Control design with transfer functions: An application illustration
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This paper provides a tutorial overview of the linear quadratic Gaussian with loop transfer recovery (LQG/LTR) design procedure for linear multivariable feedback systems. LQR/LTR is interpreted as the solution of a specific weighted H-squared tradeoff between transfer functions in the frequency domain. Properties of this solution are examined for both minimum-phase and nonminimum-phase systems. This leads to a formal weight augmentation procedure for the minimum-phase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights. While such arbitrary specifications are not possible for nonminimum-phase problems, a direct relationship between weights and sensitivities is developed for nonminimum-phase SISO and certain nonminimum-phase MIMO cases which guides the weight selection process.
High gain, high frequency flexible responses in gimbaled multibody systems are discussed. Their origin and physical significance are described in terms of detailed mass and stiffness modeling at actuator/sensor interfaces. Guyan Reduction, Generalized Dynamic Reduction, inadequate mass modeling detail, as well as system mode truncation, are shown to suppress the high gain high frequency response and thereby lose system flexibility important for stability and performance predictions. Model validation by modal survey testing is shown to risk similar loss of accuracy. Difficulties caused by high frequency responses in component mode simulations, such as DISCOS, and also linearized system mode simulations, are described, and approaches for handling these difficulties are discussed.
The output of this task will be a program plan which will delineate how MSFC will support and implement its portion of the Inter-Center Computational Controls Program Plan. Another output will be the results of looking at various multibody/multidegree of freedom computer programs in various environments.
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The state-space H2/H(infinity) theory is employed to develop a design procedure that addresses the performance-robustness problem. A numerical example is used to illustrate both the advantages and limitations of the procedure and how it compares to linear-quadratic-Gaussian loop transfer recovery (LQG/LTR). A less rigorous procedure that compares favorably to the LQG/LTR is also constructed.
A new method for targeted robustness optimization is presented. This method allows the analyst to 'target' the most critical performance parameter (or family of design requirements with almost the same criticality) for enhanced protection from uncertainties in the model. To create this protection, this method uses knowledge about the uncertainties in some of the parameters of the model - this information is usually available to the structural analyst. The power of the targeted robustness method is demonstrated numerically using an active damping example. The results show that the most critical damping ratio is protected - its sensitivity to the uncertainties is far below those of non-critical damping ratios.
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