Internal model control design for input‐constrained multivariable processes

Abstract

Multivariable plants under input constraints such as actuator saturation are liable to performance deterioration due to control windup and directionality change. A twostage internal model control (IMC) antiwindup design for open loop stable plants is presented. The design is based on the solution of two low-order quadratic programs at each time step, which addresses both transient and steady-state behaviors of the system. For analyzing the robust stability of such systems against any infinity-norm bounded uncertainty, stability test have also been developed. In particular, we note that the controller input-output mappings satisfy certain integral quadratic constraints. Simulated examples show that the two-stage IMC has superior performance when compared with other existing optimization-based antiwindup methods. The stability test is illustrated for a plant with left matrix fraction uncertainty. A scenario where the proposed two-stage IMC competes favorably with a long prediction horizon model predictive control is described.

Two-stage multivariable IMC Antiwindup (TMIA) control of a Quadruple Tank process using a PLC

“…A novel TMIA control structure proposed in [15] directly addresses the problems of windup and directionality change which affect multivariable plants under input constraints such as actuator saturation. Two low-order Quadratic Programs (QPs) are solved at each sample step: the dynamic QP (QP 1 ) shown in Figure 2 addresses transient behaviour of the plant ensuring that the constrained system response is as close as possible to the unconstrained, while the steady-state QP (QP 2 ) ensures optimal steady-state performance.…”

“…There is current research into fast online MPC implementation [10]- [13] on platforms such as Programmable Logic Controllers (PLCs) and Programmable Automation Controllers (PACs) [14]. A novel IMC-based online optimizing anti-windup control structure that simultaneously handles the issues of windup and directionality is proposed in [15]. This Two-stage Multivariable IMC Antiwindup (TMIA) control structure does not require the receding horizon computation of MPC and may serve as an alternative to MPC which is computationally less expensive and more transparent in terms of tuning and robustness.…”

“…This is particularly attractive because it can be implemented on a cheap digital industrial platform as we demonstrate in this paper. Simulation results presented in [15] show that the TMIA controller competes favourably with long horizon MPC (where the number of optimization variables and constraints is a multiple of the prediction horizon [8]) while only requiring the computation capacity of a single horizon MPC.…”

Alternative approach to anti-windup synthesis for double integrator systems

“…Notice that because the saturation element destroys the decoupling of the system, hence the system may exhibit traditional windup effects as well as directionality issues [27]. The nonlinearity Figure 5 is not a pure saturation function as in equations (19)- (20) but instead has the form However, it transpires, via analysis similar to that given in [13], that stability of the above system can be guaranteed by implementing an AW compensator of the form…”

Robust Linear Output Regulation Using Extended State Observer

“…The principle is also instrumental in addressing the problem of robust output regulation. On this basis, robust design methods have been proposed in the literature for linear systems with uncertain parameters [3][4][5][6]. These methods consider the effect of external disturbances by an exogenous signal which belongs to the solution space of a particular differential equation.…”