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DESIGN INNOVATION

Automatic Loop Shaping of MIMO Controllers Satisfying Sensitivity Specifications

[+] Author and Article Information
O. Yaniv

Faculty of Engineering, Department of Electrical Engineering Systems, Tel Aviv University, Tel Aviv 69978, Israelyaniv@eng.tau.ac.il

J. Dyn. Sys., Meas., Control 128(2), 463-471 (Mar 28, 2005) (9 pages) doi:10.1115/1.2199856 History: Received August 04, 2004; Revised March 28, 2005

An existing automatic loop shaping algorithm for designing SISO controllers is extended to automatic loop shaping of MIMO controllers that is based on the sequential QFT method. The algorithm is efficient and fast and can search for controllers satisfying many types of restrictions, including constraints on each one of the controller’s elements such as hard restrictions on the high-frequency amplitude or damping factor of notch filters. Moreover, the algorithm can be applied to unstructured uncertain plants, be they stable, unstable, or nonminimum phase, including pure delay.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

A MIMO feedback system, P, may be any member of the set {P}

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Figure 2

Nichols plot of the uncertain open loop transfer function L1; it must not enter the shaded region in order to guarantee the specs on s11

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Figure 3

Nichols plot of the uncertain open loop transfer function L2; it must not enter the shaded region in order to guarantee the specs on s22

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Figure 4

Sensitivity simulation; specs require that the diagonal plots will be less than 4.8dB in any frequency

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Figure 5

Nichols plot of the uncertain open loop transfer function L1; it must not enter the shaded region in order to guarantee the specs on s11

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Figure 6

Nichols plot of the uncertain open loop transfer function L2; it must not enter the shaded region in order to guarantee the specs on s22

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Figure 7

Sensitivity simulation for k1,k2 taking the values 0.8, 0.9, 1, 1.1, 1.2; specs require that the diagonal plots will be less than 6dB in any frequency

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Figure 8

Step response simulation: The shaded domain Rij denote all outputs of channel i for a step input in channel j and zero in the other one, where k1,k2 taking the values 0.8 to 1.2 in steps of 0.05 and where the delay is replaced by the second order Padé approximation for uncorrelated T1=0,0.05,1 and T2=0,0.05,1

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