MIMO PID Tuning via Iterated LMI Restriction

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MIMO PID Tuning via Iterated LMI Restriction. / Boyd, Stephen; Hast, Martin; Åström, Karl Johan.

In: International Journal of Robust and Nonlinear Control, Vol. 26, No. 8, 2015, p. 1718–1731.

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TY - JOUR

T1 - MIMO PID Tuning via Iterated LMI Restriction

AU - Boyd, Stephen

AU - Hast, Martin

AU - Åström, Karl Johan

PY - 2015

Y1 - 2015

N2 - We formulate multi-input multi-output (MIMO) proportional-integral-derivative (PID) controller design as an optimization problem that involves nonconvex quadratic matrix inequalities. We propose a simple method that replaces the nonconvex matrix inequalities with a linear matrix inequality (LMI) restriction, and iterates to convergence. This method can be interpreted as a matrix extension of the convex-concave procedure, or as a particular majorization-minimization (MM) method. Convergence to a local minimum can be guaranteed. While we do not know that the resulting controller is globally optimal, the method works well in practice, and provides a simple automated method for tuning MIMO PID controllers. The method is readily extended in many ways, for example to the design of more complex, structured controllers.

AB - We formulate multi-input multi-output (MIMO) proportional-integral-derivative (PID) controller design as an optimization problem that involves nonconvex quadratic matrix inequalities. We propose a simple method that replaces the nonconvex matrix inequalities with a linear matrix inequality (LMI) restriction, and iterates to convergence. This method can be interpreted as a matrix extension of the convex-concave procedure, or as a particular majorization-minimization (MM) method. Convergence to a local minimum can be guaranteed. While we do not know that the resulting controller is globally optimal, the method works well in practice, and provides a simple automated method for tuning MIMO PID controllers. The method is readily extended in many ways, for example to the design of more complex, structured controllers.

KW - MIMO PID tuning Convex optimization

U2 - 10.1002/rnc.3376

DO - 10.1002/rnc.3376

M3 - Article

VL - 26

SP - 1718

EP - 1731

JO - International Journal of Robust and Nonlinear Control

JF - International Journal of Robust and Nonlinear Control

SN - 1099-1239

IS - 8

ER -