Multivariable Controllers with Time-Domain Inequality Constraints
The application of Fenchel duality to the design of optimal controllers which include time-domain inequality constraints is discussed. The linear programming framework that is developed allows the inclusion of inequality constraints on any signal within the closed-loop. Many practical engineering constraints or performance specifications are expressible as inequalities, and it is important to be able to design such constraints into the control system. One such case is the control signal saturation problem, which is also examined in this paper. A convex optimization problem is formulated in the dual through the use of the fenchel duality theorem, and is set up to minimize quantities which are subject to not only performance constraints, but stability constraints as well. Performance constraints can be effectively handled by setting them up as convex functionals with the required time-domain properties. The method is based in the time-domain and deals with linear, discrete-time, time-invariant plants.
KeywordsConvolution Settling Nite Doyle Verse
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- P. Chandrasekharan, Robust Control of Linear Dynamical Systems. Academic Press, New York, 1996.Google Scholar
- J. C. Doyle, B. A. Francis, and A. R. Tannenbaum, Feedback Control Theory. Maxwell Macmillan, Singapore, 1992.Google Scholar
- R. D. Hill and M. E. Halpern, Minimum overshoot design for siso discrete- time systems. IEEE Transactions on Automatic Control, 38, No.l, 55–59, 1993.Google Scholar
- J. Maciejowski, Multivariable Feedback Design. Addison-Wesley, New York, 1993.Google Scholar
- J. Redmond and L. Silverberg, Fuel consumption in optimal control. Journal of Guidance, Control and Dynamics, 15, No. 2, 1992.Google Scholar
- J. Vethecan, Design of Compensators for LTI Feedback Systems by Convex Optimization. Doctoral Thesis, Royal Melbourne Institute of Technology, 1996.Google Scholar
- M. Vidyasagar, Control Systems Synthesis: A Factorization Approach. M.I.T. Press, Cambridge, MA, 1985.Google Scholar