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This paper reexamines the stability of uncertain closed-loop systems resulting from the nonsequential (NS) MIMO QFT design methodology. By combining the effect of satisfying both the robust stability and robust performance specifications in a NS MIMO QFT design, a proof for the stability of the uncertain closed-loop system is derived. The stability theorem proves that, subject to the satisfaction of a critical necessary and sufficient condition, the original NS MIMO QFT design methodology will provide a robustly stable closed-loop system. This necessary and sufficient condition provides a useful existence test for a successful NS MIMO QFT design. The results expose the salient features of the NS MIMO QFT design methodology. Two 2×2 MIMO design examples are presented to illustrate the key features of the stability theorem.

The problem of tracking a known reference without overshooting is of great practical importance in a number of applications. However, nonminimum phase systems have received little attention in connection with obtaining a nonovershooting response. Using state feedback, this paper develops an eigenvector placement technique to construct an invariant set which guarantees a nonovershooting step response for a class of nonminimum phase SISO systems.

SUMMARYThis paper presents a generalized formulation for multi-input multi-output (MIMO) quantitative feedback theory (QFT) based controller design and analysis, and its application to the control of the X-29 aircraft. The formulation is based on a more general control structure, where input and output transfer function matrices are included to provide additional degrees of freedom in the decentralized MIMO QFT feedback structure, that facilitates the exploitation of directions in MIMO QFT designs. The formulation captures existing design approaches for fully populated MIMO QFT controller design and provides for a directional design logic involving the plant and controller alignment and the directional properties of their multivariable poles and zeros. Horowitz's Singular-G design methodology is placed in the context of the generalized formulation and the Singular-G design for the X-29 is analysed and redesigned using nonsequential MIMO QFT and the formulation, demonstrating its utility. The results highlight a fundamental trade-off between multivariable controller directions for stability and performance in classically formulated design methodologies, elucidate the properties of Singular-G designed controllers for the X-29 and validate recent contributions to the theory for non-sequential MIMO QFT.

In the absence of plant parameter uncertainty feedforward controllers can be synthesized to achieve perfect continuous tracking. When plant has uncertainties it is, in general, impossible to achieve such perfect tracking. Investigated in this paper is the role played by feedforward controllers in the presence of plant uncertainties. We show that the use of feedforward controllers cannot improve the tracking error beyond what is achievable with a properly designed feedback loop, over all plant uncertainties. Including preview in the feedforward will not alter the situation either. We present two methods of designing robust compensators so that the tracking error due to uncertainties will be made small in some sense in the frequency domain and will have zero error in the steady state.