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10.2 Optimal Output Regulator
Closely related to the function LQRegulatorGains, which optimizes a system's behavior with regard to state variables, is the function LQOutputRegulatorGains, which finds the optimal solution to the output regulator problem. The cost function for this case contains outputs  instead of states  (cf. Eq. 10.5).
LQOutputRegulatorGains calls LQRegulatorGains and accepts the same options, the syntactic difference between the two being that the output regulator function, obviously, does require matrix  (and matrix  , if necessary) in the state-space description of the input system.
Linear quadratic output regulator design.
Reconsider the mixing tank problem from Figure 10.1. We wish to design the output regulator with matrices  and  as given.
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This solves the problem.
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