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Email Address. Sign In. Constrained model predictive control based on reduced-order models Abstract: The need for reduced-order approximations of dynamical systems emerges naturally in model-based control of very large-scale systems, such as those arising from the discretisation of partial differential equation models. The controller based on the reduced-order model, when in closed-loop with the large-scale system, ought to endow certain properties, in primis stability, but also satisfaction of state constraints and recursive computability of the control law in the case of constrained control.

In this paper we introduce a new approach to the design of model predictive controllers to meet the aforementioned requirements while the on-line complexity is essentially tantamount to the one that corresponds to the low-dimensional approximate model.

Article :. DOI: Need Help?Model predictive control MPC is an advanced method of process control that is used to control a process while satisfying a set of constraints.

It has been in use in the process industries in chemical plants and oil refineries since the s. In recent years it has also been used in power system balancing models [1] and in power electronics [2]. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification.

The main advantage of MPC is the fact that it allows the current timeslot to be optimized, while keeping future timeslots in account.

constrained model predictive control based on reduced

This is achieved by optimizing a finite time-horizon, but only implementing the current timeslot and then optimizing again, repeatedly, thus differing from Linear-Quadratic Regulator LQR. Also MPC has the ability to anticipate future events and can take control actions accordingly. PID controllers do not have this predictive ability. MPC is nearly universally implemented as a digital control, although there is research into achieving faster response times with specially designed analog circuitry.

The models used in MPC are generally intended to represent the behavior of complex dynamical systems.

constrained model predictive control based on reduced

The additional complexity of the MPC control algorithm is not generally needed to provide adequate control of simple systems, which are often controlled well by generic PID controllers. Common dynamic characteristics that are difficult for PID controllers include large time delays and high-order dynamics. MPC models predict the change in the dependent variables of the modeled system that will be caused by changes in the independent variables.

In a chemical process, independent variables that can be adjusted by the controller are often either the setpoints of regulatory PID controllers pressure, flow, temperature, etc. Independent variables that cannot be adjusted by the controller are used as disturbances.

Dependent variables in these processes are other measurements that represent either control objectives or process constraints. MPC uses the current plant measurements, the current dynamic state of the process, the MPC models, and the process variable targets and limits to calculate future changes in the dependent variables. These changes are calculated to hold the dependent variables close to target while honoring constraints on both independent and dependent variables.

The MPC typically sends out only the first change in each independent variable to be implemented, and repeats the calculation when the next change is required. While many real processes are not linear, they can often be considered to be approximately linear over a small operating range. Linear MPC approaches are used in the majority of applications with the feedback mechanism of the MPC compensating for prediction errors due to structural mismatch between the model and the process.

In model predictive controllers that consist only of linear models, the superposition principle of linear algebra enables the effect of changes in multiple independent variables to be added together to predict the response of the dependent variables.

This simplifies the control problem to a series of direct matrix algebra calculations that are fast and robust. When linear models are not sufficiently accurate to represent the real process nonlinearities, several approaches can be used.

The process can be controlled with nonlinear MPC that uses a nonlinear model directly in the control application. The nonlinear model may be in the form of an empirical data fit e. The nonlinear model may be linearized to derive a Kalman filter or specify a model for linear MPC. An algorithmic study by El-Gherwi, Budman, and El Kamel shows that utilizing a dual-mode approach can provide significant reduction in online computations while maintaining comparative performance to a non-altered implementation.

Model Predictive Control with a Relaxed Cost Function for Constrained Linear Systems

The proposed algorithm solves N convex optimization problems in parallel based on exchange of information among controllers. MPC is based on iterative, finite-horizon optimization of a plant model. Only the first step of the control strategy is implemented, then the plant state is sampled again and the calculations are repeated starting from the new current state, yielding a new control and new predicted state path.

The prediction horizon keeps being shifted forward and for this reason MPC is also called receding horizon control.

Model predictive control

Although this approach is not optimal, in practice it has given very good results.Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity.

Use of this web site signifies your agreement to the terms and conditions. Personal Sign In. For IEEE to continue sending you helpful information on our products and services, please consent to our updated Privacy Policy. Email Address. Sign In. First, an event-triggering mechanism is presented by designing a threshold for the error between the actual trajectory and the predicted one, aiming at reducing the computational load.

constrained model predictive control based on reduced

Second, a model predictive control strategy is developed based on the event-triggering mechanism. Recursive feasibility is guaranteed by designing a robust terminal region and the proper parameters. We show that the tracking system is practically stable and also provides a convergence region for the tracking error. The convergence region indicates that the tracking performance is negatively related to the minimal interevent time as well as the bound of the disturbances. Finally, simulation results show that the computation load is significantly reduced and illustrate the efficiency of our proposed strategy.

Article :. Date of Publication: 07 August DOI: Need Help?The Model Predictive Control technique is widely used for optimizing the performance of constrained multi-input multi-output processes. However, due to its mathematical complexity and heavy computation effort, it is mainly suitable in processes with slow dynamics. Based on the Exact Penalization Theorem, this paper presents a discrete-time state-space Model Predictive Control strategy with a relaxed performance index, where the constraints are implicitly defined in the weighting matrices, computed at each sampling time.

Model predictive control

The performance validation for the Model Predictive Control strategy with the proposed relaxed cost function uses the simulation of a tape transport system and a jet transport aircraft during cruise flight. Without affecting the tracking performance, numerical results show that the execution time is notably decreased compared with two well-known discrete-time state-space Model Predictive Control strategies. This makes the proposed Model Predictive Control mainly suitable for constrained multivariable processes with fast dynamics.

Model Predictive Control MPC for linear systems is now a well-established discipline providing stability, feasibility, and robustness [ 1 — 6 ]. Due to its inherent ability to take into account constraints and deal with multi-input multi-output variables [ 7 — 10 ], it has been applied in a wide range of applications, including chemical processes, industrial systems, energy, health, environment, and aerospace [ 11 — 16 ].

In [ 17 ], a robust MPC strategy is presented to handle the trajectory tracking problem for an underactuated two-wheeled inverted pendulum vehicle. Moreover, based on an MPC scheme, in [ 18 ], a control strategy is designed to an unmanned aerial vehicle for its automatic carrier landing system.

Nevertheless, the computation complexity makes the multivariable MPC ineffectual for high speed applications where the controller must execute in a few milliseconds [ 19 — 23 ].

Moreover, the problem becomes much more complicated solving such an online constrained optimization problem by computing a numerical solver [ 24 — 26 ]. Several MPC techniques are used to overcome these problems.

For instance, in [ 27 ], an explicit model predictive control moves major part of computation offline, which makes it enable to be implemented in real time for wide range of fast systems. Also, in [ 28 ], to reduce the online computational time, all the state trajectories are included in the optimal control problem as the constraints in the prediction horizon, then only a quadratic programming problem is solved.

In [ 29 ], based on a mixed integer quadratic programming problem, the control input is calculated at each discrete time. In contrast to common MPC approaches, where an optimization toolbox is required, this work presents a relaxed performance index, in which the weighting matrices are computed online using the concept of Taylor series expansion and standard inverse distance weighting IDW functions.

Then, tracking performance under input-output constraints is well obtained, lighter computation load is achieved, and execution time to solve a Quadratic Program QP is reduced. Thus, a computationally efficient constrained MPC for discrete-time state-space multivariable systems is obtained.

The paper is organized as follows. Section 2 gives the preliminaries of the proposed MPC strategy. Section 3 describes the proposed relaxed cost function. Section 4 presents a tape transport system and a jet transport aircraft as study cases. Simulation results show the performance of the proposed MPC strategy and the execution time improvement compared with two well-known MPC strategies.

Finally, Section 5 discusses the conclusions. Acknowledgments and the list of references finish the paper. This section presents a brief review of MPC based on discrete-time state-space model. The original controller is proposed by Alamir in [ 7 ]. In this previous work, considering the predictions of the states, the control action is obtained through the solution of a constrained optimization problem by using a cost function with constant weighting matrices.

At each sampling time, an optimal control problem is solved whose results are computationally expensive. The system dynamics is denoted by the Linear Time Invariant LTI State-Space Model taking the following structure: where is the state vector, is the controlled input vector, is the output vector, is the state matrix, stands for the input matrix, is the output matrix, and denotes the sampling instant number.

Hence, as in [ 7 ], from 1the state predictions for the consecutive sampling instants are where and are used to represent the N-step-ahead prediction map for Linear Time Invariant LTI systems in a compactness form 2.

Thus, system 2 can be reformulated using the following vector-matrix notation: where and is the whole state trajectory ofconcatenates the computed sequence ofand is the output trajectory of :.Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

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In this paper we introduce a new approach to the design of model predictive controllers to meet the aforementioned requirements while the on-line complexity is essentially tantamount to the one that corresponds to the low-dimensional approximate model.

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Lecture 8 Optimization-based Control: Collocation, Shooting, MPC -- CS287-FA19 Advanced Robotics

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constrained model predictive control based on reduced

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