Dual mode predictive tracking of piecewise constant references for constrained linear systems

Chisci, Luigi; Zappa, G.

doi:10.1080/0020717021000049160

Cited by 63 publications

(64 citation statements)

References 20 publications

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“…In order to overcome this problem several solutions have been proposed [Camacho and Bordons, 2004, Rossiter et al, 1996, Chisci and Zappa, 2003. In [Pannocchia andKerrigan, 2005, Pannocchia, 2004] the set-point change is considered equivalent to a disturbance to be rejected and asymptotic stability and offset-free is ensured by integrating a disturbance model in the prediction model.…”

Section: Introductionmentioning

confidence: 99%

MPC for tracking periodic reference signals

Limón

Álamo

Peña

et al. 2012

IFAC Proceedings Volumes

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This paper is devoted to the design of a predictive controller for constrained linear systems to track periodic references. The only assumption on the dynamics of the reference is that it is periodic and its period is known. It is also assumed that the reference signal is a priori known by the controller. Inspired in the hierarchical control scheme based on the trajectory planification, the ideas of the MPC for tracking [Limon et al., 2008] are extended to this case. The proposed predictive controller has the future sequence of inputs and an artificial reference as decision variables. The cost function is divided into two terms: one penalizes the tracking error with the artificial reference and other penalizes the deviation of the artificial reference to the reference to be tracked. Stability is ensured thanks to the addition of two constraints: a terminal constraint on the predicted trajectory and a constraint that enforces the artificial reference to be periodic. It is proved that the proposed controller is recursively feasible and the controlled system satisfies the hard constraints, is asymptotically stable and converges to the best possible reachable trajectory. The properties of the proposed controller are illustrated in an example.

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Section: Introductionmentioning

confidence: 99%

MPC for tracking periodic reference signals

Limón

Álamo

Peña

et al. 2012

IFAC Proceedings Volumes

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“…Instead of augmenting the system with a new state as in Chisci and Zappa [2003], Limon et al [2008] the main concept here is to introduce an extra optimization variable, λ k , which scales the terminal set, T . The scaling allows us to move the terminal constraint set to an arbitrary setpoint,x k , since the terminal set can be scaled down to a single point, i.e., T =x k , eliminating the need for any online recalculation of T as in Rao and and the terminal constraint set can possibly be far simpler than the terminal set for an augmented system.…”

Section: The Proposed Controllermentioning

confidence: 99%

“…To recalculate the terminal constraint set can however require complex calculations to be performed online and might thus not be suitable for systems where the setpoint changes often. A far better approach has been proposed in different forms by several authors Chisci and Zappa [2003], Limon et al [2008] and Ferramosca et al [2009]. In Chisci and Zappa [2003] the authors augment the system with a new constant state which corresponds to the reference signal providing a terminal constraint set in the higher dimension (x, r ) which contains the whole feasible equilibrium set for any given reference, i.e., the terminal constraint set is a fixed set which can be pre-calculated.…”

Section: Introductionmentioning

confidence: 99%

“…A far better approach has been proposed in different forms by several authors Chisci and Zappa [2003], Limon et al [2008] and Ferramosca et al [2009]. In Chisci and Zappa [2003] the authors augment the system with a new constant state which corresponds to the reference signal providing a terminal constraint set in the higher dimension (x, r ) which contains the whole feasible equilibrium set for any given reference, i.e., the terminal constraint set is a fixed set which can be pre-calculated. Instead of using the reference as augmented state the authors of Ferramosca et al [2009], Limon et al [2008 introduce a new optimization variable, θ, which spans the null space of steady state equation (4.11b).…”

Section: Introductionmentioning

confidence: 99%

“…Even if it allows for the possibility to guarantee stability, the addition of the terminal constraints can add a significant complexity to the original problem that might be unnecessary and limit the applicability of MPC within certain fields. In reference tracking MPC the terminal set can become very complex and some times not even finitely determined, see e.g., Chisci and Zappa [2003] or Limon et al [2008]. Therefore it can often be beneficial to analyze and verify the stability of a certain design rather than building in the stability by adding extra constraints.…”

Section: Introductionmentioning

confidence: 99%

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Fighter Aircraft Maneuver Limiting Using MPC : Theory and Application

Simon¹

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Flight control design for modern fighter aircraft is a challenging task. Aircraft are dynamical systems, which naturally contain a variety of constraints and nonlinearities such as, e.g., maximum permissible load factor, angle of attack and control surface deflections. Taking these limitations into account in the design of control systems is becoming increasingly important as the performance and complexity of the aircraft is constantly increasing.The aeronautical industry has traditionally applied feedforward, anti-windup or similar techniques and different ad hoc engineering solutions to handle constraints on the aircraft. However these approaches often rely on engineering experience and insight rather than a theoretical foundation, and can often require a tremendous amount of time to tune.In this thesis we investigate model predictive control as an alternative design tool to handle the constraints that arises in the flight control design.We derive a simple reference tracking MPC algorithm for linear systems that build on the dual mode formulation with guaranteed stability and low complexity suitable for implementation in real time safety critical systems.To reduce the computational burden of nonlinear model predictive control we propose a method to handle the nonlinear constraints, using a set of dynamically generated local inner polytopic approximations. The main benefit of the proposed method is that while computationally cheap it still can guarantee recursive feasibility and convergence.An alternative to deriving MPC algorithms with guaranteed stability properties is to analyze the closed loop stability, post design. Here we focus on deriving a tool based on Mixed Integer Linear Programming for analysis of the closed loop stability and robust stability of linear systems controlled with MPC controllers.To test the performance of model predictive control for a real world example we design and implement a standard MPC controller in the development simulator for the JAS 39 Gripen aircraft at Saab Aeronautics. This part of the thesis focuses on practical and tuning aspects of designing MPC controllers for fighter aircraft. Finally we have compared the MPC design with an alternative approach to maneuver limiting using a command governor. v Populärvetenskaplig sammanfattningStyrsystem i moderna flygplan ska sätta stopp om piloten gör en hastig manöver som äventyrar säkerheten. Speciellt viktigt är det i jaktflygplan där piloten kan tvingas manövrera flygplanet precis på gränsen för vad konstruktionen klarar. Reglermetoder från processindustrin anpassas nu för att passa flyget.En av de viktigaste faktorerna när man konstruerar ett flygplan är att flygplanet ska vara enkelt och säkert att flyga. Därför är det av yttersta vikt att man konstruerar flygplanens styrsystem så att piloten inte kan sätta flygplanet i en sådan situation att säkerheten äventyras. En sådan situation kan vara att piloten styr flygplanet så att det tappar sin lyftkraft och därmed sin förmåga att flyga eller också att kraftig turbulens u...

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Offset‐free receding horizon control of constrained linear systems

Pannocchia

Kerrigan

2005

AIChE Journal

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This paper addresses the design of a nonlinear time-invariant, dynamic state feedback receding horizon controller, which guarantees constraint satisfaction, robust stability and offset-free control of constrained, linear time-invariant systems in the presence of time-varying setpoints and unmeasured, persistent, 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 defined. The linear (unconstrained) controller is then modified by adding a perturbation term, which 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. Proofs of robust constraint satisfaction, robust stability and offset-free control are given. The effectiveness of the proposed controller is illustrated on an example of a continuous stirred tank reactor.

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Dual mode predictive tracking of piecewise constant references for constrained linear systems

Cited by 63 publications

References 20 publications

MPC for tracking periodic reference signals

MPC for tracking periodic reference signals

Fighter Aircraft Maneuver Limiting Using MPC : Theory and Application

Offset‐free receding horizon control of constrained linear systems

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