Automatic synthesis of both the topology and parameters for a robust controller for a nonminimal phase plant and a three-lag plant by means of genetic programming

This paper describes how genetic programming can be used to automate the synthesis of the design of both the topology and parameter values for controllers. The method described in this paper automatically makes decisions concerning the total number of processing blocks to be employed in the controller, the type of each block, the topological interconnections between the blocks, the values of all parameters for the blocks, and the existence, if any, of internal feedback between the blocks of the overall controller. This design process can readily combine optimization of performance (e.g., by a metric such as the integral of the time-weighted error) with time-domain constraints and frequency-domain constraints. Genetic programming is applied to two illustrative problems of controller synthesis: the design of a robust controller for a nonminimal-phase plant and the design of a robust controller for a three-lag plant. The PID compensator of Astrom and Hagglund (1995) for the three-lag plant delivers credible performance. The automatically created controller is better than 7.2 times as effective as the previous controller as measured by the integral of the time-weighted absolute error, has only 50% of the rise time in response to the reference input, has only 35% of the settling time, and is 92.7 dB better in terms of suppressing the effects of disturbance at the plant input.