Two-degree-of-freedom design method of LQI servo systems: Use of frequency-dependent weighting matrices for sensitivity reduction

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Two-degree-of-freedom design method of LQI servo systems: Use of frequency-dependent weighting matrices for sensitivity reduction

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Recently, the present authors proposed a new method to design two-degree-of-freedom robust servo systems for step references and step disturbances. In this method, the tracking characteristics for step references are determined optimally with respect to a quadratic-integral performance index, while the feedback characteristics for step disturbances are determined also optimally with respect to another quadratic-integral performance index. The paper extends these results by introducing frequency-dependent weighting matrices into the latter performance index. By employing appropriate frequency-dependent weighting matrices, some sort of loop-shaping can be achieved for the sensitivity characteristics, and thus more design freedom is obtained. In particular, loop-shaping ability and tuning ability can be separated in some sense. A numerical example is also studied to illustrate the results.

Inspec keywords: linear quadratic control; feedback; performance index; sensitivity; control system synthesis; servomechanisms; robust control; matrix algebra; frequency-domain synthesis

Other keywords: loop-shaping; feedback characteristics; LQI servo systems; sensitivity reduction; step disturbances; frequency-dependent weighting matrices; quadratic-integral performance index; step references; 2-DOF robust servo system design; tracking characteristics

Subjects: Optimal control; Algebra; Stability in control theory; Control system analysis and synthesis methods

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