Abstract
In a PWM (pulse width modulated) control system with an actuator, the control performance expressed in terms of indices such as accuracy and settleing time often declines when the involved static frictional force is larger than the dynamic frictional force. To prevent this decline an effective control method has been proposed to provide a set of plus and minus pulses switching their polarity over at each initiation of actuator movement. In any set of pulses, the width of the first pulse is restricted by the condition that the pulse polarity must be switched over at the moment the actuator begins to move. The width of the second pulse, however, can be suitably selected to minimize the criterion function of the system. This paper deals with the computational analysis of the minimization of the function. In the first places, the width of each second pulse is slightly deviated from a given nominal valve. And resultant deviations of the state variables are computed. In the computation, the problem of discontinuity arises in the static-to-dynamic transient stage of the actuator motion. Yet, a simple approximation method has been devised to deal with the discontinuity. The deviation of the criterion function corresponding to that of each pulse width can be determined from the results of the state variable deviations over the range to the final time. The ratio of the two deviations is used as the gradient for computation. The width of the each second pulse is slightly modulated in proportion to the gradient. The modulated pulse is regarded as a new nominal pulse. Such a modulation is repeated until the optimal control pulse sequence is attained.
