Optimum transfer functions for feedback control systems with plant input saturation

A method for the determination of optimum transfer functions for systems controlling plant with input saturation is presented. The procedure is demonstrated on a specific plant well studied in the literature, and the general conclusions verified by simulator and digital computer results. It is established that the desired system bandwidth should be obtained with a dominant system transfer function of low ¿| system poles| /¿ |system zeros|. The order of the dominant system transfer function is usually physically obvious from the asymptotic Bode plot, and as in modern control theory, the Butterworth array is found to be particularly useful. Provided the right order of transfer function is chosen, the actual pole-zero geometry is not critical. Such a design is optimal with regard to small transient excursions into the non-linear mode, and with regard to the minimization of noise effects on the plant input level, yet simultaneously meets the customary deterministic performance criteria. In the comparison of series compensation designs, it is shown experimentally that some marginal reduction of sensitivity is achieved by reducing the order of the dominant transfer function, but this reduction is easily offset by the use of feedback compensation. Far-off poles added to filter high frequency noise are found to have little effect on the choice of optimum transfer function. Velocity constant requirements are met by the addition of integrating dipoles. A useful theorem providing a quantitative measure of the deterioration in non-linear performance caused by the choice of excessive bandwidth is presented and is shown to result in a power law. By expressing the conclusions as s plane constraints for the dominant poles and zeros, the results can be easily incorporated in any standard design procedure, manual or automated, and should lead to considerable reduction in the time required to obtain a satisfactory design.