Nonlinear stochastic controllers for semiactive and regenerative structural systems, with guaranteed quadratic performance margins

In many applications of vibration control, the circumstances of the application impose constraints on the energy available for the actuation of control forces. Semiactive dampers (i.e., viscous dampers with controllable coefficients) constitute the simplest example of such actuation in structural control applications. Regenerative Force Actuation (RFA) networks are an extension of semiactive devices, in which mechanical energy is first converted to electrical energy, which is then dissipated in a controllable resistive network. A fairly general class of semiactive and regenerative systems can be characterized by a differential equation which is bilinear (i.e., linear in state, linear in control input, but nonlinear in both). This paper presents a general approach to bilinear feedback control system design for semiactive and regenerative systems, which is analytically guaranteed to out-perform optimal linear viscous damping in stationary stochastic response, under the familiar Quadratic Gaussian performance measure. The design for full-state feedback and for the more practical case of noise-corrupted and incomplete measurements (i.e., output feedback) are separately discussed. Variants of the theory are shown to exist for other quadratic performance measures, including risk-sensitive and multi-objective frameworks. An illustrative application to civil engineering is presented

Robust Stochastic Design of Linear Controlled Systems for Performance Optimization

This study discusses a robust controller synthesis methodology for linear, time invariant systems, under probabilistic parameter uncertainty. Optimization of probabilistic performance robustness for [script H]_2 and multi-objective [script H]_2 measures is investigated, as well as for performance measures based on first-passage system reliability. The control optimization approaches proposed here exploit recent advances in stochastic simulation techniques. The approach is illustrated for vibration response suppression of a civil structure. The results illustrate that, for problems with probabilistic uncertainty, the explicit optimization of probabilistic performance robustness can result in markedly different optimal feedback laws, as well as enhanced performance robustness, when compared to traditional “worst-case” notions of robust optimal control

Reliability-Based Performance Objectives and Probabilistic Robustness in Structural Control Applications

A reliability-based structural control design approach is presented that optimizes a control system explicitly to minimize the probability of structural failure. Failure is interpreted as the system’s state trajectory exiting a safe region within a given time duration. This safe region is bounded by hyperplanes in the system state space, each of them corresponding to an important response quantity. An efficient approximation is discussed for the analytical evaluation of this probability, and for its optimization through feedback control. This analytical approximation facilitates theoretical discussions regarding the characteristics of reliability-optimal controllers. Versions of the controller design are described for the case using a nominal model of the system, as well as for the case with uncertain model parameters. For the latter case, knowledge about the relative plausibility of the different possible values of the uncertain parameters is quantified through the use of probability distributions on the uncertain parameter space. The influence of the excitation time duration on feedback control design is discussed and a probabilistic treatment of this time duration is suggested. The relationship to H_2 i.e., minimum variance controller synthesis is also examined

Probabilistically robust nonlinear design of control systems for base-isolated structures

A stochastic-simulation-based nonlinear controller design for base-isolation systems is discussed in this study. The performance objective is the maximization of structural reliability, quantified as the probability, based on the available information, that the structural response trajectory will not exceed acceptable thresholds. A simulation-based approach is implemented for evaluation of the performance of the controlled system. This approach explicitly takes into account nonlinear characteristics of the structural response and the control law in the design process. A realistic probabilistic model for representation of near-fault ground motions is adopted in the design stage. The variability of future earthquake events is addressed by incorporating a probabilistic description for the ground-motion model parameters, leading to a design approach that is robust to probabilistic uncertainty. The methodology is illustrated through application to the base-isolated benchmark building with elastomeric and friction pendulum isolators and an array of regenerative force actuators. Skyhook control implementation is considered and an efficient scheme is presented for the clipping of the control forces in order to satisfy the actuator force constraints. The performance of the controlled system is evaluated under seven earthquake records using a number of metrics. Comparison with the performance of a similar network of viscous dampers is also discussed