Robust Control Design Methods

Balas and Doyle [28] formulate the problem of disturbance rejection problem for a prototype space structural system. They used a structured singular value jj, synthesis approach considering uncertainties due to unmodeled dynamics and equivalent uncertainty formulations of the performance requirements on actuator limits, disturbance rejection and sensor noise by choosing appropriate weightings. 

Joshi and Kelkar [30], have developed an iterative procedure by combining LQG type synthesis with robustness and performance analysis to design 

In this study, adaptive control algorithms have been utilized for designing active controllers for smart structure test articles. Adaptive control schemes require only a limited a priori knowledge about the system in order to be controlled. The availability of limited control force and inherent deadband and saturation effects of shape memory actuators are incorporated in the selection of the reference model. The vibration suppression properties of smart structures were successfully demonstrated by implementing the conventional model reference adaptive controllers on the smart structure test articles. The controller parameters converged to steady state values within 8 s for both direct and indirect MRACs. 

Various neural network-based adaptive control techniques were discussed in this study. A major problem in implementing neural network-based MRACs is the translation of the output error between the plant and the reference model so as to train the neural controller. A technique called iterative inversion, which inverts the neural identification model of the plant for calculating neural controller gains, has been used. Due to the real-time computer hardware limitations, the performance of neural network-based adaptive control systems is verified using simulation studies only. These results show that neural-network based MRACs can be designed and implemented on smart structures. 

A neural network-based control algorithm based on a LQ performance index which can be implemented using the ETANN chip has been developed. This formulation incorporates a priori information about the structural system. Information such as limits on the control effort and limits on the bandwidths of the sensors and actuators can be incorporated in this 

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Emits concerning controller robustness, controller performance should also be considered. Robustness metrics such as Ms, Mj, GM, and PM should be evaluated in conjunction with controller design methods, especially the model-based techniques of Chapter 12. 

The outline of this paper is as follows. First, a theoretical model of unsteady motions in a combustion chamber with feedback control is constructed. The formulation is based on a generalized wave equation which accommodates all influences of acoustic wave motions and combustion responses. Control actions are achieved by injecting secondary fuel into the chamber, with its instantaneous mass flow rate determined by a robust controller. Physically, the reaction of the injected fuel with the primary combustion flow produces a modulated distribution of external forcing to the oscillatory flowfield, and it can be modeled conveniently by an assembly of point actuators. After a procedure equivalent to the Galerkin method, the governing wave equation reduces to a system of ordinary differential equations with time-delayed inputs for the amplitude of each acoustic mode, serving as the basis for the controller design. 

The third class of techniques include a frequency-domain method based on the identification of the sensitivity function S s)) and the complementary sensitivity function T s)) from plant data or CPM of multivariable systems [140]. Robust control system design methods seek to maximize closed-loop performance subject to specifications for bandwidth and peak... 

The field of application of this method is not only robustness analysis but also controller design. In this case the set of stabilizing controller parameters is determined. All controllers from this set stabilize the plant, thus, allowing to incorporate further design criteria to select the final controller. The task is to determine a controller which robustly F-stabilizes the system for the entire operating domain. 

A more comprehensive model-based design method. Internal Model Control IMC), was developed by Morari and coworkers (Garcia and Morari, 1982 Rivera et al., 1986). The IMC method, like the DS method, is based on an assumed process model and leads to analytical expressions for the controller settings. These two design methods are closely related and produce identical controllers if the design parameters are specified in a consistent manner. However, the IMC approach has the advantage that it allows model uncertainty and tradeoffs between performance and robustness to be considered in a more systematic fashion. 

Therefore, it is important in quality control measurements to use a consistent and reproducible sample preparation technique. In designing quality control methods, the robustness of the method to external factors such as sample preparation must be investigated. Using consistent sample masses is very important in producing comparable TGA data. 

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