Chapters authored
Variable, Fractional-Order PID Controller Synthesis Novelty Method
The novelty method of the discrete variable, fractional order PID controller is proposed. The PID controllers are known for years. Many tuning continuous time PID controller methods are invented. Due to different performance criteria there are optimized three parameters: proportional, integral and differentiation gains. In the fractional order PID controllers there are two additional parameters: fractional order integration and differentiation. In the variable, fractional order PID controller fractional orders are generalized to functions. Nowadays all PID controllers are realized by microcontrollers in a discrete time version. Hence, the order functions are discrete variable bounded ones. Such controllers offer better transient characteristics of the closed loop systems. The choice of the order functions is still the open problem. In this Section a novelty intuitive idea is proposed. As the order functions one applies two spline functions with bounded functions defined for every time subinterval. The main idea is that in the final time interval the variable, fractional order PID controller transforms itself to the classical one preserving the stability conditions and zero steady-state error signal. This means that in the last time interval the discrete integration order is −1 and differentiation is 1.
Part of the book: Control Based on PID Framework