In this chapter, we shall present some numerical techniques for designing proportional-integral-derivative algorithm control, which is considered to be the classical control algorithm in automatic systems engineering, and the polynomial R (regulation), S (sensitivity) and T (tracking) (RST) control using a more flexible digital approach with two degrees of freedom, which is easy to integrate in real-time industrial applications. We have also developed a predictive control structure whose horizon is finite and unitary. The methods based on pole placement, which are the foundation for the development of these types of control algorithms, are used in the design of closed-loop systems, which ensure a high level of performance in driving industrial processes.
3.1. Digital proportional-integral-derivative algorithm control
For the design of proportional-integral-derivative PID algorithms in control systems, the required performances in the closed-loop system must be specified and the dynamic model of the process must be known (control and disturbance model).
Starting with this remark, the goal is to determine the structure and the parameters of the control algorithm.
This takes us back to the classic diagram of the continuous PID regulator, with filtering on the derivative component, presented in the literature [LAN 93, BIT 93, POP 00, POP 01, DAF 04].
The discrete version of relation [3.1], which uses a sampling period h, expressed ...