Abstract
In model predictive control, the control law is synthesised by formulating the control objective as a constrained optimal control problem. This allows us to formulate in a straightforward way a wide range of control objectives for a wide range of systems where an explicit model of the dynamics is available. This chapter describes the typical problem classes that arise in the control of switched electronics systems, which are characterised by the hybrid nature of their dynamics. It describes the associated model predictive control classes and discusses how to formulate an optimisation problem tractable in real time. The tractability issue is particularly important due to the switching and sampling frequencies that typically range from a few hundred hertz to a few megahertz. Finally, the chapter also develops problem formulations that optimise the system switched behaviour in order to tackle objectives such as minimising the harmonic distortion or system losses.
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References
Almér, S., Mariéthoz, S., Morari, M.: Piecewise affine modeling and control of a step-up DC–DC converter. In: Proc. of the American Control Conference, Baltimore, Maryland, USA, pp. 3299–3304 (2010)
Baotic, M., Borrelli, F., Bemporad, A., Morari, M.: Efficient on-line computation of constrained optimal control. SIAM J. Control Optim. 47(5), 2470–2489 (2008)
Bemporad, A., Borrelli, F., Morari, M.: Optimal controllers for hybrid systems: stability and piecewise linear explicit form. In: Proc. of the IEEE Conference on Decision and Control, Sydney, Australia, pp. 1810–1815 (2000)
Bemporad, A., Borrelli, F., Morari, M.: Piecewise linear optimal controllers for hybrid systems. In: Proc. of the American Control Conference, Chicago, Illinois, USA, pp. 1190–1194 (2000)
Bemporad, A., Borrelli, F., Morari, M.: Model predictive control based on linear programming—the explicit solution. IEEE Trans. Autom. Control 47(12), 1974–1985 (2002)
Bemporad, A., Morari, M., Dua, V., Pistikopoulos, E.N.: The explicit linear quadratic regulator for constrained systems. Automatica 38(1), 3–20 (2002)
Cortes, P., Kazmierkowski, M.P., Kennel, R.M., Quevedo, D.E., Rodriguez, J.: Predictive control in power electronics and drives. IEEE Trans. Ind. Electron. 55(12), 4312–4324 (2008)
Dua, V., Pistikopoulos, E.N.: An algorithm for the solution of multiparametric mixed integer linear programming problems. Ann. Oper. Res. 99(1–4), 123–139 (2000)
García, C.E., Prett, D.M., Morari, M.: Model predictive control: Theory and practice—A survey. Automatica 25(3), 335–348 (1989)
Geyer, T., Papafotiou, G., Morari, M.: Model predictive direct torque control—Part I: Concept, algorithm, and analysis. IEEE Trans. Ind. Electron. 56(6), 1894–1905 (2009)
Mariéthoz, S., Morari, M.: Explicit model-predictive control of a PWM inverter with an LCL filter. IEEE Trans. Ind. Electron. 56(2), 389–399 (2009)
Mariéthoz, S., Almér, S., Bâja, M., Beccuti, A.G., Patino, D., Wernrud, A., Buisson, J., Cormerais, H., Fujioka, H., Geyer, T., Jönsson, U.T., Kao, C.Y., Morari, M., Papafotiou, G., Rantzer, A., Riedinger, P.: Comparison of hybrid control techniques for buck and boost DC–DC converters. IEEE Trans. Control Syst. Technol. 18(5), 1126–1145 (2010)
Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.M.: Constrained model predictive control: Stability and optimality. Automatica 36(6), 789–814 (2000)
Middlebrook, R.D., Ćuk, S.: A general unified approach to modeling switching-converter power stages. In: Proc. of the IEEE Power Electronics Specialist Conference, Cleveland, Ohio, USA, pp. 18–34 (1976)
Naouar, M.W., Naassani, A.A., Monmasson, E., Belkhodja, I.S.: FPGA-based predictive current controller for synchronous machine speed drive. IEEE Trans. Power Electron. 23(4), 2115–2126 (2008)
Qin, S.J., Badgwell, T.A.: A survey of industrial model predictive control technology. Control Eng. Pract. 11(7), 733–764 (2003)
Sontag, E.D.: Nonlinear regulation: The piecewise linear approach. IEEE Trans. Autom. Control 26(2), 346–358 (1981)
Tøndel, P., Johansen, T.A., Bemporad, A.: An algorithm for multi-parametric quadratic programming and explicit MPC solutions. Automatica 39(3), 489–497 (2003)
Tøndel, P., Johansen, T.A., Bemporad, A.: Evaluation of piecewise affine control via binary search tree. Automatica 39(5), 945–950 (2003)
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© 2012 Springer-Verlag London Limited
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Mariéthoz, S., Almér, S. (2012). Model Predictive Control. In: Vasca, F., Iannelli, L. (eds) Dynamics and Control of Switched Electronic Systems. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-2885-4_11
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DOI: https://doi.org/10.1007/978-1-4471-2885-4_11
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