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## Constrained dynamic decoupling

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In Chapter 4, we described a methodology to achieve the closed-loop dynamic decoupling of multivariable systems. Although some difficulties arising from right half plane (RHP) zeros were pointed out, the decoupling design implicitly assumed unconstrained systems and centralised controllers, as in general do the great majority of the existing techniques. Hereinafter (Chapters 5-7), we will take advantage of the sliding mode reference conditioning (SMRC) features to improve the closed-loop decoupling in the presence of either physical (actuator saturations), structural (decentralised controllers) or dynamic (non-minimum phase (NMP) plants) limitations. When the unavoidable physical limits of the real actuators are taken into account, the activation of any of them produces a change in the direction of the plant input with respect to the controller output and, as a consequence, the decoupling obtained for linear operation is lost. In this chapter, we first illustrate the control directionality problem briefly introduced in Chapter 1, and we then present a compensation method using SMRC ideas to preserve the closed-loop dynamic decoupling in presence of input constraints.

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