Performance issues in the individual channel desigm of 2-input 2-output systems Part 3. Non-diagonal control and related issues

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Abstract
A new applications-oriented approach—individual channel design (ICD)—to multivariable feedback control—was presented in an earlier paper (O'Reilly and Leithead 1991). This paper is the final part of a three-part investigation into the performance issues raised by ICD for 2-input 2-output strongly coupled multivariable systems. Parts 1 and 2 (Leithead and O'Reilly 1991, 1992 a) respectively show that fixed stabilizing controllers exist regardless of the structure of the multivariable system and that the use of phase and gain margins and SISO Nyquist-Bode loop shaping design is justified. The three-part series of papers also develops an analytic framework for investigating and understanding the potential and limitations of the feedback design of any linear time-invariant controller. The main results of this final part are threefold. First, restriction to diagonal feedback control in ICD (O'Reilly and Leithead 1991) or elsewhere is not a significant restriction on performance. Second, non-diagonal feedback control cannot improve system structure beyond that attainable by swapping the assignment of control inputs to plant outputs. Third, lack of robustness is not alleviated by either system pre-compensation or post-compensation.

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