Mapping of Frequency Response Performance Specifications Into Parameter Space

Links between the parameter space and frequency domain methods of robust control

“…While no attempt is made to give a complete list, the authors are aware of the works of Djaferis [27], Saeki [28], Besson and Shenton [29], B . u unte [30], Odenthal [31] and Odenthal and Blue [32]. To the best of the authors' knowledge, the first use of one frequency at a time mapping of frequency domain constraints into controller parameter space has been carried out by Djaferis [27].…”

“…In this approach, a frequency value is selected and ranges of values of two selected controller parameters in the structurally fixed controller that satisfy these criteria are solved for algebraically. Repetition of this procedure called the point condition solution here (this is also the terminology used in References [30,32]) for a sufficient number of frequency points with subsequent display of the superposed solution region satisfying the constraint at all of the chosen frequencies results in a graphical characterization of the solution. Djaferis [27] has also investigated this technique for plants with real parameter uncertainty.…”

“…Odenthal [31] and Odenthal and Blue [32] have mapped nominal performance and robust stability type frequency domain specifications into parameter space. Odenthal [31] has applied his symbolic computation based method to a wide range of examples.…”

“…For the two controller parameter values chosen, the solution procedure in (10)-(11) above yields the point condition solution at that frequency. The tangent condition z which essentially states that the derivative of the constraint with respect to frequency should vanish at the boundary of the solution region has been used along with symbolic manipulation of the point and tangent conditions for the constraints (2) and (3) by Odenthal and Blue [32]. The symbolic computation method, however, fails for the robust performance problem (4).…”

Verification Techniques for Sensitivity Analysis and Design of Controllers for Nonlinear Dynamic Systems with Uncertainties

“…In this case, design criteria for robust controllers for linear dynamical systems with uncertain parameters are usually specified using the notions of Γ-stability or B-stability. Using these notions, robustness can either be specified by regions in the complex domain containing all admissible poles of the closed-loop transfer function (Γ-stability) or by specifications of worst-case bounds for the frequency response (B-stability) (Ackermann et al, 2002;Sienel et al, 1996;Odenthal and Blue, 2000;Bünte, 2000). Then, the parameterization of linear feedback controllers with a predefined structure is possible using the parameter space approach introduced by Ackermann and Kaesbauer (Ackermann et al, 2002).…”