Algorithm of robust stability region for interval plant with time delay using fractional order PID controller

By using PI^λD^μ controller, we investigate the problem of computing the robust stability region for interval plant with time delay. The fractional order interval quasi-polynomial is decomposed into several vertex characteristic quasi-polynomials by the lower and upper bounds, in which the value set of the characteristic quasi-polynomial for vertex quasi-polynomials in the complex plane is a polygon. The D-decomposition technique is used to characterize the stability boundaries of each vertex characteristic quasi-polynomial in the space of controller parameters. We investigate how the fractional integrator order λ and the derivative order μ in the range (0, 2) affect the stabilizability of each vertex characteristic quasi-polynomial. The stability region of interval characteristic quasi-polynomial is determined by intersecting the stability region of each quasi-polynomial. The parameters of PI^λD^μ controller are obtained by selecting the control parameters from the stability region. Using the value set together with zero exclusion principle, the robust stability is tested and the algorithm of robust stability region is also proposed. The algorithm proposed here is useful in analyzing and designing the robust PI^λD^μ controller for interval plant. An example is given to show how the presented algorithm can be used to compute all the parameters of a PI^λD^μ controller which stabilize a interval plant family.