Last updated Jun 5, 2023 Edit Source

• Review: Pole Placement Control Design for MIMO Systems – Limitations
• Infinite number of possible solutions for state feedback gain K
• Difficult to modify control effort like R.L. (k $\leftrightarrow$ u)
• Introduction to MIMO Linear Quadratic (LQ) Optimal Control – Quadratic cost functions – Solution of optimal u for Finite-horizon cost – infinite-horizon case
• Special LQ: Symmetric Root Locus for SISO systems – LQ cost for SISO systems – Design tradeoff between control effort and state convergence – Determine SLR from closed-loop characteristic equations

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• A strategy for determining the feedback gains: – Choose the “best” (optimal) K to optimize some closedloop performance, e.g.,:
  • the control effort (maximum force; energy spent)
  • the transient and/or steady-state errors
  • the dollar cost of an operation
  • … – Specify a cost function (performance index) in a optimization problem from which K can be solved by using mathematical optimization

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