Antonio Ferramosca

Input-to-State Stability: A Unifying Framework for Robust Model Predictive Control

This paper deals with the robustness of Model Predictive Controllers for constrained uncertain nonlinear systems. The uncertainty is assumed to be modeled by a state and input dependent signal and a disturbance signal. The framework used for the analysis of the robust stability of the systems controlled by MPC is the wellknown Input-to-State Stability. It is shown how this notion is suitable in spite of the presence of constraints on the system and of the possible discontinuity of the control law.

Technical communique: MPC for tracking with optimal closed-loop performance

In the recent paper [Limon, D., Alvarado, I., Alamo, T., & Camacho, E.F. (2008). MPC for tracking of piece-wise constant references for constrained linear systems. Automatica, 44, 2382-2387], a novel predictive control technique for tracking changing target operating points has been proposed. Asymptotic stability of any admissible equilibrium point is achieved by adding an artificial steady state and input as decision variables, specializing the terminal conditions and adding an offset cost function to the functional. In this paper, the closed-loop performance of this controller is studied and it is demonstrated that the offset cost function plays an important role in the performance of the model predictive control (MPC) for tracking. Firstly, the controller formulation has been enhanced by considering a convex, positive definite and subdifferential function as the offset cost function. Then it is demonstrated that this formulation ensures convergence to an equilibrium point which minimizes the offset cost function. Thus, in case of target operation points which are not reachable steady states or inputs for the constrained system, the proposed control law steers the system to an admissible steady state (different to the target) which is optimal with relation to the offset cost function. Therefore, the offset cost function plays the role of a steady-state target optimizer which is built into the controller. On the other hand, optimal performance of the MPC for tracking is studied and it is demonstrated that under some conditions on both the offset and the terminal cost functions optimal closed-loop performance is locally achieved.

Economic MPC for a changing economic criterion

In the process industries it is often desirable that model predictive controllers (MPC) use a stage cost function that incorporates some types of economic criteria. In [1] it is proved that this kind of controller provides better economic performance than the standard setpoint-tracking MPC formulations. In [2] a Lyapunov function is provided for the economic MPC formulation. In [3], [4] an MPC for setpoint tracking is presented that ensures feasibility for a changing setpoint, enlarging the domain of attraction of the controller. In this paper, a new MPC controller is proposed, which is a hybrid of these two previous controllers, and inherits their best properties. Three examples are presented that demonstrate the advantages of the new formulation.

MPC for tracking with optimal closed-loop performance

In this paper, a novel model predictive control (MPC) formulation has been proposed to solve tracking problems, considering a generalized offset cost function. Sufficient conditions on this function are given to ensure the local optimality property. This novel formulation allows to consider as target operation points, states which may be not equilibrium points of the linear systems. In this case, it is proved in this paper that the proposed control law steers the system to an admissible steady state (different to the target) which is optimal with relation to the offset cost function. Therefore, the proposed controller for tracking achieves an optimal closed-loop performance during the transient as well as an optimal steady state in case of not admissible target. These properties are illustrated in an example.

Economic MPC for a Changing Economic Criterion for Linear Systems

Economic Model Predictive Controllers, consisting of an economic criterion as stage cost for the dynamic regulation problem, have shown to improve the economic performance of the controlled plant, as well as to ensure stability of the economic setpoint. However, throughout the operation of the plant, economic criteria are usually subject to frequent changes, due to variations of prices, costs, production demand, market fluctuations, reconciled data, disturbances, etc. A different economic criterion determines a change of the optimal operation point and this may cause a loss of feasibility and/or stability. In this paper a stabilizing economic MPC for changing economic criterion for linear prediction models is presented. The proposed controller always ensures feasibility for any given economic criterion, thanks to the particular choice of the terminal ingredients. Asymptotic stability is also proved, providing a Lyapunov function.

Optimal MPC for tracking of constrained linear systems

Model predictive control (MPC) is one of the few techniques which is able to handle constraints on both state and input of the plant. The admissible evolution and asymptotic convergence of the closed-loop system is ensured by means of suitable choice of the terminal cost and terminal constraint. However, most of the existing results on MPC are designed for a regulation problem. If the desired steady-state changes, the MPC controller must be redesigned to guarantee the feasibility of the optimisation problem, the admissible evolution as well as the asymptotic stability. Recently, a novel MPC has been proposed to ensure the feasibility of the optimisation problem, constraints satisfaction and asymptotic evolution of the system to any admissible target steady-state. A drawback of this controller is the loss of a desirable property of the MPC controllers: the local optimality property. In this article, a novel formulation of the MPC for tracking is proposed aimed to recover the optimality property maintaining all the properties of the original formulation.

MPC for tracking of constrained nonlinear systems

This paper deals with the tracking problem for constrained nonlinear systems using a model predictive control (MPC) law. MPC provides a control law suitable for regulating constrained linear and nonlinear systems to a given target steady state. However, when the target operating point changes, the feasibility of the controller may be lost and the controller fails to track the reference. In this paper, a novel MPC for tracking changing constant references is presented. The main characteristics of this controller are: (i) considering an artificial steady state as a decision variable, (ii) minimizing a cost that penalizes the error with the artificial steady state, (iii) adding to the cost function an additional term that penalizes the deviation between the artificial steady state and the target steady state (the so-called offset cost function) and (iv) considering an invariant set for tracking as extended terminal constraint. The calculation of the stabilizing parameters of the proposed controller is studied and some methods are proposed. The properties of this controller has been tested on a constrained CSTR simulation model.

A gradient-based strategy for integrating Real Time Optimizer (RTO) with Model Predictive Control (MPC)

Abstract In the process industries it is often desirable that advanced controllers, such as model predictive controllers (MPC), control the plant ensuring stability and constraints satisfaction, while an economic criterion is minimized. Usually the economic objective is optimized by an upper level Real Time Optimizer (RTO) that passes steady state targets to a lower dynamic control level. The drawback of this structure is that the RTO employs complex stationary nonlinear models to perform the optimization and has a sampling time larger than the controller one. As a consequence, the economic setpoints calculated by the RTO may be inconsistent for the dynamic layer. In this paper an MPC that explicitly integrates the RTO structure into the dynamic control layer is presented. To overcome the complexity of this one-layer formulation a first order approximation of the RTO cost function is proposed, which provides a low-computational-cost suboptimal solution. It is shown that the proposed strategy ensures convergence and recursive feasibility under any change of the economic function. The strategy is tested in a simulation on a subsystem of a fluid catalytic cracking (FCC) unit.

Model Predictive Control for Changing Economic Targets

Abstract The objective of this paper is to present recent results on model predictive control for tracking in the context of economic operation of a industrial plants. The well-established hierarchical economic control is based on a Real Time Optimizer that calculates the economic target to the advanced controller, in this case model predictive controllers. The change of the economic parameters or constraints, or the existence of disturbances and modelling errors make that this target may change throughout the plant evolution. The MPC for tracking is an appealing formulation to deal with this issue since maintain the recursive feasibility and convergence under any change of the target. Thus, this MPC formulation is summarized as well as its properties. In virtue of these properties, it is demonstrated how the economic operation can be improved by integrating the Steady State Target Optimizer in the MPC. Then it is also shown how the proposed MPC can deal with practical problems such us zone control or distributed control. Finally, the economic control of the plant can be enhanced by adopting an economic MPC approach. A formulation capable to ensure economic optimality and target tracking is also shown.

Robust tubed-based MPC for tracking applied to the quadruple-tank process

This paper presents the application of a robust tube-based MPC for tracking of piece-wise constant references to a plant based on the quadruple-tank process . This controller, defined for LTI system subject to additive and bounded disturbances, ensures: (i) the feasibility for any admissible setpoint, (ii) the robust constraint satisfaction, (iii) robust stability and convergence to (a neighborhood of) the desired steady state.