Abstract
The paper presents a practical algorithm of the proportional-internal model control (P-IMC) type that can be applied to control a wide class of processes: Stable proportional processes, integral processes and some unstable processes. The P-IMC algorithm is a suitable combination between the P0-IMC algorithm and the P1-IMC algorithm, which are characterized by a too weak and a too strong impact of the tuning gain on the control action, respectively. The overall controller has five parameters: A tuning parameter K, three model parameters (steady-state gain, settling time, and time delay) and a process feedback gain used only for integral or unstable processes, to turn them into a compensated process (stable and of proportional type). For a step setpoint, the initial value of the compensated process input is approximately K times its final value. Furthermore, for K = 1 , the compensated process input is close to a step shape (step control principle). These properties enable a human operator to check and adjust online the model parameters. Due to its control performance, robustness to modeling error, and capability to be easily tuned and applied for all industrial processes, the P-IMC algorithm could be a viable alternative to the known PID algorithm. Numerical simulations are given to highlight the performance and the flexibility of the algorithm.
Highlights
In spite of all recent advances in control technology, the old proportional-integral-derivative (PID)algorithm is still by far the most widely used in practice due to its simplicity, feasibility, and capacity to control almost all plant types [1,2,3]
We have presented in 2017 and 2018 two unified control algorithms [20,21] of P0-IMC type and P1-IMC type, respectively, whose bloc-diagrams are illustrated in Figures 1 and 2, where GP (s) is the process transfer function, G M (s) is the transfer function of the compensated process model, K M is the model steady-state gain, K f is the process feedback gain, K is the tuning gain, Y is the Processes 2020, 8, 165; doi:10.3390/pr8020165
As mentioned in the previous section, the impact of the tuning gain K on the control action is too weak for the P0-IMC algorithm and too strong for the P1-IMC algorithm
Summary
In spite of all recent advances in control technology, the old proportional-integral-derivative (PID). Since the model of the compensated plant is stable and of proportional type, both algorithms are unified and quasi-universal, in the sense that they have a unique form (as the PID algorithm) and may be used to control almost all industrial plants: Stable plants of proportional type (with or without overshoot, time delay and oscillations, of minimum or non-minimum phase), integral plants, and unstable plants. Using MATLAB/SIMULINK environments, some numerical applications are given in Section 6 to show the control performance, the robustness with respect to parameter uncertainty, and how the algorithm can be implemented to control various types of process.
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