Linear parameter varying lpv systems are a particular class of nonlinear systems which can be thought of as varyingsystems, for which the variation depends explicitly on a timevarying parameter referred to as the scheduling or weight sequence 12. Control of linear parameter varying systems with applications. This paper proposes a robust model predictive controller for linear parameter varying lpv systems subject to additive disturbances. The polytopic linear parameter varying model is established using tensorproduct modeling method, and tubemodel predictive control controller is designed to satisfy all vertices of the polytopic linear parameter varying model. Explicit model predictive control for systems with linear parametervarying state transition matrix thomas besselmann johan lo fberg manfred morari automatic control laboratory, eth zurich, zurich, switzer land, email. Hence, the model will be a time varying, nonlinear system, with the future time variation unknown, but measured by the sensors in realtime. By running closedloop simulations, you can evaluate controller performance. Anticipative model predictive control for linear parameter varying.
Model predictive control for linear parameter varying systems using pathdependent lyapunov functions marc jungers rodrigo p. Stabilizing nonlinear mpc using linear parametervarying. Adaptive model predictive control for constrained, linear time varying systems m. Jun 02, 2017 in this paper, a new offline model predictive control strategy is presented for a kind of linear parameter varying system with polytopic uncertainty. The proposed controller relies on the constraint tightening method to guarantee that the mpcs optimization problem remains feasible in the presence of additive disturbances. Adaptive mpc control of nonlinear chemical reactor using. The subspace predictors are derived by qr decomposition of inputoutput and laguerre. Pdf explicit model predictive control for systems with.
Development of linear parameter varying models are a key step in applying lpv control synthesis. A polyhedral offline model predictive control algorithm for linear parameter varying systems. The main objective of the controller is to allow the wind turbine to extract from the wind a prespecified desired amount of power according to the wind speed and to guara ntee the stability. Abstract this paper introduces a novel fast model predictive control mpc methodology based on linear parameter varying lpv systems.
Linearparametervarying approximation of nonlinear dynamics for model predictive flow control of urban multiregion systems. Blending approach of linear parameter varying control synthesis for f. An offline robust constrained model predictive control mpc algorithm for linear time varying ltv systems is developed. Adaptive model predictive control for constrained, linear. Pdf wind turbine control based on a modified model predictive. In this paper, a new offline model predictive control strategy is presented for a kind of linear parameter varying system with polytopic uncertainty. A linear parametervarying lpv system is a linear statespace model whose dynamics vary as a function of certain timevarying parameters called scheduling parameters. Closedloop asymptotic stability is guaranteed by including a quadratic terminal cost and an ellipsoidal terminal set. The controller is designed based on two different approaches and results have been compared. The array of stateconsistent linear models that define an lpv model are represented by an array of statespace model objects. An improved robust model predictive control for linear parameter. This paper describes a new robust model predictive control mpc scheme to control the discrete. Pdf explicit model predictive control for linear parameter. Offline robust constrained mpc for linear timevarying.
Chapter1 introductiontononlinearmodel predictivecontroland movinghorizon estimation tor a. Firstly, the nominal model predictive control law is. Anticipative model predictive control for linear parameter varying systems hanema, j. Balanced truncation,12 lmis, bounded parameter variaton rates,14 coprime factorizations17,18 and singular perturbation15,16 are presented as an extension of the model reduction techniques for linear time invariant lti systems. Variations on optimal control problem time varying costs, dynamics, constraints discounted cost. The parameter is not known but its evolution is measured in real time and used for control. Model predictive control of a nonlinear system with. Control of linear parameter varying systems compiles stateoftheart contributions on novel analytical and computational methods for addressing system identification, model reduction, performance analysis and feedback control design and addresses address theoretical developments, novel. A twotier modeling scheme is proposed in which the deterministic and stochastic components of the model are updated online by two separate recursive pseudolinear regression schemes.
In this work, we propose the linear parameter varying model predictive control lpvmpc approach as a novel option to solve the driving control problem. An ellipsoidal offline model predictive control strategy for linear parameter varying systems with applications in chemical processes. This study presents a successful application of a model predictive control mpc design approach based on linear parameter varying lpv models subject to inputoutput constraints to control a. This paper is concerned with the design of model predictive control mpc for linear parameter varying lpv discretetime systems. The toolbox lets you specify plant and disturbance models, horizons, constraints, and weights. Publishers pdf, also known as version of record includes final. Adaptive model predictive control of multivariable time. Linearparametervarying approximation of nonlinear dynamics. Control of linear parameter varying systems compiles stateoftheart contributions on novel analytical and computational methods for addressing system identification, model reduction, performance analysis and feedback control design and addresses address theoretical developments, novel computational approaches and illustrative applications to various fields. Robust linear parameter varying model predictive control. Linearparametervarying model predictive control for multi. Explicit model predictive control for systems with linear parameter varying state transition matrix thomas besselmann johan lo fberg manfred morari automatic control laboratory, eth zurich, zurich, switzer land, email. Linearparametervarying model predictive control for. Gligorovski 1 introduction this manuscript contains technical details of recent results developed by the authors on adaptive model predictive control for constrained linear, time varying systems.
The subspace predictors are derived by qr decomposition of inputoutput and. Linear parameter varying lpv theory is used to model the dynamics of the vehicle and implement an lpv model predictive controller lpvmpc that can be computed online with reduced computational cost. Linearparametervarying model predictive control for multiregion traffic systems. Pdf an ellipsoidal offline model predictive control.
An improved robust model predictive control for linear parametervarying inputoutput models. In this paper we propose a closedloop minmax mpc algorithm based on dynamic programming, to compute explicit control laws for systems with a linear parametervarying state transition matrix. This article presents an innovative control approach for autonomous racing vehicles. In order to reduce the online computational burdens, a sequence of explicit control laws corresponding to a. Output feedback model predictive control of linear parameter. Use model arrays to create linear parameter varying models. Linear parametervarying models what are linear parametervarying models. This study presents a successful application of a model predictive control mpc design approach based on linear parametervarying lpv models subject to inputoutput constraints to control a. Model predictive control for linear parameter varying systems.
New methods for computing the terminal cost for minmax model predictive control. However, the computational effort is a crucial issue for lpvmpc, which has severely limited its application especially in embedded control. This information is used to construct state tubes to which the future trajectories of the state are confined. Linear parameter varying lpv systems are a particular class of nonlinear systems which can be thought of as varyingsystems, for which the variation depends explicitly on a time varying parameter referred to as the scheduling or weight sequence 12. This paper introduces a tubebased model predictive control mpc for linear parametervarying lpv systems which exploits knowledge about bounds on the parameters rate of change to extrapolate its admissible values over the prediction horizon. The problem above is based on a single linear model of the plant around one operating point. Explicit model predictive control for systems with linear. This paper describes a new robust model predictive control mpc scheme to control the discretetime linear parameter varying inputoutput models subject to input and output constraints. An offline robust constrained model predictive control mpc algorithm for linear timevarying ltv systems is developed.
Fast linear parameter varying model predictive control of. Autonomous racing using linear parameter varyingmodel. Model predictive control based on lpv models with parameter. The polytopic linear parameter varying model is established using tensorproduct modeling method, and tubemodel predictive control controller is designed to satisfy all vertices of the polytopic. First, by putting the advantages of the mpc approach into practice, the optimal output power regulation of the wind turbine is obtained using a control oriented linear parameter varying lpv model of the wind turbine. Model predictive control, linear parameter varying, nonlinear systems, wind turbines. Linear parameter varying lpv theory is used to model the dynamics of the vehicle and implement an lpvmodel predictive controller lpvmpc that can be computed online with reduced computational cost. The proposed approach can deal with largescale problems better than conventional fast mpc methods. Model predictive control of a wind turbine based on linear. To incorporate good longrange prediction capability with respect to manipulated. A novel feature is the fact that both model uncertainty and bounded. Pdf polytopic linear parameter varying modelbased tube.
The three approaches used to obtain the quasilpv models are jacobian linearization, state transformation, and function substitution. Model predictive controller design based on the linear. Pdf development of linearparametervarying models for. Model predictive control for linear parameter varying systems using. Model predictive controller design based on the linear parameter varying model method for a class of turboshaft engines. International journal of advanced polytopic linear. Chapter1 introductiontononlinearmodel predictivecontroland. Model predictive control for linear parameter varying. Sufficient linear matrix inequality lmi conditions are provided for the existence of a pathdependent lyapunov function which generalizes previous results based on affine parameterdependent lyapunov functions.
Output feedback model predictive control of linear. Pdf an efficient noncondensed approach for linear and. Explicit model predictive control for linear parametervarying systems conference paper pdf available in proceedings of the ieee conference on decision and control january 2009 with 119 reads. Computationally efficient model predictive control for a. The authors perform a comparison against the corresponding non linear mpc version showing the.
They are written similar to linear time invariant form albeit the inclusion in time variant parameter. A new datadriven predictive control method based on subspace identification for continuoustime linear parameter varying lpv systems is presented in this paper. However, the updated model and conditions remain constant over the prediction horizon. Tubebased model predictive control for linear parameter. Abstract this paper introduces a novel fast model predictive control mpc methodology based on linear parametervarying lpv systems.
Indeed, for dynamical systems of dimension commonly found in. Sufficient linear matrix inequality lmi conditions are provided for the existence of a pathdependent lyapunov function which generalizes previous results based on affine parameter dependent lyapunov functions. Control engineering 1418 linear mpc nonlinearity is caused by the constraints if constraints are inactive, the qp problem solution is u q. The models are obtained for the upandaway flight envelope of the boeing 747100200. Pdf wind turbine control based on a modified model.
Pdf robust shrinking ellipsoid model predictive control. An improved robust model predictive control for linear. Anticipative model predictive control for linear parametervarying systems. Pdf this study presents a successful application of a model predictive control mpc design approach based on linear parametervarying. Wind turbines power regulation using a lowcomplexity linear. Chapter 3 nonlinear model predictive control in this chapter, we introduce the nonlinear model predictive control algorithm in a rigorous way. First, the equality constraints given by the model equations are not. Model predictive control for linear parameter varying systems using a new parameter dependent terminal weighting matrix. For more information on model arrays, see model arrays. It is developed by reformulating the continuoustime lpv system which utilizes laguerre filters to obtain the subspace prediction of output. The polytopic linear parameter varying model is established using tensorproduct modeling method, and tube model predictive control controller is designed to satisfy all vertices of the polytopic. The system array size is equal to the grid size in scheduling space.
A linear parameter varying lpv system consisting of three linear plant models is constructed offline to describe the local plant dynamics across the operating range. In this paper we propose a closedloop minmax mpc algorithm based on dynamic programming, to compute explicit control laws for systems with a linear parameter varying state transition matrix. Model predictive control of linear parameter varying systems. Robust linear parameter varying model predictive control and its. Index termslinear matrix inequality lmi, linear parameter varying lpv system, model predictive control mpc, parameter dependent lyapunov function.
Model predictive control of linear parameter varying. In practical control systems, the plant states are not always measurable, so state estimation becomes essential before the state feedback control is applied. Model predictive control of a nonlinear system with known. Johansen abstract nonlinear model predictive control and moving horizon estimation are related methods since both are based on the concept of solving an optimization problem that involves a. To adapt to changing operating conditions, adaptive mpc supports updating the prediction model and its associated nominal conditions at each control interval. This paper presents a model predictive control approach to discretetime linear parameter varying systems based on a recurrent neural network. A novel feature is the fact that both model uncertainty and bounded additive disturbance are explicitly taken into account in the offline formulation of mpc. Model predictive control based on lpv models with parametervarying delays fatemeh karimi pour, vicenc. Abstractwe propose a model predictive control approach for nonlinear systems based on linear parametervarying representations. Datadriven predictive control for continuoustime linear. Puig and carlos ocampomartinez abstractthis paper presents a model predictive control mpc strategy based on linear parameter varying lpv models with varying delays affecting states and inputs. Summary this paper describes a new robust model predictive control mpc scheme to control the discrete. The polytopic linear parameter varying model is established using tensorproduct modeling method, and tube model predictive control controller is designed to satisfy all vertices of the polytopic linear parameter varying model. Anticipative model predictive control for linear parametervarying systems hanema, j.
This paper describes a new robust model predictive control mpc scheme to control the discretetime linear parametervarying inputoutput models subject to input and output constraints. Linear, parameter varying model reduction for aeroservoelastic systems. If the above equation of parameter dependent system is linear in time then it is called linear parameter dependent systems. The proposed method is derived by using the parameter dependent. The use of linear parameter varying lpv prediction models has been proven to be an effective solution to develop model predictive control mpc algorithms for linear and nonlinear systems. Pdf robust shrinking ellipsoid model predictive control for. Wind turbines power regulation using a lowcomplexity. Model predictive control linear convex optimal control.
Must be coupled with online state model parameter update. In this work, we develop a novel adaptive model predictive control ampc formulation for multivariable timevarying systems. First, by putting the advantages of the mpc approach into practice, the optimal output power regulation of the wind turbine is obtained using a control oriented linear parameter varying lpv model of. Anticipative model predictive control for linear parameter. However below we formulate our problem using linear parameter varying systems lpv in which the scheduling variable is known for the entire prediction horizon. The adaptive mpc controller then uses the lpv system to update the internal predictive model at each control interval and achieves nonlinear control successfully. In this brief, we propose a method of synthesizing a model predictive control mpc law for linear parameter varying systems. The use of linear parameter varying lpv prediction models has been proven to be an effective solution to develop model predictive control mpc algorithms for linear and non linear systems. This paper presents a new approach to solving linear and nonlinear model predictive control mpc problems that requires minimal memory footprint and throughput and is particularly suitable when the model andor controller parameters change at runtime. The model predictive control problem is formulated as a. Robust linear parameter varying model predictive control and.