Tuning of a time-delayed controller for a general class of second-order LTI systems with dead-time

What is it about?

In this paper the problem of \sigma-stabilizing a general class of second-order LTI systems with dead-time using a Proportional-Integral-Retarded (PIR) controller is considered. The \sigma-stability of a system determines the exponential decay in its response. Here the \sigma-stability of the closed-loop system is ensured by assigning up to four dominant real roots at -\sigma. For the tuning of the controller gains an extensive analysis of all the possible allocations of the gains according to the response of the closed-loop system is presented. The D-partition method is used to provide important insight into the problem. As a consequence of this analysis, to achieve the desired decay rate, exact analytic expressions for tuning the PIR controller parameters are given. To illustrate the theoretical results obtained, the underactuated mechanical system called Inverted Pendulum is used.

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Why is it important?

In this paper the tuning of a PIR control law to \sigma-stabilize a general class of second-order LTI systems with dead-time is presented. The \sigma-stabilization analysis of the closed-loop system in the frequency domain is performed using the D-partition method

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