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A Generalized H-infinity Mixed Sensitivity Convex Approach to Multivariable Control Design Subject to Simultaneous Output and Input Loop-Breaking Specifications

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gms

A Generalized H-infinity Mixed Sensitivity Convex Approach to Multivariable Control Design Subject to Simultaneous Output and Input Loop-Breaking Specifications

Computes a H-infinity based Feedback Controller based on multiobjective constrained convex optimization.

Outline of steps for GMS problem setup:

  • Form the design plant:

    • Define the original plant
    • Integrator augmentation if needed
    • Bilinear transformation values if needed
  • Select weighting functions:

    • Tradeoff param rho
    • W for obj
    • W for constraint
  • Select optimization params:

    • LB and UB
    • Init point
    • Maximum number of iterations
  • Select Youla/Zames parametrization:

    • Select Youla or Zames
    • Initial controller
  • Finite Dimensionality

    • Basis params
  • Objective function: - sum/max/stacking

  • Find initial controller (Ko, F, L)

  • Youla parameterization

  • Find Initial Q parameter using initial controller (Ko, F, L)

  • Extract required data from problem setup

  • Vectorize the optimization problem

  • Optimization process

    • define how subgradient is picked based on sum/max/stacking
  • form Q using the optimized variables and bases

  • form Controller K using the obtained Q

  • Inverse bilinear transformation if needed

  • Inverse of integrator augmentation if needed

  • Compute OL and CL maps

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A Generalized H-infinity Mixed Sensitivity Convex Approach to Multivariable Control Design Subject to Simultaneous Output and Input Loop-Breaking Specifications

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