Transcription of 19 LINEAR QUADRATIC REGULATOR - MIT OpenCourseWare
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19 LINEAR QUADRATIC REGULATOR - MIT OpenCourseWare
19 LINEAR QUADRATIC REGULATOR Introduction The simple form of loopshaping in scalar systems does not extend directly to multivariable (MIMO) plants, which are characterized by transfer matrices instead of transfer functions. The notion of optimality is closely tied to MIMO control system design. Optimal controllers, , controllers that are the best possible, according to some figure of merit, turn out to generate only stabilizing controllers for MIMO plants. In this sense, optimal control solutions provide an automated design procedure we have only to decide what figure of merit to use.
chosen to be continuous in x, u, and t. We write the variation as ζJ¯ = ω xζx(tf) T+ t f Lxζx + TLuζu + ηTfxζx + η fuζu − η ζx˙ dt, (215) to where subscripts denote partial derivatives. The last term above can be evaluated using integration by parts as t f t f xdt = −ηT(t f)ζx(tf) + η T(t − o)ζx(to) + η˙Tζxdt, (216) to
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