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.
KeywordsInequality Constraint Sample Index Convex Functional Coprime Factorization Block Diagonal Structure
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