Integrated optimum design of structures and control systems is studied by using H
 2 and $$ H_{\infty }$$
 robust control formulations. It is derived that conventional simultaneous optimization approach by using these robust control laws can be approximated by a decoupled optimization approach in which the structures are optimized by shaping the structural singular values and then the controllers can be designed, namely, decoupled, sequential or successive design approach. It is shown that the proposed decoupled optimization approach can be used to design optimum robust structures and has certain advantages over the conventional simultaneous optimization procedures such as it avoids the drawbacks of pure robust control laws and faster, especially if the number of degrees of freedom (DOF) of the associated structure is large. The bounds for achievable robustness measures are also obtained. Following, simultaneous and decoupled optimization approaches are applied to active control of two structures. The optimization results are presented, and it is concluded that the proposed decoupled optimization approach yields the achieved global minimum much faster than the simultaneous optimization approach.

Decoupled approach to integrated optimum design of structures and robust control systems

A spacecraft-like optical interferometry system is investigated experimentally over several different optimized controlled structures configurations. Configurations represent common and not-so-common approaches to mitigating pathlength errors induced by disturbances of two different spectra. Results show that an optimized controlled structure for low frequency broadband disturbances achieves modest performance gains over a mass equivalent regular structure, while an optimized structure for high frequency narrow band disturbances is four times better in terms of rms pathlength. These results are predictable given the nature of the physical system and the optimization design variables. Fundamental limits on controlled performance are discussed based on average system transfer function gains and system phase loss.

Experimental investigation of optimized precision optical controlled structures

A novel Integrated Robust Optimal Design (IROD) methodology is presented in this work which combines a traditional sensitivity theory with relatively new advancements in Bilinear Matrix Inequality (BMI) constrained optimization problems. IROD provides the least conservative approach for robust control synthesis. The proposed methodology is demonstrated using numerical examples of integrated control-structure design problem for combine harvester header and excavator linkages. The IROD methodology is compared with the state of the art sequential design method using the two application examples, and the results show that the proposed methodology provides a viable alternative for robust controller synthesis and often times offers even a better performance than competing methods. Although this method requires linearization of nonlinear system at each system parameter optimization step, a technique to linearized Differential Algebraic Equations (DAE) is presented which allows use of symbolic approach for linearization. This technique avoids repetitive linearizations. For the nonlinear systems with parametric uncertainties which can not be linearized at operating points, a new methodology is proposed for robust feedback linearization using sensitivity dynamics-based formulation. The feedback linearization approach is used for systems with augmented sensitivity dynamics and used to refine control input to improve robustness. The method is demonstrated using an example of a position tracking control of a hydraulic actuator. The robustness of controller design is demonstrated by considering variations in fluid density parameter. The results show that the proposed methodology improves robustness of the feedback linearization to parametric variations.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=5018&context=etd

Integrated Robust Optimal Design (IROD) via sensitivity minimization

Integrated Robust Optimal Design Using Bilinear Matrix Inequality Approach Via Sensitivity Minimization

This paper introduces a methodology for simultaneously designing a minimum weight structure and robust active controls to reduce vibrations in an aircraft structure due to external disturbances. The design problem is posed as a mathematical optimization problem with the principal objective function being the weight of the structure. The robust control design is achieved by specifying appropriate constraints on singular values of the closed-loop transfer matrices. The control approach selected for this purpose is based on designing a dynamic compensator that simultaneously minimizes the upper bound of a quadratic performance index H2 and the H∞ norm of a disturbance transfer function of a multi-input/multi-output system. The controller can tolerate both real parameter uncertainty in the structural frequencies and damping, and unmodelled dynamics. The design variables are the crosspsectional areas of the structure and the parameters used in the design of a control system. The method was applied to three structures idealized with membrane elements, shear panels and bar elements with embedded actuators and sensors simulating an active flexible aircraft wing.

N. S. Khot

Papers

Optimum structural design and robust active control using singular value constraints