1,720,970 research outputs found
Disturbance Models for Offset-free Model Predictive Control
No full textModel predictive control algorithms achieve offset-free control objectives by adding integrating disturbances to the process model. The purpose of these additional disturbances is to lump the plant-model mismatch and/or unmodeled disturbances. Its effectiveness has been proven for particular square cases only. For systems with a number of measured variables (p) greater than the number of manipulated variables (m), it is clear that any controller can track without offset at most m controlled variables. One may think that m integrating disturbances are sufficient to guarantee offset-free control in the m controlled variables. We show this idea is incorrect and present general conditions that allow zero steady-state offset. In particular, a number of integrating disturbances equal to the number of measured variables are shown to be sufficient to guarantee zero offset in the controlled variables. These results apply to square and nonsquare, open-loop stable, integrating and unstable systems
Cooperative, distributed model predictive control for managing resource coupled constraints
No full textA discussion on cooperative model predictive control, a method for coordinating multiple optimization-based controllers, covers the technical description; coupled constraints; two methods that ensure the inputs are plant-wide feasible, i.e., input augmentation and constraint management; and an example showing the performance of the two methods
On the convergence of numerical solutions to the continuous-time constrained LQR problem
No full textA numerical procedure for computing the solution to the continuous-time infinite-horizon constrained linear quadratic regulator was presented in [1], which is based successive strictly convex QP problems where the decision variables are the control input value and slope at selected grid points. Each QP generates an upper bund to the optimal cost, and the accuracy is increased by using gradually refined grids computed offline to avoid any online integration. In this work we propose an adaptive method to gradually refine the grid where it is most needed, still without having to perform integration online, and we address the convergence properties of such algorithm as the number of grid points is increased. By means of suitable optimality functions, each iteration given the current upper bound cost, we compute: (i) a lower bound approximation of the optimal cost which can be used to stop the algorithm within a guaranteed tolerance; (ii) for each grid interval, an estimate of the cost reduction that can obtained by bisecting it
A Candidate to Replace PID Control: SISO Constrained LQ control
No full textIt is commonly believed that for single-input/single-output (SISO) systems, well-tuned proportional, integral, derivative (PID) controllers work as well as model-based controllers and that PID controllers are more robust to model errors. In this paper we present a novel offset-free constrained linear quadratic (LQ) controller for SISO systems, which is implemented in an efficient way so that the total controller execution time is similar to that of a PID. The proposed controller has three modules: a state and disturbance estimator, a target calculation, and a constrained dynamic optimization. It is shown that the proposed controller outperforms PID both in setpoint changes and disturbance rejection, it is robust to model errors, it is insensitive to measurement noise, and it handles constraints better than common anti-windup PID. Tuning the proposed controller is simple. In principle there are three tuning parameters to choose, but in all examples presented only one was actually varied, obtaining a clear and intuitive effect on the closed-loop performance. © 2005 American Institute of Chemical Engineers
Fast, Large-scale Model Predictive Control by Partial Enumeration
No full textPartial enumeration (PE) is presented as a method for treating large, linear model predictive control applications that are out of reach with available MPC methods. PE uses both a table storage method and online optimization to achieve this goal. Versions of PE are shown to be closed-loop stable. PE is applied to an industrial example with more than 250 states, 32 inputs, and a 25-sample control horizon. The performance is less than 0.01% suboptimal, with average speedup factors in the range of 80-220, and worst-case speedups in the range of 4.9-39.2, compared to an existing MPC method. Small tables with only 25-200 entries were used to obtain this performance, while full enumeration is intractable for this example. © 2007 Elsevier Ltd. All rights reserved
On Computing Solutions to the Continuous Time Constrained Linear Quadratic Regulator
No full textWe propose in this note a method for computing the solution to the infinite horizon continuous-time constrained linear quadratic regulator. The method is based on two main ingredients: A multigrid method for placing a finite number of time intervals, and a piece-wise linear parameterization of the input within the intervals. The input values at the decision-time points and slopes within the time intervals are computed via quadratic programs (QPs). The grids are gradually refined to efficiently improve the accuracy of the solution, and the required matrices and vectors for all QPs are computed offline and stored to improve the online efficiency. Two examples are presented to show the main characteristics of the proposed method. © 2010 IEEE
Cooperative Distributed Model Predictive Control
No full textIn this paper we propose a cooperative distributed linear model predictive control strategy applicable to any finite number of subsystems satisfying a stabilizability condition. The control strategy has the following features: hard input constraints are satisfied; terminating the iteration of the distributed controllers prior to convergence retains closed-loop stability; in the limit of iterating to convergence, the control feedback is plantwide Pareto optimal and equivalent to the centralized control solution; no coordination layer is employed. We provide guidance in how to partition the subsystems within the plant. We first establish exponential stability of suboptimal model predictive control and show that the proposed cooperative control strategy is in this class. We also establish that under perturbation from a stable state estimator, the origin remains exponentially stable. For plants with sparsely coupled input constraints, we provide an extension in which the decision variable space of each suboptimization is augmented to achieve Pareto optimality. We conclude with a simple example showing the performance advantage of cooperative control compared to noncooperative and decentralized control strategies. © 2010 Elsevier B.V. All rights reserved
Efficient Cooperative Distributed MPC using Partial Enumeration
No full textWe discuss in this paper a novel and efficient implementation of distributed Model Predictive Control (MPC) systems for large-scale systems. The method is based on Partial Enumeration (PE), an approach that allows to compute the (sub)optimal solution of the Quadratic Program associated to the MPC problem by using a solution table that stores only a few most recently optimal active sets. This method is applied to the each local MPC system with significant improvements in terms of computational efficiency, and the original PE algorithm is modified to guarantee robust stability of the overall closedloop system. We also discuss how input constraints that involve different units, e.g. on the summation of common utility consumption, can be appropriately handled. We illustrate the benefits of proposed method by means a simulated example comprising three units
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