A combined QFT/H ∞ design technique for TDOF uncertain feedback systems

Abstract

A new way of incorporating QFT principles into H 1 -control design techniques for solving the two-degrees of freedom feedback problem with highly uncertain plants is developed. The proposed practical design approach consists of two stages. In the ®rst stage, the robustness problem, due to plant uncertainties, is solved by H 1 -norm optimization. In this stage, the controller inside the loop (the ®rst degree of freedom) is designed, with the ultimate goal of minimizing the cost of feedback. Minimization of the sensor white noise ampli®cation at the input to the plant is also performed using QFT principles. In the second stage of the design, the pre®lter outside the loop (the second degree of freedom), is used to achieve the tracking speci®cations by conventional classical control theory, as practiced by the QFT design procedure. The combined QFT=H 1 design procedure for single input±single output (SISO) feedback systems is directly applicable to multi input±multi output (MIMO) feedback uncertain systems. The e ciency of the proposed technique is demonstrated with SISO and MIMO design examples for higly uncertain plants.

Design, Fabrication, and Control of Components in MEMS-Based Optical Pickups

“…While simple in principle, it is less efficient and more susceptible to the variation of component characteristics. Therefore, a more systematic and roubust approach combining the quantitative feedback theory (QFT) and the theory [24] is demonstrated for the servo control design in optical disk drives. In this approach, the theory improves the complicated Nichol charts in the QFT design.…”

Non‐sequential MIMO QFT control of the X‐29 aircraft using a generalized formulation

“…The limitations due to NMP transmission zeros were also considered in [60], where loop transmission cross-over frequency limitations were presented on specific SISO loops in a multivariable design. However, as noted in [61], constructive bandwidth limitations for individual loop designs in MIMO systems are still required. For MIMO QFT designs the question of optimality of the overall multivariable controller for a given plant has received little attention.…”

“…This pinning property is equivalent to aligning the directions of the offending multivariable pole or zero to the input and output subspaces orthogonal to the basis vector 0 iÀ1 1 0 nÀi  à T : It should be stated, however, that a formal understanding of the basis for which the favourable pole-zero alignment of the plant is achieved, for single and multiple RHP poles and zeros, and hence how the alleviation of design prohibitive spurious poles and zeros of the SISO plants is achieved, remains unresolved. However, as theory providing constructive bandwidth limitations for individual loop designs in NMP and unstable MIMO systems has not been realized [61], even for fully populated multivariable controller designs, one cannot determine a priori what pole-zero structure of the DPD and IPD SISO plants is possible. Therefore, the design of M and N matrices for good alignment will generally be a heuristic procedure, akin to other classical tools for multivariable design conditioning, such as RGA, which aims to provide similar features.…”

RST Controller Design by Convex Optimization Using Frequency-Domain Data

“…Many different methods can be found in the literature to tune the feedback or feedforward terms separately. An example is shown in Sidi [2002] where a combined QF T /H ∞ design technique is proposed. The classical H ∞ method is used to tune the feedback controller to minimize the maximum value of the sensitivity function and the noise amplification for a desired frequency range.…”