Abstract
Robust pole-placement based on convex DR-regions belongs to the efficient control design techniques for real systems, providing computationally tractable pole-placement design algorithms. The problem arises in the discrete-time domain when the relative damping is prescribed since the corresponding discrete-time domain is non-convex, having a “cardioid” shape. In this paper, we further develop our recent results on the inner convex approximations of the cardioid, present systematical analysis of its design parameters and their influence on the corresponding closed loop performance (measured by standard integral of absolute error (IAE) and Total Variance criteria). The application of a robust controller designed with the proposed convex approximation of the discrete-time pole region is illustrated and evaluated on a real laboratory magnetic levitation plant.
Highlights
Robust control belongs to widely used control strategies implemented in real applications, since the real world plants always include uncertainties due to modeling errors, nonlinearities and other influences
Their maximum modulus is about 0.9985, γ is above 70◦, see Figure 3, the closed-loop performance is too oscillating, which is caused by insufficient damping
AE approximation and cardioid xe; stability degree represented by radius r—is presented to illustrate possibilities of their tuning to improve the closed-loop performance
Summary
Robust control belongs to widely used control strategies implemented in real applications, since the real world plants always include uncertainties due to modeling errors, nonlinearities and other influences. Various approaches exist to consider performance both in state space and frequency domains; pole-placement belongs to efficient techniques for achieving the prescribed closed-loop dynamics, [4,5,6,7,8] and others. In real plant control design, it is often desirable to place the closed-loop poles into the prescribed region of the complex plane instead of prescribing their exact position, for example, to achieve the determined stability degree or relative damping. Significant results have been obtained in this field during the past two decades when the so-called LMI, or more generally, the DR region approaches have been established and used for robust control design in state space [3,4,9]
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