Practical design of feedback systems with uncertain multivariable plants†

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Abstract
A previous paper was devoted to the rigorous development of an exact synthesis technique for uncertain multiple-input-output feedback systems. This paper is devoted to practical design execution, by means of two detailed 2×2 examples with large plant parameter uncertainty. The outstanding features are : (1) The problem muat be quantitative. Performance bounds must be assigned to the matrix of closed-loop. transfer functions, and the parameter uncertainty sets defined. (2) The design problem is translated into separate quantitative single-loop systems such with i1« own sets of parameter uncertainty, disturbances and performance tolerances. The solutions (compensation functions) for the single-loop problems are guaranteed to solve the multiple-input-output problem. There is no need to consider the characteristic equation of the latter or any of its other system functions. (3) There is considerable design transparency. As he proceeds, the designer can see the trade-offs between the loops, and may, if desirable, sacrifice one for the other. Also he may modify the original performance tolerances, without violating them, so as to economize on the compensation function band widths. (4) The design is tuned to the problem. The larger the uncertainty and the more narrow the tolerances, the larger the required compensation bandwidths. In the case of no uncertainty, the design emerges with no need for feedback at all.