Robust Predictive Control of Water Level in an Experimental Pilot Plant with Uncertain Input Delay

Abstract

This paper is concerned with the predictive control of water level in an experimental pilot plant, in the presence of input constraints and uncertain time delays. Robustness is achieved by casting the delay uncertainty into a polytopic form and using a predictive control formulation based on linear matrix inequalities. Integral action is introduced into the controller to ensure offset-free tracking of step changes in the setpoint. Moreover, an integrator resetting procedure based on the concept of regions of guaranteed cost is proposed to improve the resulting transient response. The results show that the introduction of robustness into the predictive control formulation is indeed of value to avoid closed-loop instability in the presence of time delays. In addition, the integrator resetting procedure was found to provide substantial performance improvements in terms of overshoot and settling time.

Direct discrete time design of robust state derivative feedback control laws

“…which can be recast into the form of a polytopic model, with vertices associated to the possible values of d (Huang & Wang, 2009;Rossi & Galvão, 2014). The case of different delays for each input variable can be treated in a similar manner, with vertices associated to the possible delay combinations.…”

Intelligent Mechatronics in the Measurement, Identification, and Control of Water Level Systems: A Review and Experiment

“…As a subsequent example, the toolbox for solving LMIs-linear matrix inequalities, can be employed in order to deal with many problems of semidefinite programming. The authors of [22] implemented it to satisfy the robustness of a model-predictive control, called the MPC method. The most important challenge usually lies in the uncertainty of the model.…”

“…A single-tank dynamical system (eventually, equipped with a reservoir-a basin of water), which is investigated in [39,60,61] (state-space approach, PI, PID), [22,37] (state-space representation in a discrete form), [2,7,19,26,62,63] (transfer function approach), [3,5,6,26,[62][63][64][65] (FL, PSO), [22,37] (predictive control), [18,20,27] (geometryvarying tank: conical and spherical) and others [34,46]; 2.…”

“…For example, such a single-tank model of the h-dependent area is studied in [20] using Equation (2). Some papers, e.g., [22,37] address a model description in the discrete state-space, where the state is represented by the height of the water level. Such an approach is not so frequently practiced, since it may be very much desired in the real process of data acquisition.…”

“…In the work [22], a three-phase induction machine drives a pump that transfers water from the reservoir to the process tank, analogous to Figure 1a. The liquid leaves the tank through a bottom valve.…”