小型挖掘機底盤行駛液壓系統(tǒng)設計【行走機構履帶式】

小型挖掘機底盤行駛液壓系統(tǒng)設計【行走機構履帶式】,行走機構履帶式,小型挖掘機底盤行駛液壓系統(tǒng)設計【行走機構履帶式】,小型,挖掘機,底盤,行駛,液壓,系統(tǒng),設計,行走,機構,履帶式 .Automation in Construction 10 2001 477486 rlocaterautcon Semi-automatic control system for hydraulic shovel Hirokazu Araya ) , Masayuki Kagoshima Mechanical Engineering Research Laboratory, Kobe Steel, Ltd., Nishi-ku, Kobe Hyogo 651 2271, Japan Accepted 27 June 2000 Abstract A semi-automatic control system for a hydraulic shovel has been developed. Using this system, unskilled operators can operate a hydraulic shovel easily and accurately. A mathematical control model of a hydraulic shovel with a controller was constructed and a control algorithm was developed by simulation. This algorithm was applied to a hydraulic shovel and its effectiveness was evaluated. High control accuracy and high-stability performance were achieved by feedback plus feedforward control, nonlinear compensation, state feedback and gain scheduling according to the attitude. q2001 Elsevier Science B.V. All rights reserved. Keywords: Construction machinery; Hydraulic shovel; Feedforward; State feedback; Operation 1. Introduction A hydraulic shovel is a construction machinery that can be regarded as a large articulated robot. Digging and loading operations using this machine require a high level of skill, and cause considerable fatigue even in skilled operators. On the other hand, operators grow older, and the number of skilled operators has thus decreased. The situation calls for hydraulic shovels, which can be operated easily by wx any person 15 . The reasons why hydraulic shovel requires a high level of skill are as follows. 1. More than two levers must be operated simulta- neously and adjusted well in such operations. ) Corresponding author. .E-mail address: arayahrknedo.go.jp H. Araya . 2. The direction of lever operations is different from that of a shovels attachment movement. For example, in level crowding by a hydraulic shovel, we must operate three levers arm, boom, . bucket simultaneously to move the top of a bucket . along a level surface Fig. 1 . In this case, the lever operation indicates the direction of the actuator, but this direction differs from the working direction. If an operator use only one lever and other free- doms are operated automatically, the operation be- comes very easily. We call this system a semi-auto- matic control system. When we develop this semi-automatic control system, these two technical problems must be solved. 1. We must use ordinary control valves for auto- matic control. 2. We must compensate dynamic characteristics of a hydraulic shovel to improve the precision of control. 0926-5805r01r$ - see front matter q2001 Elsevier Science B.V. All rights reserved. .PII: S0926-5805 00 00083-2 ()H. Araya, M. KagoshimarAutomation in Construction 10 2001 477486478 Fig. 1. Level crowding of an excavator and frame model of an excavator. We have developed a control algorithm to solve these technical problems and confirm the effect of this control algorithm by experiments with actual hydraulic shovels. Using this control algorithm, we have completed a semi-automatic control system for hydraulic shovels. We then report these items. 2. Hydraulic shovel model To study control algorithms, we have to analyze numerical models of a hydraulic shovel. The hy- draulic shovel, whose boom, arm, and bucket joints are hydraulically driven, is modeled as shown in Fig. 2. The details of the model are described in the following. 2.1. Dynamic model 6 Supposing that each attachment is a solid body, from Lagranges equations of motion, the following expressions are obtained: 2 2 J u qJ cos u yuuqJ cos u yuuqJ sin u yuuqJ sin u yuuyK sinu st. . . . 11 l 12 1 2 2 13 1 3 3 12 1 2 2 13 1 3 3 1 1 1 22 J cos u yuuqJ u qJ cos u yuuyJ sin u yuuqJ sin u yuuyK sinu st. . . . 12 1212223 23312 12123 233 2 22 J cos u yuuqJ cos u yuuqJ u yJ sin u yuuqJ sin u yuuyK sinu st. . . . 13 1 3 1 23 2 3 2 33 3 13 1 3 1 23 2 3 3 3 3 3 1. 2 . 2 where, J s m 1 q m q m 1 q I ; J s 11 1 g123 112 m 11 qm 11 ; J sm 11 ; J sm 1 2 q 21g 231g 313 31g 322 2g 2 m 1 2 qI ; J sm 11 ; J sm 1 2 qI ; K s 32 2 23 32g 333 3g 33 1 . m 1 qm 1 qm 1 g; K s m 1 qm 1 g; 1 g1213 2 2g 233 K sm 1 g; and gsgravitational acceleration. 33g 3 u is the joint angle, t is the supply torque, 1 is ii the attachment length, 1 is the distance between gi the fulcrum and the center of gravity, m is the mass i of the attachment, I is the moment of inertia around i the center of gravity subscripts is13, mean boom, . arm, and bucket, respectively . 2.2. Hydraulic model Each joint is driven by a hydraulic cylinder whose flow is controlled by a spool valve, as shown in Fig. 3. We can assume the following: 1. The open area of a valve is proportional to the spool displacement. 2. There is no oil leak. 3. No pressure drop occurs when oil flows through piping. ()H. Araya, M. KagoshimarAutomation in Construction 10 2001 477486 479 Fig. 2. Model of hydraulic shovel. 4. The effective sectional area of the cylinder is the same on both the head and the rod sides. In this problem, for each joint, we have the following equation from the pressure flow character- istics of the cylinder: V i AhsKXPysgn X P y P 2( . . ii 0 ii si i 1i 1i K when, K scB 2rg P sP yP 0 ii 1i 1i 2 i where, A seffective cross-sectional area of cylin- i der; h scylinder length; X sspool displacement; P ssupply pressure; P scylinder head-side pres- si 1i sure; P scylinder rod-side pressure; V soil vol- 2 ii ume in the cylinder and piping; B sspool width; i gsoil density; Ksbulk modulus of oil; and cs flow coefficient. 2.3. Link relations In the model shown in Fig. 1, the relation be- tween the cylinder length change rate and the attach- ment rotational angular velocity is given as . follows: 1 boom f u. 11 h 1 s u 1 OA OC sin u qb. 11 1 1 sy , 22 (OA qOC q2OA OC cos u qb. 11 1111 . 2 arm .f u ,u 212 h 2 s u yu 21 .OAOCsin u yu qb qa 2222 2 1 2 2 sy , 22 ( .OAqOCq2OAOCcos u yu qb qa 22 22 2222 2 1 2 2 . 3 bucket when ODsOBsBCsCD 33 33 33 33 Y hABCsin u yu qg ya qu. 3333232 f u ,u ssy . 3. 323 22 Y u yu ( AB qBC q2ABBCcos u yu qg ya qu. 32 33 33 3333 3 2 3 3 2 ()H. Araya, M. KagoshimarAutomation in Construction 10 2001 477486480 Fig. 3. Model of hydraulic cylinder and valve. 2.4. Torque relations From the link relations of Section 2.3, the supply torque t is given as follows, taking cylinder friction i into consideration: t syf u P1 A qf u ,u P1 A. . 111 121222 qf u ,u P1 A y Cfuu. . 323 33 c11 1 1 qsgn u Ffu 4. . ./ 1111 t syf u ,u P1 A y Cfu ,uuyu. . /221222c22 1 2 2 1 qsgn u yu Ffu ,u. 5/212212 t syf u ,u P1 A y Cfu ,uuyu. . /332333c33 2 3 3 2 qsgn u yu Ffu ,u . 5/323323 Where, C is the viscous friction coefficient and ci F is kinetic frictional force of a cylinder. i 2.5. Response characteristics of the spool Spool action has a great effect on control charac- teristics. Thus, we are assuming that the spool has the following first-order lag against the reference input. 1 X X s X .5. ii TSq1 spi Where, X X is the reference input of spool dis- i placement and T is a time constant. spi 3. Angle control system As shown in Fig. 4, the angle u is basically controlled to follow the reference angle u by posi- g tion feedback. In order to obtain more accurate control, nonlinear compensation and state feedback are added to the position feedback. We will discuss details of these algorithms as follows. 3.1. Nonlinear compensation In the ordinary automatic control systems, new control devices such as servo valves are used. In our semi-automatic system, in order to realize the coexis- tence of manual and automatic operations, we must use the main control valves, which are used in manual operation. In these valves, the relation be- tween spool displacement and open area is nonlinear. Then, in automatic operation, using this relation, the spool displacement is inversely calculated from the required open area, and the nonlinearity is compen- . sated Fig. 5 . .Fig. 4. Block diagram of control system u . ()H. Araya, M. KagoshimarAutomation in Construction 10 2001 477486 481 Fig. 5. Nonlinear compensation. 3.2. State feedback Based on the model discussed in Section 2, if the dynamic characteristics for boom angle control are linearized in the vicinity of a certain standard condi- tion spool displacement X , cylinder differential 10 . pressure P , and boom angle u , the closed-loop 110 10 transfer function can be expressed by K p u s ug 6. 1132 asqasqasqK 210p where, K is position feedback gain; and p f u ACfu. . 110 1 c11 10 a sq 0 2 APyP.KPyP ( 1 s111001 s1110 XJqJ cosu X qJ cos u X qu X DC44. 10 11 12 2 13 2 3 a s 1 2 Af u P yP. . 11 10 s1 110 Cfu V. c11 10 1 q AKK P yP( 101s1110 VJqJ cosu X qJ cos u X qu X DC44. 111 12 2 13 2 3 a s . 2 Af u KK P yP. ( 1 1 10 01 s1 110 This system has a comparatively small coefficient a , so the response is oscillatory. For instance, if in 1 our large SK-16 hydraulic shovel, X is 0, the 10 coefficients are given as a s2.7=10 y2 , a s6.0 01 =10 y6 , a s1.2=10 y3 . Addingthe acceleration 2 feedback of gain K , to this the upper loop in Fig. a . 4 , the closed loop transfer function is given as K p u s u .7. 1 r132 asq a qKsqasqK. 21a 0 p Adding this factor, the coefficient of s 2 becomes larger, thus, the system becomes stable. In this way, acceleration feedback is effective in improving the response characteristics. However, it is generally difficult to detect acceler- ation accurately. To overcome this difficulty, cylin- der force feedback was applied instead of accelera- . tion feedback the lower loop in Fig. 4 . In this case, cylinder force is calculated from detected cylinder pressure and filtered in its lower-frequency portion wx 7,8 . This is called pressure feedback. 4. Servo control system When one joint is manually operated and another joint is controlled automatically to follow the manual operation, a servo control system must be required. For example, as shown in Fig. 6, in the level crowd- ing control, the boom is controlled to keep the arm . end height Z calculated from u and u to refer- 12 ence Zr. In order to obtain more accurate control, the following control actions are introduced. ()H. Araya, M. KagoshimarAutomation in Construction 10 2001 477486482 .Fig. 6. Block diagram of control system Z . 4.1. Feedforward control Calculating Z from Fig. 1, we obtain Zs1 cosu q1 cosu .8. 1122 . Differentiating both sides of Eq. 8 with respect to time, we have the following relation, Z 1 sinu 22 u sy y u .9. 12 1 sinu 1 sinu 11 11 The first term of the right-hand side can be taken . as the expression feedback portion to convert Z to u , and the second term of the right-hand side is the 1 expression feedforward portion to calculate how much u should be changed when u is changed 12 manually. Actually, u is determined using the difference 2 value of Du . To optimize the feedforward rate, 2 feedforward gain K is tunned. ff There may be a method to detect and use the arm . operating-lever condition i.e. angle instead of arm angular velocity, since the arm is driven at an angu- lar velocity nearly proportional to this lever condi- tion. 4.2. Adaptie gain scheduling according to the atti- tude In articulated machines like hydraulic shovels, dynamic characteristics are greatly susceptible to the attitude. Therefore, it is difficult to control the ma- chine stably at all attitudes with constant gain. To solve this problem, the adaptive gain scheduling according to the attitude is multiplied in the feedback . loop Fig. 6 . As shown in Fig. 7, the adaptive gain . KZ or Ku is characterized as a function of two variables, u X and Z. u X means how the arm is 22 extended, and Z means the height of the bucket. 5. Simulation results The level crowding control was simulated by applying the control algorithm described in Section 4 to the hydraulic shovel model discussed in Section 2. In the simulation, our large SK-16 hydraulic shovel . was employed. Fig. 8 shows one of the results. Five seconds after the control started, load disturbance ()H. Araya, M. KagoshimarAutomation in Construction 10 2001 477486 483 Fig. 7. Gain scheduling according to the attitude. was applied stepwise. Fig. 9 shows the use of feed- forward control can reduce control error. 6. Semi-automatic control system Based on the simulation, a semi-automatic control system was manufactured for trial, and applied to the SK-16 shovel. Performance was then ascertained by field tests. This section will discuss the configuration and functions of the control system. 6.1. Configuration As illustrated in Fig. 10, the control system con- sists of a controller, sensors, manmachine interface, and hydraulic control system. The controller is based on a 16-bit microcomputer which receives angle input signals of the boom, arm, and bucket from the sensor; determines the condition of each control lever; selects control modes and calculates actuating variables; and outputs the results from the amplifier as electrical signals. The hy- Fig. 8. Simulation result of level crowding. draulic control system generates hydraulic pressure proportional to the electrical signals from the electro- magnetic proportional-reducing valve, positions the spool of the main control valve, and controls the flow rate to the hydraulic cylinder. In order to realize high-speed, high-accuracy con- trol, a numeric data processor is employed for the Fig. 9. Effect of feedforward control on control error of Z. ()H. Araya, M. KagoshimarAutomation in Construction 10 2001 477486484 Fig. 10. Schema of control system. controller, and a high-resolution magnetic encoder is used for the sensor. In addition to these, a pressure transducer is installed in each cylinder to achieve pressure feedback. The measured data are stored up to the memory, and can be taken out from the communication port. 6.2. Control functions This control system has three control modes, which are automatically switched in accordance with lever operation and selector switches. These func- tions are the following . 1 Level crowding mode: during the manual arm pushing operation with the level crowding switch, the system automatically controls the boom and holds the arm end movement level. In this case, the refer- ence position is the height of the arm end from the ground when the arm lever began to be operated. Operation of the boom lever can interrupt automatic control temporarily, because priority is given to man- ual operation. . 2 Horizontal bucket lifting mode: during the manual boom raising operation with the horizontal bucket lifting switch, the system automatically con- trols the bucket. Keeping the bucket angle equal to that at the beginning of operation prevents material spillage from the bucket. . 3 Manual operation mode: when neither the level crowding switch nor the horizontal bucket lift- ing switch are selected, the boom, arm, and bucket are controlled by manual operation only. The program realizing these functions is primarily written in C language, and has well-structured mod- ule to improve maintainability. 7. Results and analysis of field test We put the field test with the system. We con- firmed that the system worked correctly and the effects of the control algorithm described in Chaps. 3 and 4 were ascertained as follows. 7.1. Automatic control tests of indiidual attach- ments For each attachment of the boom, arm, and bucket, the reference angle was changed 58 stepwise from the initial value, and the responses were measured; thus, the effects of the control algorithm described in Chap. 3 were ascertained. ()H. Araya, M. KagoshimarAutomation in Construction 10 2001 477486 485 Fig. 11. Effect of nonlinear compensation on boom angle. 7.1.1. Effect of nonlinear compensation Fig. 11 shows the test results of boom lowering. Because dead zones exist in the electro-hydraulic systems, steady-state error remains when simple po- sition feedback without compensation is applied OFF . in the figure . Addition of nonlinear compensation . ON in the figure can reduce this error. 7.1.2. Effect of state feedback control For the arm and bucket, stable response can be obtained by position feedback only, but adding ac- celeration or pressure feedback can improve fast-re- sponse capability. As regards the boom, with only the position feedback, the response becomes oscilla- tory. Adding acceleration or pressure feedback made the response stable without impairing fast-response capability. As an example, Fig. 12 shows the test results when pressure feedback compensation was applied during boom lowering. 7.2. Leel crowding control test Control tests were conducted under various con- trol and operating conditions to observe the control Fig. 12. Effect of pressure feedback control on boom angle. Fig. 13. Effect of feedforward control on control error of Z. characteristics, and at the same time to determine the optimal control parameters such as the control gains . shown in Fig. 6 . 7.2.1. Effects of feedforward control In the case of position feedback only, increasing gain K to decrease error DZ causes oscillation due p to the time delay in the system, as shown by AOFFB in Fig. 13. That is, K cannot be increased. Apply- p ing the feedforward of the arm lever value described in Section 4.1 can decrease error without increasing K as shown by AONB in the figure. p 7.2.2. Effects of compensation in attitude Level crowding is apt to become oscillatory at the raised position or when crowding is almost com- pleted. This oscillation can be prevented by changing gain K according to the attitude, as has been p discussed in Section 4.2. The effect is shown in Fig. 14. This shows the result when the level crowding was done at around 2 m above ground. Compared to the case without the compensation, denoted by OFF in the figure, the ON case with the compensation provides stable response. Fig. 14. Effect of adaptive gain control on control error of Z. ()H. Araya, M. KagoshimarAutomation in Construction 10 2001 477486486 7.2.3. Effects of control interal The effects of control interval on control perfor- mance were investigated. The results are: 1. when the control interval is set to more than 100 ms, oscillation becomes greater at attitudes with large moments of inertia; and 2. when the control interval is less than 50 ms, control performance cannot be improved so much. Consequently, taking calculation accuracy into ac- count, the control interval of 50 ms was selected for this control system. 7.2.4. Effects of load A shovel with this control system carried out actual digging to investigate the effects of loading. No significant difference was found in control accu- racy from that at no load. 8. Conclusions This paper has shown that combining state feed- back and feedforward controls makes it possible to accurately control the hydraulic shovel, and also showed that nonlinear compensation makes it possi- ble to use ordinary control valves for automatic controls. The use of these control techniques allows even unskilled operators to operate hydraulic shovels easily and accurately. We will apply these control techniques to other construction machinery such as crawler cranes, and improve the conventional construction machinery to the machines which can be operated easily by any- one. References wx1 J. Chiba, T. Takeda, Automatic control in construction ma- . .chines, Journal of SICE 21 8 1982 4046. wx2 H. Nakamura, A. Matsuzaki, Automation in construction ma- . .chinery, Hitachi Review 57 3 1975 5562. wx3 T. Nakano et al., Development of large hydraulic excavator, . .Mitsubishi Heavy Industries Technical Review 22 2 1985 4251. wx4 T. Morita, Y. Sakawa, Modeling and control of power shovel, . .Transactions of SICE 22 1 1986 6975. wx5 H. Araya et al., Automatic control system for hydraulic exca- . .vator, R&D Kobe Steel Engineering Reports 37 2 1987 7478. wx6 P.K. Vaha, M.J. Skibniewski, Dynamic model of excavator, . .Journal of Aerospace Engineering 6 2 1990 April. wx7 H. Hanafusa, Design of electro-hydraulic servo system for articulated robot, Journal of the Japan Hydraulics and Pneu- . .