Modular Model Predictive Control upon an Existing Controller

The availability of predictions of future system inputs has motivated research into preview control to improve set-point tracking and disturbance rejection beyond that achievable via conventional feedback control. The design of preview controllers, typically based upon model predictive control (MPC) for its constraint handling properties, is often performed in a monolithic nature, coupling the feedback and feed-forward problems. This can create problems, such as: (i) an additional feedback loop is introduced by MPC, which alters the closed-loop dynamics of the existing feedback compensator, potentially resulting in a deterioration of the nominal sensitivities and robustness properties of an existing closed-loop and (ii) the default preview action from MPC can be poor, degrading the original feedback control performance. In our previous work, the former problem is addressed by presenting a modular MPC design on top of a given output-feedback controller, which retains the nominal closed-loop robustness and frequency-domain properties of the latter, despite the addition of the preview design. In this paper, we address the second problem; the preview compensator design in the modular MPC formulation. Specifically, we derive the key conditions that ensure, under a given closed-loop tuning, the preview compensator within the modular MPC formulation is systematic and well-designed in a sense that the preview control actions complement the existing feedback control law rather than opposing it. In addition, we also derive some important results, showing that the modular MPC can be implemented in a cascade over any given linear controllers and the proposed conditions hold, regardless of the observer design for the modular MPC. The key benefit of the modular MPC is that the preview control with constraint handling can be implemented without replacing the existing feedback controller. This is illustrated through some numerical examples.

[1]  Sten Bay Jørgensen,et al.  Unreachable Setpoints in Model Predictive Control , 2008, IEEE Transactions on Automatic Control.

[2]  J. A. Rossiter,et al.  Preview predictive control layer design based upon known wind turbine blade-pitch controllers: MPC layer design based upon known blade-pitch controllers , 2017 .

[3]  A. Jameson,et al.  Optimality of linear control systems , 1972 .

[4]  Elmer G. Gilbert,et al.  Constrained linear systems with hard constraints and disturbances: An extended command governor with large domain of attraction , 2011, Autom..

[5]  Edward N. Hartley,et al.  Designing Output-Feedback Predictive Controllers by Reverse-Engineering Existing LTI Controllers , 2013, IEEE Transactions on Automatic Control.

[6]  Marcello Farina,et al.  An MPC-based reference governor approach for offset-free control of constrained linear systems , 2013, Int. J. Control.

[7]  Manfred Morari,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[8]  J. A. Rossiter,et al.  Improving the Tracking of Generalized Predictive Control Controllers , 1996 .

[9]  Graham C. Goodwin,et al.  Feedforward model predictive control , 2011, Annu. Rev. Control..

[10]  David W. Clarke,et al.  Generalized predictive control - Part I. The basic algorithm , 1987, Autom..

[11]  K. Muske,et al.  Conditions for which linear MPC converges to the correct target , 2010 .

[12]  Manfred Morari,et al.  Soft Constrained Model Predictive Control With Robust Stability Guarantees , 2014, IEEE Transactions on Automatic Control.

[13]  D. Q. Mayne,et al.  A simple tube controller for efficient robust model predictive control of constrained linear discret , 2005 .

[14]  Eduardo F. Camacho,et al.  MPC for tracking piecewise constant references for constrained linear systems , 2008, Autom..

[15]  James B. Rawlings,et al.  Model predictive control with linear models , 1993 .

[16]  Antonio Ferramosca,et al.  MPC for tracking with optimal closed-loop performance , 2009, Autom..

[17]  Basil Kouvaritakis,et al.  Efficient robust predictive control , 2000, IEEE Trans. Autom. Control..

[18]  Mark Rice,et al.  A numerically robust state-space approach to stable-predictive control strategies , 1998, Autom..

[19]  J. Rawlings,et al.  Feasibility issues in linear model predictive control , 1999 .

[20]  F. Borrelli,et al.  Reference governor for constrained piecewise affine systems , 2009 .

[21]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[22]  Alberto Bemporad,et al.  Model Predictive Control Tuning by Controller Matching , 2010, IEEE Transactions on Automatic Control.

[23]  G Valencia-Palomo,et al.  Improving the feed-forward compensator in predictive control for setpoint tracking. , 2014, ISA transactions.