Concept Of Positive Invariance Research Articles

A constrained closed loop MPC based on positive invariance concept for a wastewater treatment plant

ABSTRACTThis paper presents a new methodology to design a closed loop model predictive control (CLMPC) using polyhedral invariant sets. This methodology gives a simple solution to this type of control, ensuring stability and respecting non-symmetrical constraints on control magnitudes, as well as moving in both modes of operation of the dual controller. The proposed algorithm takes advantage of the design of the state feedback control law in the CLMPC to increase the degrees of freedom, in contrast to other CLMPC approaches. In order to design the controller so that it respects constraints on both control magnitudes and its increments, necessary and sufficient conditions for asymptotic stability at the origin have been developed for linear systems. The controller is applied to an illustrative linear example and the activated sludge process in a wastewater treatment plant, showing the efficiency of the proposal.

Modelling, analysis and control of electroplating line modelled by P-time event graphs

In this paper, we propose a method to deal with performance evaluation and control of electroplating line modelled by P-time event graphs. The dater functions allow us to describe the dynamical behaviour of a given P-time event graphs in the standard algebra by means of implicit discrete system. From this formalism, different problems can be addressed. When we assume that the behaviour of the modelled system is 1-periodic, a linear programming problem can be derived from the discrete implicit system, to answer both, the minimum (maximum) cycle time and the optimal initial sojourn time of tokens. In a control context, we show how the discrete implicit system may be used to design a control law for a electroplating system using the concept of positive invariance.

Feedback Stabilization of Infinite-Dimensional Linear Systems with Constraints on Control and its Rate

The feedback stabilization problem in the presence of nonsymmetrical constraints on both control and its rate is addressed for a class of distributed parameter systems. Necessary and sufficient conditions are established, under which the constraints are satisfied for autonomous infinitedimensional systems. The approach is developed using the semigroup formulation and the positive invariance concept. The main result allows us to determine some suitable positively invariant sets of admissible initial states, in which the constraints are satisfied, with respect to the asymptotically stable closed-loop system.

Stabilization of a class of partially observed infinite-dimensional systems with control constraints

The stabilization by a finite-dimensional compensator for a class of infinite-dimensional linear systems with control inequality constraints is investigated. The main result shows that the corresponding state feedback results cannot be directly extended to the composite system including a full-state observer. However, we get conditions of asymptotic stability for a particular subclass of systems with control constraints by an appropriate use of the positive invariance concept.

On the Approximation of Maximal Output Admissible Set and Reachable Set via Forward Euler Discretization

The concept of positive invariance is involved with several problems in control theory, such as constrained control, disturbance rejection and robustness analysis. This paper considers the two types of positively invariant set, so called maximal output admissible set and reachable set, determined for linear continuous-time system. In this paper, the inner approximation of maximal output admissible set and the outer approximation of reachable set are established. The main purpose is to show that there exists the inclusion between the aforementioned positively invariant sets of linear continuous-time system and its forward Euler approximated discrete-time system. The inclusion also holds monotonically in the case of forward Euler approximated systems, discretized by different sampling periods. Finally, the volume of each approximated positively invariant set is recovered at any accuracy when sampling period is decreased.

TWO-COUPLED-TANKS LEVEL REGULATION WITH CONSTRAINTS ON THE CONTROL AND THE OUTPUT

This paper presents the application of the positive invariance concept to real-time control of a two-tanks system in the presence of hard constraints on the output and control signals. Results show that it is possible to regulate correctly the laboratory plant without violating the output and control constraints, when controlling the system with the output-feedback controller designed using the positive invariance concept.

Constrained State Regulation of Linear Continuous-time Singular Systems

In this paper, we consider a new approach dealing with the constrained state regulation problem for the continuous-time singular systems. The basic idea is to transform the original problem into a regular reduced order one that is much easier to solve. The application of the positive invariance concept leads to a suitable regulator that eliminates all impulsive modes and keeps the states of system in the polyhedron defined by the specified constraints while transferring them asymptotically to the equilibrium point.

On the dynamic improvement in linear constrained control discrete-time systems

In the control of linear systems with asymmetrical input constraints, larger domains of initial states can be obtained by allowing slow initial dynamics of the system in a closed loop, and making it faster during its evolution. The positive invariance concept application leads to piecewise linear constrained control laws using asymmetrical polyhedral sets.

On the dynamic improvement in linear constrained control discrete-time systems

In the control of linear systems with asymmetrical input constraints, larger domains of initial states can be obtained by allowing slow initial dynamics of the system in a closed loop, and making it faster during its evolution. The positive invariance concept application leads to piecewise linear constrained control laws using asymmetrical polyhedral sets.

Piecewise linear constrained control for continuous-time systems

In the control of linear systems with nonsymmetrical input constraints, larger domains of initialization can be obtained by allowing slow initial dynamics of the system in closed loop and making it faster during its evolution. The positive invariance concept application leads to a piecewise linear constrained control using nonsymmetrical nested polyhedral sets.

Constrained observer-based controller for linear continuous-time systems

Abstract The observer-based controller design in the presence of inequality constraints on the system input is considered. The solution is obtained by an adequate use of the positive invariance concept

The resolution of equation XA+XBX=HX and the pole assignment problem

This paper deals with the resolution of equation XA+XBX=HX, which plays a fundamental rule in the design of controllers of linear systems with constrained control by the use of the recently developed concept of positive invariance. It is also shown that this equation represents a partially pole assignment problem. Such resolution allows us to build a new method, called the inverse procedure, to design these controllers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Feedback control of linear discrete-time systems under state and control constraints

In this paper the problem of stabilizing linear discrete-time systems under state and control linear constraints is studied. Based on the concept of positive invariance, existence conditions of linear state feedback control laws respecting both the constraints are established. These conditions are then translated into an algorithm of linear programming.