Optimal PID controller design using multiobjective Normal Boundary Intersection technique

Parametric optimization techniques is an established practice for designing controllers. It was used, for example, to obtain the parameters of PI and PID controllers in several works. An important criticism to this technique is the dependence of the design from a parametric model of the plant, which have to be very accurate. In the current work, the problem of designing a continuous-time PID controller based on parametric optimization under parameter uncertainty is treated by using multi-objective optimization. The parameter uncertainty is given in the form of interval polynomials, where a nominal model is not necessary for the design. The optimization process is carried out by means of the normal boundary intersection technique (NBI) method, which yields a regular Pareto front with an acceptable computational burden. A simulation example shows satisfactory results obtained by the proposed method.