A Generalized PI Sliding Mode and PWM Control of Switched Fractional Systems

The control of a special class of Single Input Single Output (SISO) switched fractional order systems (SFOS) is addressed from the viewpoints of the Generalized Proportional Integral (GPI) feedback control approach and a sliding mode based Σ − Δ modulation implementation of an average model based designed feedback controller. Alternatively, a Pulse Width Modulation (PWM) duty ratio synthesis approach is also developed for the approximate discontinuous control of the same class of systems. A fractional order GPI controller is proposed which transforms the average model of the system into a pure, integer order, chain of integrations with desired closed loop dynamics achieved through a classical compensation network robustly acting in the presence of constant load perturbations. A sliding mode based Σ − Δ modulation and a PWM based Σ − Δ modulation implementation of the continuous, bounded, dynamic average output feedback control signal is adopted for the switched system. An illustrative simulation example dealing with an electric radiator system is presented.