Multi-model PID controller design: Polynomial chaos approach

The dynamic behavior of many systems can be approximated by a linear model at each operating point. Therefore, if the process works in several operating points, a set of linear models can be constructed to represent the system behavior. Those multi-models can be viewed as a system with random uncertain bounded parameters with definite influence over the behavior of the solution. Stability and performance of a system can be inferred from the evolution of statistical characteristic of system states with random parameters. The polynomial chaos of Wiener provides a framework for the statistical analysis of dynamical systems, with computational cost far superior to Monte Carlo simulations. Hence, in this work, we design robust integer and fractional order PID controller for multi-model systems by using Legendre Chaos.