A parameter tracking servo for adaptive control systems

This paper describes one very general approach to the design of adaptive control systems. The particular systems considered are process adaptive. The dynamic characteristics of the physical process are determined by the parameter tracking servo. The parameters thus determined are used to program the process' controller. The parameter tracking servo is a closed loop self-adjusting system. It consists of the following elements; 1) the physical process, 2) the learning model, 3) the adjusting mechanism. The learning model and the physical process are subjected to the same input signals. Their outputs are compared and the resultant error is fed to the adjusting mechanism where some function of this error is used to adjust the parameters of the learning model. The mechanism will continuously track the parameters of the physical process as they change with time in some unknown manner. The adjusting mechanism operates on an approximation to the method of steepest descent. These equations are derived for a first order process and the over-all systems is analyzed. The equations describing the tracking servo's operation are both non-linear and non-autonamous. System response as a function of input signal, gain, and error function are described analytically. Experimental results are included to demonstrate the validity of the analytic solutions.