Offset-free control of constrained linear discrete-time systems subject to persistent unmeasured disturbances

This paper addresses the design of a dynamic, nonlinear, time-invariant, state feedback controller that guarantees constraint satisfaction and offset-free control in the presence of unmeasured, persistent, non-stationary, additive disturbances. First, this objective is obtained by designing a dynamic, linear, time-invariant, offset-free controller, and an appropriate domain of attraction for this linear controller is denned. Following this, the linear (unconstrained) control input is modified by adding a perturbation term that is computed by a robust receding horizon controller. It is shown that the domain of attraction of the receding horizon controller contains that of the linear controller, and an efficient implementation of the receding horizon controller is proposed.Published versio

Distributed Model Predictive Control

Distributed model predictive control refers to a class of predictive control architectures in which a number of local controllers manipulate a subset of inputs to control a subset of outputs (states) composing the overall system. Different levels of communication and (non)cooperation exist, although in general the most compelling properties can be established only for cooperative schemes, those in which all local controllers optimize local inputs to minimize the same plantwide objective function. Starting from state-feedback algorithms for constrained linear systems, extensions are discussed to cover output feedback, reference target tracking, and nonlinear systems. An outlook of future directions is finally presented

Handbook of model predictive control

Handbook of Model Predictive Control / by Saša V. Raković and William S. Levine (Editors) This handbook contains 27 chapters that are organized into three parts. Part 1 is on theory and comprises 12 chapters, ranging from basic MPC theory to advanced studies and model predictive control (MPC) formulations. Part 2, on computation, includes eight chapters and covers numerical implementation of MPC-related optimization algorithms. Part 3 discusses applications of MPC in numerous fields, such as automotive, power and energy systems, health care, and finance. The book is designed for a wide audience. It is an excellent reference for graduate students, researchers, and practitioners in the field of control systems and numerical optimization who want to understand the potential, challenges, and benefits of MPC and its applications. Alternately, it is an up-to-date reference for MPC research experts (both in academia and industry). For this audience, the book helps experts address new MPC-related problems and research directions. The book provides a thorough and comprehensive reference of the underlying theory, implementation, and applications of MPC. The content of the book, contributed by various experts in the field, is well written and suitably organized into three parts. Furthermore, this book does an excellent job meeting several competing goals: clarity of communication to a diversified audience, formal rigor, and a self-contained presentation of the topics in each chapter. This handbook enables the reader to gain a panoramic viewpoint of MPC theory and practice as well as provides a state-of-the art overview of new and exciting areas of application at the forefront of MPC research

An economic MPC formulation with offset-free asymptotic performance

This paper proposes a novel formulation of economic MPC for nonlinear discrete-time systems that is able to drive the closed-loop system to the (unknown) optimal equilibrium, despite the presence of plant/model mismatch. The proposed algorithm takes advantage of: (i) an augmented system model which includes integrating disturbance states as commonly used in offset-free tracking MPC; (ii) a modifier-adaptation strategy to correct the asymptotic equilibrium reached by the closed-loop system. It is shown that, whenever convergence occurs, the reached equilibrium is the true optimal one achievable by the plant. An example of a CSTR is used to show the superior performance with respect to conventional economic MPC and a previously proposed offset-free MPC still based on a tracking cost. The implementation of this offset-free economic MPC requires knowledge of plant input-output steady-state map gradient, which is generally not available. To this aim a simple linear identification procedure is explored numerically for the CSTR example, showing that convergence to a neighborhood of the optimal equilibrium is possible

State Space Realization of Model Predictive Controllers Without Active Constraints

To enable the use of traditional tools for analysis of multivariable controllers such as model predictive control (MPC), we develop a state space formulation for the resulting controller for MPC without constraints or assuming that the constraints are not active. Such a derivation was not found in the literature. The formulation includes a state estimator. The MPC algorithm used is a receding horizon controller with infinite horizon based on a state space process model. When no constraints are active, we obtain a state feedback controller, which is modified to achieve either output tracking, or a combination of input and output tracking. When the states are not available, they need to be estimated from the measurements. It is often recommended to achieve integral action in a MPC by estimating input disturbances and include their effect in the model. We show that to obtain offset free steady state the number of estimated disturbances must equal the number of measurements. The estimator is included in the controller equation, and we obtain a formulation of the overall controller with the set-points and measurements as inputs, and the manipulated variables as outputs. One application of the state space formulation is in combination with the process model to obtain a closed loop model. This can for example be used to check the steady-state solution and see whether integral action is obtained or not

Offset-free tracking MPC: A tutorial review and comparison of different formulations

Offset-free Model Predictive Control formulations refer to a class of algorithms that are able to achieve output tracking of reference signals despite the presence of plant/model mismatch or unmeasured nonzero mean disturbances. The general approach is to augment the nominal system with disturbances, i.e. to build a disturbance model, and to estimate the state and disturbance from output measurements. Some alternatives are available, which are based on a non augmented system with state disturbance observer, or on velocity form representations of the system to be controlled. In this paper, we review the disturbance model approach and two different approaches in a coherent framework. Then, differently from what is reported in the literature, we show that the two alternative formulations are indeed particular cases of the general disturbance model approach

Implementation of an economic MPC with robustly optimal steady-state behavior

Designing an economic model predictive control (EMPC) algorithm that asymptotically achieves the optimal performance in presence of plant-model mismatch is still an open problem. Starting from previous work, we elaborate an EMPC algorithm using the offset-free formulation from tracking MPC algorithms in combination with modifier-adaptation technique from the real-time optimization (RTO) field. The augmented state used for offset-free design is estimated using a Moving Horizon Estimator formulation, and we also propose a method to estimate the required plant steady-state gradients using a subspace identification algorithm. Then, we show how the proposed formulation behaves on a simple illustrative example