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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 16.323 Principles of Optimal Control Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 16.323 Lecture 16 Model Predictive Control • Allgower, F., and A. Zheng, Nonlinear Model Predictive Control, SpringerVerlag, 2000. • Camacho, E., and C. Bordons, Model Predictive Control, SpringerVerlag, 1999. • Kouvaritakis, B., and M. Cannon, NonLinear Predictive Control: Theory & Practice, IEE Publishing, 2001. • Maciejowski, J., Predictive Control with Constraints, Pearson Education POD, 2002. • Rossiter, J. A., ModelBased Predictive Control: A Practical Approach, CRC Press, 2003. Spr 2008 16.323 16–1 MPC • Planning in Lecture 8 was effectively “openloop” – Designed the control input sequence u ( t ) using an assumed model and set of constraints. – Issue is that with modeling error and/or disturbances, these inputs will not necessarily generate the desired system response. • Need a “closedloop” strategy to compensate for these errors. – Approach called Model Predictive Control – Also known as receding horizon control • Basic strategy: – At time k , use knowledge of the system model to design an input sequence u ( k  k ) , u ( k + 1  k ) , u ( k + 2  k ) , u ( k + 3  k ) ,..., u ( k + N  k ) over a finite horizon N from the current state x ( k ) – Implement a fraction of that input sequence, usually just first step. – Repeat for time k + 1 at state x ( k + 1) June 18, 2008 Reference "Optimal" future outputs "Optimal" future inputs Future outputs, no control Future inputs, no control Old outputs Old inputs Past Present Future Time MPC: basic idea (from Bo Wahlberg) Figure by MIT OpenCourseWare. Spr 2008 16.323 16–2 • Note that the control algorithm is based on numerically solving an optimization problem at each step – Typically a constrained optimization • Main advantage of MPC: – Explicitly accounts for system constraints. Doesn’t just design a controller to keep the system away from them. – Can easily handle nonlinear and timevarying plant dynamics, since the controller is explicitly a function of the model that can be mod ified in realtime (and plan time) • Many commercial applications that date back to the early 1970’s, see http://www.che.utexas.edu/ ~ qin/cpcv/cpcv14.html – Much of this work was in process control very nonlinear dynamics, but not particularly fast....
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This note was uploaded on 11/07/2011 for the course AERO 16.323 taught by Professor Jonathanhow during the Spring '08 term at MIT.
 Spring '08
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