A Numerical Comparison of Infinite-Spectrum-Shaping Techniques When Controlling Stable and Unstable Dead-Time Systems via the Standard PID Controller

This contribution aims to compare several numerical techniques for optimizing or shaping the infinite spectrum of system poles. These techniques use a quasi-continuous shifting of the dominant poles. One of the methods (Quasi-Continuous Pole Shifting) attempts to minimize the spectral abscissa, while the simultaneous goals of the other two methods (Quasi-Direct Pole Placement and Zero-Pole Placement Shifting) are to place the desired root loci and reach the minimum abscissa of the remaining spectrum. The framework problem of the infinite spectrum shaping is interpreted as a feedback control of habitual finite-dimensional stable, integrative, and unstable systems with dead time (i.e., the input-output delay) controlled by the standard Proportional-Integral-Derivative (PID) controllers in this contribution. In addition, the obtained results are also benchmarked with some well-established and recent PID controller tuning methods designed to optimize selected performance measures. Surprisingly, the spectral shaping techniques surpass them in some cases.