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Multivariable PID controller design via approximation of the attainable performance

The tuning of multivariable PID controllers for industrial applications is still a challenging task. In this paper, we describe a method to compute multivariable PID controllers based on the idea of the approximation of the optimal attainable closed-loop performance computed by convex optimization. The key idea is to use the Youla parameterization of all closed-loop systems, which is affine in a free transfer matrix, and to optimize the free parameter for linear constraints (such as maximal values of inputs and outputs for certain test signals) and quadratic performance criteria (e.g. the integral mean-squared regulation error). The advantage of this method is that the trade-off between a simple controller structure and the best attainable performance is no longer left to an intuitive decision. The approximated controller can be compared directly to the attainable performance and therefore evaluated by an objective criterion. On the other hand, the structure of the controller and the orders of its elements can be chosen freely and experimented with by the designer. The efficiency of the method is demonstrated for the example of a fluidized catalytic cracker.