Optimal control with structure constraints and its application to the design of passive mechanical systems

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Page 214 blank.Includes bibliographical references.Structured control (static output feedback, reduced-order control, and decentralized feedback) is one of the most important open problems in control theory and practice. In this thesis, various techniques for synthesis of structured controllers are surveyed and investigated, including H2 optimization, H[infinity] optimization, L1 control, eigenvalue and eigenstructure treatment, and multiobjective control. Unstructured control-full- state feedback and full-order control-is also discussed. Riccati-based synthesis, linear matrix inequalities (LMI), homotopy methods, gradient- and subgradientbased optimization are used. Some new algorithms and extensions are proposed, such as a subgradient-based method to maximize the minimal damping with structured feedback, a multiplier method for structured optimal H2 control with pole regional placement, and the LMI-based H2/H[infinity]/pole suboptimal synthesis with static output feedback. Recent advances in related areas are comprehensively surveyed and future research directions are suggested. In this thesis we cast the parameter optimization of passive mechanical systems as a decentralized control problem in state space, so that we can apply various decentralized control techniques to the parameter design which might be very hard traditionally. More practical constraints for mechanical system design are considered; for example, the parameters are restricted to be nonnegative, symmetric, or within some physically-achievable ranges. Marginally statable systems and hysterically damped systems are also discussed. Numerical examples and experimental results are given to illustrate the successful application of decentralized control techniques to the design of passive mechanical systems, such as multi-degree-of-freedom tuned-mass dampers, passive vehicle suspensions, and others.by Lei Zuo.S.M

Element and system design for active and passive vibration isolation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, February 2005.Includes bibliographical references (p. 277-294).This thesis focusses on broadband vibration isolation, with an emphasis on control of absolute payload motion for ultra-precision instruments such as the MIT/Caltech Laser-Interferometric Gravitational Wave Observatory (LIGO), which is designed to measure spatial strains on the order of 10-²¹. We develop novel passive elements and control strategies as well as a framework for concurrent design of the passive and active elements of single-stage and multi-stage isolation systems. In many applications, it is difficult to construct passive isolation systems compliant enough to achieve specifications on low-frequency ground transmission without introducing hysteresis as well as high-frequency transmission resonances. We develop and test a compliant support that employs a post-buckled structure in con- junction with a compliant spring to attain a low-frequency, low-static-sag mount in a compact package with a large range of travel and very clean dynamics. Most passive damping techniques increase ground transmission at high frequency, but tuned-mass dampers are decoupled from the ground. We explore the tuned-mass damper as a passive realization of the skyhook damper, obtain the optimal designs for multiple-SDOF systems of dampers, propose the concept of a multi-DOF damper, and show that MDOF dampers that couple translational and rotational motion have the potential to provide performance many times better than that traditional tuned-mass dampers. Active control can be used to improve low-frequency performance, but high-gain control can amplify sensor and actuator noise or cause instability. We study several control strategies for uncertain plants with high-order dynamics.(cont.) In particular, we develop a novel control strategy, "model-reaching" adaptive control, that drives the system onto a dynamic manifold defined directly in terms of the states of the target. The method can be used to robustly increase the apparent compliance of an isolation mount and maintain a -40 dB/decade roll-off above the resulting corner frequency.by Lei Zuo.Ph.D