Computation of transfer function matrices of periodic systems

We present a numerical approach to evaluate the transfer function matrices of a periodic system corresponding to lifted state-space representations as constant systems. The proposed pole-zero method determines each entry of the transfer function matrix in a minimal zeros-poles- gain representation. A basic computational ingredient for this method is the extended periodic real Schur form of a periodic matrix, which underlies the computation of minimal realizations and system poles. To compute zeros and gains, fast algorithms are proposed, which are specially tailored to particular single-input single-output periodic systems. The new method relies exclusively on reliable numerical computations and is well suited for robust software implementations

Periodic control of the individual-blade-control helicopter rotor

Results of an investigation into methods of controller design for an individual helicopter rotor blade in the high forward-flight speed regime are described. This operating condition poses a unique control problem in that the perturbation equations of motion are linear with coefficients that vary periodically with time. The design of a control law was based on extensions to modern multivariate synthesis techniques and incorporated a novel approach to the reconstruction of the missing system state variables. The controller was tested on both an electronic analog computer simulation of the out-of-plane flapping dynamics, and on a four foot diameter single-bladed model helicopter rotor in the M.I.T. 5x7 subsonic wind tunnel at high levels of advance ratio. It is shown that modal control using the IBC concept is possible over a large range of advance ratios with only a modest amount of computational power required

Value of Information in Feedback Control

In this article, we investigate the impact of information on networked control systems, and illustrate how to quantify a fundamental property of stochastic processes that can enrich our understanding about such systems. To that end, we develop a theoretical framework for the joint design of an event trigger and a controller in optimal event-triggered control. We cover two distinct information patterns: perfect information and imperfect information. In both cases, observations are available at the event trigger instantly, but are transmitted to the controller sporadically with one-step delay. For each information pattern, we characterize the optimal triggering policy and optimal control policy such that the corresponding policy profile represents a Nash equilibrium. Accordingly, we quantify the value of information $\operatorname{VoI}_k$ as the variation in the cost-to-go of the system given an observation at time $k$. Finally, we provide an algorithm for approximation of the value of information, and synthesize a closed-form suboptimal triggering policy with a performance guarantee that can readily be implemented

Analysis, estimation and control for perturbed and singular systems for systems subject to discrete events.

"The principle investigator for this effort is Professor Alan S. Willsky, and Professor George C. Verghese is co-principal investigator."--P. [3].Includes bibliographical references (p. [20]-[25]).Final technical report for grant AFOSR-88-0032.Supported by the AFOSR. AFOSR-88-003

Resource-aware motion control:feedforward, learning, and feedback

Controllers with new sampling schemes improve motion systems’ performanc

Multiplexed Control of Smart Structure Using Piezoelectric Actuators

Active control of smart structures containing a large number of actuators and sensors presents a tradeoff between increased system performance and the cost and bulk of the required hardware and computational resources. A technique called multiplexed control offers advantages when software and hardware resources are scarce and performance specifications call for a large number of actuators and sensors. In structural control applications, in particular those using smart materials, it is often desirable to increase the number of actuators to enhance controllability.The focus of this research is to demonstrate real-time multiplexing on the hardware side of the actively controlled structure. Multiplexing effectively reduces the number of power units by sharing them among a large number of actuators according to a switching schedule. Multiplexing introduces periodicity in the closed-loop plant, requiring the use of periodic linear systems theory to tune as optimal quadratic regulator. In this thesis a multiplexed implementation is developed to control the three actuators mounted on single smart beam, where the control inputs are updated sequentially and cyclically instead of simultaneously, thus allowing the use of a single power amplifier. Focus was placed on the application of multiplexed control theory to a smart structure, including experimental procedures to obtain a plant model using system identification tools, and tuning of a discrete-time periodic quadratic regulator. An observer was also implemented. Simulations and real-time implementation validate the approac