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

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

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

On the use of dynamic process simulators for the quantitative assessment of industrial accidents

The present work discusses the use of dynamic process simulators as supporting tools for the quantitative risk assessment of industrial facilities. In particular, a commercial process simulator was set up for the analysis of industrial accidents, obtaining on one side a detailed characterization of the source term in case of release events from process equipment or pipes. On the other, the possibility of implementing in the simulator control actions, interlocks, emergency shut-down, allowed monitoring the response of a given process unit, verifying the effectiveness and robustness of safety devices in emergency situations. The application to two case studies was used to demonstrate the potentialities of dynamic process simulators in the framework of industrial safety analyses. © Copyright 2014, AIDIC Servizi S.r.l

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

Reducing the computational effort of MPC with closed-loop optimal sequences of affine laws

We consider the classical infinite-horizon constrained linear-quadratic regulator (CLQR) problem and its receding-horizon variant used in model predictive control (MPC). If the terminal constraints are inactive for the current initial condition, the optimal input signal sequence that results for the open-loop CLQR problem is equal to the closed-loop optimal sequence that results for MPC. Consequently, the closed-loop optimal solution is available from solving only one CLQR problem instead of the usual infinite number of CLQR problems solved on the receding horizon. In the presence of disturbances or because of plant-model mismatch, the system will eventually leave the predicted optimal trajectory. Consequently, the solution of the single open-loop CLQR problem is no longer optimal, and the receding horizon problem must resume. We show, however, that the open-loop solution is also robust. Robustness essentially is given, because the solution of the CLQR problem not only provides the sequence of nominally optimal input signals, but a sequence of optimal affine laws along with their polytopes of validity. We analyze the degree of robustness by computational experiments. The results indicate the degree of robustness is practically relevant

Parsimonious cooperative distributed MPC algorithms for offset-free tracking

We propose in this paper novel cooperative distributed MPC algorithms for tracking of piecewise constant setpoints in linear discrete-time systems. The available literature for cooperative tracking requires that each local controller uses the centralized state dynamics while optimizing over its local input sequence. Furthermore, each local controller must consider a centralized target model. The proposed algorithms instead use a suitably augmented local system, which in general has lower dimension compared to the centralized system. The same parsimonious parameterization is exploited to define a target model in which only a subset of the overall steady-state input is the decision variable. Consequently the optimization problems to be solved by each local controller are made simpler. We also present a distributed offset-free MPC algorithm for tracking in the presence of modeling errors and disturbances, and we illustrate the main features and advantages of the proposed methods by means of a multiple evaporator process case study

Achieving a large domain of attraction with short-horizon linear MPC via polyhedral Lyapunov functions

Polyhedral control Lyapunov functions (PCLFs) are exploited in this paper to propose a linear model predictive control (MPC) formulation that guarantees a “large” domain of attraction (DoA) even for short horizon. In particular, the terminal region of the proposed finite-horizon MPC formulation is chosen as a level set of an appropriate PCLF. For small dimensional systems, this terminal region can be explicitly computed as an arbitrarily close approximation to the entire (infinite-horizon) stabilizable set. Global stability of the origin is guaranteed by using an “inflated” PCLF as terminal cost. The proposed MPC scheme can be formulated as a (small dimensional) quadratic programming problem by introducing one additional scalar variable. Numerical examples show the main benefits and achievements of the proposed formulation in terms of trade-off between volume of the DoA, computational time and closed-loop performance

Quantitative consequence assessment of industrial accidents supported by dynamic process simulators

In the present work, process simulators are adopted in the framework of consequence assessment support. A novel methodology is developed, with particular reference to consequence assessment specific for O&G offshore sector. A commercial, high-fidelity process simulator, Honeywell UniSim® Design R460, is applied for the analysis of accidental scenarios in order to perform a detailed evaluation of dynamic response of a given process unit and to support the consequence assessment of industrial accidents. A specific set-up of process simulator is developed to reproduce either source term, e.g. estimation of gas or liquid flow rate from process leaks, and physical effects dynamics. In particular, the physical effects evaluation through integral models of hydrocarbon fires is integrated in the dynamic process simulator, possibly accounting for the presence of safety barriers. Specific features of simulators are exploited to evaluate the consequences of possible failures in actuators and safety barriers. Some case studies of industrial interest are discussed to demonstrate the application of the methodology