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Optimal Control of Processes with a Singular Static Gain Matrix


H. Seki, M. Morari

vol. AUT98-01

A control technique is developed for 1) a linear time-invariant (LTI) stable process with a singular static gain matrix, 2) a LTI stable process with different numbers of inputs and outputs, and 3) a nonlinear stable process whose static gain matrix may become singular in its operating region. For this purpose, the linear quadratic optimal control problem is formulated for a linear process, which is augmented with an integrator at its input, with penalty on the control input as well as on its time-derivative in the performance index. In the nonlinear case, receding horizon control is used; the nonlinear process model is linearized around the trajectory, and the LQ problem is applied to the locally linearized model. The local linearization approach is shown to be asymptotically stable and achieve an offset free response if the set-point is ``reachable'' and the static gain matrix is nonsingular. It is also shown that the closed loop can be made asymptotically stable by specifying an "unreachable" set-point in the singular static gain matrix case.


Type of Publication:

(04)Technical Report

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% Autogenerated BibTeX entry
@TechReport { SekMor:1998:IFA_1440,
    author={H. Seki and M. Morari},
    title={{Optimal Control of Processes with a Singular Static Gain
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