【正文】 shovel to improve the precision of control. 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 actualhydraulic this control algorithm,we have pleted a semiautomatic control system for hydraulic then report these items. shovel modelTo study control algorithms,we have to analyze numerical models of a hydraulic hy draulic shovel,whose boom,arm,and bucket jointsare hydraulically driven,is modeled as shown in Fig. details of the model are described in the following. model [6]Supposing that each attachment is a solid body,from Lagrange’s equations of motion,the following expressions are obtained: K 3 s m 3 1 g3g。and g s gravitational acceleration. u is the joint angle,t is the supply torque the attachment length,1 g iis the distance between the fulcrum and the center of gravity,m iis the mass of the attachment,I iis the moment of inertia around the center of gravity ?subscripts i s 1–3,mean boom, arm,and bucket,respectively.. model Each joint is driven by a hydraulic cylinder whose flow is controlled by a spool valve,as shown in Fig. can assume the following: open area of a valve is proportional to the spool displacement. is no oil leak. pressure drop occurs when oil flows through, Automation in Construction 10 (2001) 477–486 479 of hydraulic shovel. 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 characterstics of the cylinder:時(shí)；where,A is effective crosssectional area of cylinder。h i s cylinder length。X is spool displacement。Ps i s supply pressure。P1 is cylinder headside pressure。P 2 i s cylinder rodside pressure。Vi s oil volume in the cylinder and piping。B is spool width。 gsoil density。Ksbulk of hydraulic cylinder and valve.modulus of oil。and cs flow coefficient. relationsIn the model shown in ,the relation between the cylinder length change rate and the attachment rotational angular velocity is given asfollows:?1. boom relations From the link relations of Section ,the supplytorque t is given as follows,taking cylinder friction I into consideration:Where,C ciis the viscous friction coefficient and Fi is kinetic frictional force of a cylinder characteristics of the spool Spool action has a great effect on control ,we are assuming that the spool hasthe following firstorder lag against the reference input. iis the reference input of spool dis placement and Ts piis a time constant. control systemAs shown in ,the angle u is basically controlled to follow the reference angle ug by position order to obtain more accuratecontrol,nonlinear pensation and state feedback are added to the position will discuss details of these algorithms as follows. pensationIn the ordinary automatic control systems,new control devices such as servo valves are our semiautomatic system,in order to realize the coexistence of manual and automatic operations,we must use the main control valves,which are used in manual these valves,the relation between 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 pensated ?.. diagram of control system ?u.., Automation in Construction 10 (2001) 477–486 481 pensation. feedbackBased on the model discussed in Section 2,if thedynamic characteristics for boom angle control are linearized in the vicinity of a certain standard condition ?spool displacement X10,cylinder differential pressure P,and boom angle u.,the closedlooptransfer function can be expressed by This system has a paratively small coefficient a1so the response is instance,if in our large SK16 hydraulic shovel,X 10is 0,thecoefficients are given as a s =10 accelerationfeedback of gain Ka,to this ?the upper loop in Fig.4.,the closed loop transfer function is given as Adding this factor,the coefficient of s2 bees larger,thus,the system bees this way,acceleration feedback is effective in improving the response characteristics.However,it is generally difficult to detect acceleration overe this difficulty,cylinder force feedback was applied instead of acceleration feedback ?the lower loop in ..In this case,cylinder force is calculated from detected cylinder pressure and filtered in its lowerfrequency portion w 7, is called pressure feedback. control systemWhen 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 ,in the level crowding control,the boom is controlled to keep the arm end height Z ?calculated from u and u .to reference order to obtain more accurate control,thefollowing control actions are , Automation in Construction 10 (2001) 477–486 diagram of control system ?Z.. control Calculating Z from ,we obtain Differentiating both sides of Eq.?8. with respect to time,we have the following relation,The first term of the righthand side can be taken as the expression ?feedback portion. to convert Z˙ to u˙,and the second term of the righthand side is the expression ?feedforward portion. to calculate how much u should be changed when u is changed 1 2 manually.Actually,u˙ is determined using the difference 2 value of optimize he feedforward rate,feedforward gain K ffis tunned. There may be a method to detect and use the arm operatinglever condition ?. instead of arm angular velocity,since the arm is driven at an angular velocity nearly proportional to this lev