On a Model Based Practical Control Algorithm 

Abstract

Abstract:The design of the proposed algorithm relies on three basic ideas: (1) finding a model-based controller so that for any stable process of proportional type, the closed-loop controller output to a step reference has a step shape (or close to this form) and removes the steady-state error; (2) refining the controller structure so that the initial value of the controller output to a step reference is K times its final value, where K is a tuning parameter with standard value 1; (3) extending the controller structure to address integral processes and some unstable processes by turning them into stable compensated processes of proportional type. The overall controller is a series connection P-IMC of two systems: one of pure proportional type and another one of IMC type. There is a simple procedure to verify online if the model parameters (steady-state gain, time delay and transient time) have suitable values and to adjust them to improve the model. As the PID control algorithm, the proposed method is quasi-universal and practical, but it is superior by its control performance and the simplicity of the tuning procedure (which enables poorly trained workers to easily operate the control system). Also, it is more practical than the classical IMC algorithm because its equations have a unique form for all process types (as the PID algorithm), and has a control gain as tuning parameter instead of a filter time constant. Several applications are given to show the effectiveness of the algorithm for different types of process.

A Practical Unified Algorithm of P-IMC Type

“…For practical reasons, we will consider that the parameters of the compensated plant model are K M , τ M , and T s . As shown in [20] for α = 0 and in [21] for α = 1, if the tuning gain K is suitably selected, then an estimation of the model parameters with an error less than 15% does not significantly diminish the control performance. We claim that this robustness property is also satisfied for 0 < α < 1.…”

“…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 G P (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 controlled variable, R is the setpoint (reference), E is the error (offset), U is the control variable, V is the disturbance, and C is the internal control variable. The direct feedback path of the process, characterized by the gain K f , is used only for integral and some unstable processes, in order to convert the original process P into a stable proportional process P0 (with the gain K P 0 bounded and nonzero), called compensated process.…”

“…The P0-IMC algorithm can lead to such undesirable situations when the parameters of the compensated plant are inaccurately selected (K M >> K P 0 or τ M >> τ P 0 or T s >> T sP 0 ) and the tuning gain K has a weak influence on the control action [20]. On the contrary, such situations are not possible by using the P1-IMC algorithm, characterized by a strong influence of K on the control action [21]. By using the new proposed algorithm, the best control performance is usually obtained for 1 < K < 5, and the response c(t) to a step reference is smoother than the response of the first algorithm and sharper than the one of the second algorithm.…”

On a Practical Algorithm of P-IMC Type

“…The proportional-internal model control (P-IMC) is a simple and practical control algorithm, which is easily accessible to a controller user and achieves a robust and efficient control (Cirtoaje, 2017;Cirtoaje & Baiesu, 2018;Cirtoaje, 2020). The IMC concept is based on the idea that a robust and accurate control can be obtained by inserting a suitable process model in the controller structure (Francis & Wonham, 1976;Garcia & Morari, 1982;Morari & Zafiriou, 1989).…”