| This study was motivated by the cheap implementation and wide use of Proportional-Integral-Derivative (PID) controllers which, in part, is a consequence of the lack of control adequacy that often results from the implementation of high-order modern optimal controllers. In addition, the method of design of a PID controller can have a significant impact on its robustness and fragility.; In this study a method of robust design of PID controllers for an uncertain plant is developed in the context of Quantitative Feedback Theory (QFT) and balanced controller reduction using a suitable frequency interval as a weighting function. The basic idea is the efficient reduction of a higher order QFT controller to a PID structure that offers equivalent performance. This gives the designer the opportunity to evaluate the performance of both controllers and shows the “cost” of the reduction process on system performance. Implicit in the reduction process is an understanding of the achievable performance of a PID controller. This is accounted for by specifying the “critical” frequency interval over which the reduction process is emphasized.; The problem is first developed as a model reduction using a QFF controller of fixed order. Thereafter, performance indices used in model reduction are employed to obtain the critical frequency range. This forms the weight for the subsequent step which can be efficiently solved as an optimization problem.; The method developed is applicable in the presence of different types of performance specifications—bringing to bear the full power of QFT. Some existence conditions have been developed for a class of PID controllers which aid in the design and analysis.; The procedure is illustrated with two examples, namely a standard parametric plant and a flexible rotating beam, to demonstrate its effectiveness and practical usefulness. In addition, a procedure for reducing the high frequency magnitude of a PID controller is developed by reducing/optimizing its gain-bandwidth area—a procedure which reduces the ‘cost of feedback’. |
