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Discrete-time simplified adaptive control algorithm and its application to a motor control

Simplified adaptive control (SAC) is originally proposed for the class of plant which satisfies an almost strictly positive real (ASPR) condition. There have been two main methods to circumvent this condition. One is to add parallel feedforward compensation to an original plant resulting in a new augmented plant which satisfies the ASPR condition. The other is to contrive the signal in parameter adjustment law which is a linear combination of output error and control law. One of the authors has proposed a discrete-time algorithm which belongs to the former. In this paper, a new discrete-time algorithm is proposed which belongs to the latter. This algorithm can reduce the output error between plant and model to be bounded and moreover to zero if the steady state gain of the plant is kept constant under parameter variation. The stability of the algorithm is proved by using a Lyapunov function. This algorithm is applied to the position control of a DC servomotor. Experimental results illustrate satisfactory performance even if its load is largely changed.