Adaptive PI control method

An adaptive proportional-plus-integral control method for a motor control system including a proportional-plus-integral loop as a speed loop, comprising the steps of:

• determining a torque command .tau. to be supplied to a motor in accordance with the following equation on the basis of an equation of motion
• .tau.=K2.multidot.Suf+J*.multidot.r'+A*.multidot.y+Gr*.multidot.sin .theta.+Fr*+Cf*+.tau.1 and;
• obtaining terms of K2.multidot.Suf and Fr* of the above equation as proportional and integral terms of an ordinary proportional-plus-integral control,
• wherein K2 represents a proportional constant, Suf represents a speed deviation obtained by subtracting an actual motor speed from a speed command, r' represents a differential of the speed command with respect to time which is a command acceleration, J*, A*, Gr*, Fr*, and Cf* represent estimated values of inertia, coefficient of dynamic friction, coefficient of gravitational disturbance, constant gravitational disturbance, and Coulomb's friction, respectively, and .theta. represents a rotational angle of a robot arm which will give the greatest effect on the gravitational disturbance, and wherein
• the estimated value J* of the inertia is obtained by integrating the value obtained by multiplying the speed deviation Suf by the command acceleration r' and a reciprocal (1/.alpha.) of an adjusting parameter .alpha. determining an adaptive speed with respect to time,
• the estimated value A* of the coefficient of dynamic friction is obtained by integrating the value obtained by multiplying the speed deviation Suf by the actual motor speed y and a reciprocal (1/.beta.) of an adjusting parameter .beta. with respect to time,
• the estimated value Gr* of the coefficient of gravitational disturbance is obtained by integrating the value obtained by multiplying the speed deviation Suf by sin .theta. corresponding to a rotational angle .theta. of said arm and a reciprocal (1/.gamma.) of an adjusting parameter .gamma. with respect to time,
• the estimated value Fr* of the constant gravitational disturbance is obtained by integrating the value obtained by multiplying the speed deviation Suf by a reciprocal (1/.delta.) of an adjusting parameter .delta. with respect to time,
• the estimated value Cf* of the Coulomb's friction is obtained by integrating the value obtained by multiplying the speed deviation Suf by a reciprocal (1/.epsilon.) of an adjusting parameter .epsilon. with respect to time, and
• the switching input .tau.1 is determined to be a maximum value of gravitational disturbances given by rotational angles of arms other than said robot arm which will give the greatest effect on said gravitational disturbance when said speed deviation Suf is zero or positive, and is determined to be a minimum value of the gravitational disturbances when said speed deviation Suf is negative.