the introduction to the natural tracking law. The second part consists of the structure and model of the system. The last part deals with simulation and experimental results.

1

:11 I I

i I I ~ I I I 1

i i i

1 I

i i

I

-

L_

2. NATURAL TRACKING LAW

0

J

S(p>

According to the authors (Grujic and Mounfield, 1991; Mounfield and Grujic, 1992), the natural tracking law which provides the exponential tracking for the system is defined by the following expression:

Fig.2. Axial piston pump with the swashplate control 2000

n[min-']

1800 1600

(1)

1400 '200

'000

Where u(t) is control, e(t) is output error, u(I)Ct)and e(J) (t)are the first derivatives of control and output error

respectively,

(a~.-l),

k = (1-

at 1,

I3=G- 1, G is static gain,

800 600

a E (0,1], kp

400

E(O,+oo),

U [V]

200 0

k l E(O,+oo). From (1) it is clear that this control algorithm uses information on the plant error. The gain G is defined by the static characteristics of the plant. The parameters a, kpand k1should be chosen

0

0.5

3.5

Fig. 3. Static characteristic of the plant The symbolic diagram of the variable displacement axial piston pump with the swashplate control is given in Fig.2.

So that quality of tracking is provided.

The mathematical model developed by authors (Nedic, at al.,1996; Bucevac and Nedic, 1996) fully describes the dynamic and static behavior of the hydroelectric control system using analy1ical and ex-perimental methods. The model is nonlinear as can be seen from the static characteristic of the plant(Fig.3.).In order to find the appropriate

3. SYSTEM DESCRIPTION AND MODELLING The diagram of the hydroelectric control system with computer implementation of the control algorithm is shown in Fig. I.

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MOTOR PUMP CONTROLLER Ul

Tm

m

'----------Iqm 1..------'

TRACKING CONTROL ALGORITHM:

Fig.4. Block diagram of the hydroelectric system 4. SIMULATION AND EXPER.Tht1ENT

mathematical model, for applying the control algorithm, the following basic assumptions have been made for the system:

The plant under consideration is the pump controlled hydraulic motor with time variable speed control. The behavior of the plant for time varying desired output value obtained by experiment is shown on Fig.5. This figure necessarily show demand for implementation of the control.

1. The main load of the motor is the load pressure of the load simulator. 2. The dynamics of the pump and the pump output line are significant. 3. The relationship between the control piston displacement and its derivatives can be linearly related to the swashplate angular displacement and appropriate derivatives. 4. The springs are assumed to be linear. 5. Turbulent flow is assumed to be linear through all orifices. 6.- Laminar flow is assumed in all leakage paths. 7. Viscous friction is not insignificant, but Coulomb friction is neglected. 8. The relationship between the electromagnetic force and current is linear.

Control algorithm specified by (2) is implemented to the fourth order linear plant (Fig.4.). Trackability condition within a finite time interval according to Mounfield and Grujic (1992) for this plant is satisfied. The constants from Fig.4. are : K pu

=0.0858

K py = 24.875

[m/.'\j

[rad / s}

Tu = 0.078 s

qm = 11.94 lOo-{; m 3 / rad

C;u = 0.000064

Tm = O.Ols Kw =2.410 2 Vs / rad

=0.175 s K p = 3.19 10-4

Tr

In fact, the fourth order linear model of the system (plant) is assumed (Fig.4.) where: Ul m - motor speed, i-input current, y - swashplate angle, Qp - pump outlet flow, Tp - torque on motor due to the pressure

5 Km = 5.4 10 Nms/m 3 b m = 0.25 Nms I rad

n p = 16.33 s

m 3 / rad

-1

K A = 0.086.'\ I V

K I =1.0 K p = 0.8

[3=4

0.25.---------------,

load, Tm -torque on motor due to pressure in the pump output line, U m - speed voltage, U md - desired speed voltage. The computer control algorithm, according to (1) is defined by:

0'

u(k) = au(k - 1) +(1- a)u o + ~{kp [e(k) - eo] + k

+k I T2:e(i)

(2)

;=0

-0.' 0 ' - - - - - ' 0 - - ' - 5--20--25--30--35--'40

Fig.5.. The plant beha\ior

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According to very low damping ratio of the pump controller, the implementation of the control algorithm to the plant has made problems. For solving the problem another high-pass filter is implemented. Simulation and experimental results given in this paper present relative change off desired speed, real speed and control. The illustration of the results achieved by the tracking algorithm with high-pass filter simulation results can be seen in Fig.6a. for a. = 0.75 and in Fig.6b. for a. =0.9. Fig.6c. shows beha'Viour of the system speed and control with the load (Tp) change for a. = 0.75. 0.1

The action of the load has not significant influence on output signal error. Initial error of the system eo = 0.03. Typical results obtained after comprehensive e>.:perimental work are given in Fig.7. Fig.7a. presents behaviour of the system with classical PI controller. Investig:ltion of this system with the natural tracking control algorithm has shown that the maximum possible value for parameter a is 0.75 with the sampling rate v = 1100Hz. Experimental results sho\\-n in this paper are based on these

.-----_--~--~--~-_____,

0.06 0.0< 0.02

~.02

~.O<

~.06

~.08

t[s] ~"o~--"7---~--6::------:---:'0

~.1

0

'0

(a)

0.'5 U

01

r

0.05

~05

~.,

~.'5 ~.2

t[S] ~.,

0

~.25

10

0

--~-

2

'0

(b)

0.' U

0.08

r

0.06 00< 002 0 ~.02 ~.O<

~06 ~.08 ~.1

0

t[SJ

~.;

10

0

(C)

Fig.6. The left side figures show results of the relative speed behavior, the right side figures show results of the relative control behavior

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10

0.

35

r--_-_-_-_-

-oosL---o '0'5

___,

--::":_ _,----_t[5] _--' 20

25

30

35

40

40

(a) 0.' r---------------~___,

-0.2

0

'0

15

20

25

30

35

'0

15

20

25

30

35

(b) 025

0.'5

CJ)c!r,CJ)r

Ur

0.2 0.1

0.15 O."j

0.05 0.05

-0.05

·0.'

-0.05

-0.'5 -0.'

10

0

'5

20

25

30

·0.2

40

35

t[5] 0

40

(c) 0.2

04

CJ)c!r·CJ)r

Ur

0.15

-0.15

-0.3

t[5] -0.2'-----------o 10 15 20 25

30

35

t[5]

---' 40

4 -0. :--:'40 0 ---:----:":,0=--~'5:----:20~---:2~5---:":3O=--~3::-5

(d)

Fig.7. The left side figures show results of the relative speed behaviour, the right side figures show results of the relative control behaviour (experimental results)

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parameters. Trackability of the system with the load is presented in Fig.7b., but trackability of the system with the load (Tp = 95Nm) is presented in Fig.7c.

REFERENCES Backe, W. and H. Murrenhoff (1994). The present and future of fluid power. In: International

For the illustration of the effect of rate change of the desired value on trackability, the e,,:perimental results can be seen in Fig.7d.

Workshop on Trends in Hydraulic and Pneumatic Components and Systems.. Chicago, pp. 1-34. Bucevac Z.M. and N.N.Nedic (1996). Computer structurally variable automatic control of axial piston pump BPV-IOO as time varying plant. InHeavy Machinery HM '96., Kraljevo, pp. 5.11-5.16. GrujiC, Lj.T. (1985). Phenomenon's, concepts and problems of automatic tracking: continual stationary systems with variable inputs. In: Proceedings of the First International Seminar - Automat and Robot., Belgrade, pp. 309-330. Grujic, Lj.T. and W.P.Mounfield (1991). Natural tracking control of linear systems. In: Proceedings of the 13th IA1ACS World Congres on Computation and Applied Mathematics., Vol.3, pp. 1269-1270., Dublin. Mounfield W.P. and Grujic, Lj.T (1992). High gain PI natural control for e,,:ponential tracking of linear single output with state space description. In: Theorie de la commande., Vol.26 No 2, pp. 125-146. Nedic N.N. and D.H. Prsic (1994). Pneumatic position control using natural tracking law. In: International Workshop on Trends in Hydraulic and Pneumatic Components and Systems, Chicago, pp. 1-13. Nedic N.N. at al. (1996). Experimental analysis and identification of axial piston pump BPV 100. Heavy Machinery HM'96., KraIjevo, pp 5.31-5.36.

5. CONCLUSION Applicability of the high gain PI natural control for experimental tracking to pump controlled hydraulic motor with time variable speed is presented in this paper. This investigation is based on comprehensive e>..-perimental and simulation work. Simulation results obtained by the control algorithm on the fourth order linear plant, with and without the load, show good trackability for time-varying desired speed with implementation of high pass filter.. The real system has shown better tracking ability with regard to it's mathematical model with limiting value of parameter u to 0.75 with sampling rate v = 1100Hz. Also, the results have shown that the system shows better tracking ability with the smaller sampling rate The smaller sampling rate gives possibilities of increasing the value of parameter U. For example, for sampling rate v= 1400Hz. it is possible to increase the value of parameter· u to 0.85.

ACKNOWLEDGMENTS This work was partly supported by the National Science Foundation under project No. llE08P71.

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