Stabilizing and Robust Fractional PID Controller Synthesis for Uncertain First-Order plus Time-Delay Systems

In this paper, by using the noninteger P I λ D μ controllers, we conduct an investigation into the subject of robust stability area of time-delay interval process. Our method is based on setting up of the noninteger interval closed-loop characteristic equation using the inferior and superior bounds of uncertain parameters into several vertexes. We have combined the composition of the value set of vertex with the zero exclusion principle to analyse the stability of the uncertain process. A generalized version of the Hermite–Biehler theorem, applicable to fractional quasipolynomials, is exploited to determine the stability region of each vertex. The robust stability region of the noninteger regulator can be given by the crossing of the stability area of all the vertex characteristic noninteger quasipolynomials. By using the value set method and zero exclusion theory, the effectiveness of the stability region can be tested. Also, we propose a suitable procedure to determine the whole of stabilizing parameters for an interval process. An explicative example is given to point out the advantage and reliability of the approach.