Adaptive sliding mode control method for object of control including spring system

An adaptive sliding mode control method for controlling a control object, including a spring system, being driven by a servomotor, comprising the steps of:

• obtaining a phase plane Suf for use in sliding mode control in accordance with an equation:
• Suf=.epsilon.+Kp.multidot..epsilon.-K1.multidot..epsilon.t,
• where:
• .epsilon. is a position of deviation between a command position and a position of the servomotor;
• .epsilon. is a speed deviation;
• .epsilon.t is a difference between a position of the servomotor and a position of a moving part of the control object;
• Kp is a position loop gain;
• and
• K1 is a feedback gain of the difference between the position of the servomotor and the position of the moving part of the control object driven by said servomotor;
• and
• obtaining a torque command .tau. for the servomotor according to the following equation:
• .tau.=K2.multidot.Suf+Jhat(.theta.r-Kp.sup.2 .epsilon.+Kp.multidot.K1.multidot..epsilon.t-K1.multidot..epsilon.t)+Ahat. multidot..theta.+Grhat+.tau.1,
• where:
• Jhat, Ahat, and Grhat are estimated values of an inertia term, a coefficient of dynamic friction, and a gravity term, respectively;
• .theta.r and .theta.r are a position command speed and an acceleration, respectively;
• .epsilon.t is a differential of the difference between the position of the servomotor and the position of the moving part of the control object driven by the servomotor;
• and
• .tau.1is a switching input, said switching input being adjusted to a maximum value of a disturbance when the value of the phase plane Suf is not smaller than 0, and to a minimum value of the disturbance when the value of the phase plane Suf is smaller than 0.

A method for applying adaptive sliding mode control to a robot, including a spring system, being driven by a servomotor, comprising the steps of:

• (a) setting and entering, in a memory of a servo circuit coupled to the servomotor, selected constants required for sliding mode control processing and observer processing, and a maximum value Dis(max) and a minimum value Dis(min) of a foreseen disturbance;
• (b) starting the operation of the robot at an initial time, the robot operating for a time, said time being divided into periods, and reading a position command value .theta.r and a position feedback amount .theta. for every period of said periods of time;
• (c) calculating a motor speed .theta., a command speed .theta.r, a command acceleration .theta.r, a position deviation .epsilon. equivalent to a difference between the position command value .theta.r and the position feedback amount .theta., and a speed deviation .epsilon., based on the position command value .theta.r and the position feedback amount .theta.;
• (d) executing the observer processing in accordance with the motor speed .theta. obtained in step (b);
• (e) obtaining an estimated torsion .epsilon.tf and an estimated torsional speed .epsilon.tf between the servomotor and a distal end of the robot, and filter processing deviations based on a transfer function;
• (f) obtaining a filtered estimated torsion .epsilon.t and a filtered estimated torsional speed .epsilon.t;
• (g) obtaining a phase plane Suf having a value, in accordance with the position deviation .epsilon. and the speed deviation .epsilon. obtained in step (c) and the filtered estimated torsion .epsilon.t between the servomotor and the distal end of the robot obtained in step (f);
• (h) obtaining an estimated value Grhat of a gravity term in accordance with the phase plane Suf obtained in step (g);
• an estimated value Ahat of a coefficient of dynamic friction in accordance with the phase plane Suf and the motor speed .theta. obtained in step (b);
• and an estimated value Jhat of an inertia term in accordance with the phase plane Suf, the position deviation .epsilon. and the command acceleration .theta.r obtained in step (c), and the estimated torsion .epsilon.t and the estimated torsional speed .epsilon.t obtained in step (f);
• (i) determining whether the value of the phase plane Suf obtained in step (g) is smaller than 0 so that a switching input .tau.1 can be adjusted to the maximum value Dis(max) of the foreseen disturbance inputted in step (a) when the value is not smaller than 0, and so that the switching input .tau.1 can be adjusted to the minimum value Dis(min) of the foreseen disturbance inputted in step (a) when the value is smaller than 0;
• (j) obtaining a torque command .tau. for the servomotor in accordance with the motor speed .theta., position deviation .epsilon., and command acceleration .theta.r, obtained in steps (b) and (c), the filtered estimated torsion .epsilon.t and the filtered estimated torsional speed .epsilon.t between the motor and the distal end of the robot obtained in step (f), the phase plane Suf obtained in step (g), the estimated value Jhat of the inertia term, the estimated value Ahat of the coefficient of dynamic friction, and the estimated value Grhat of the gravity term which are obtained in step (h), and the switching input .tau.1 obtained in step (i);
• and
• (k) delivering the torque command, obtained in step (j), to a current loop of the servo circuit.