Improvement of parametric stability margin under pole assignment

In this paper, the improvement of the parametric stability margin of state-space uncertain systems via a maximization formulation under the constraints of pole assignment is investigated. The class of systems considered is where the uncertainty may be modeled as the, possibly nonlinear, variation of a parameter appearing in the entries of the system and input matrices. The continuity and differentiability properties of the stability margin are discussed. A gradient-based approach is presented for the improvement of the stability margin and a compact formula to compute the gradient is provided. Numerical examples are used to demonstrate the effectiveness of the approach.published_or_final_versio

Regelungstheorie

[no abstract available

Conditions on the boundary of the zero set and application to stabilization of systems with uncertainty

AbstractWe describe an analytic method for finding the location of the zero set of a vector-valued function which depends on m real variables and n complex parameters. We apply the method to robust stabilization of multivariable linear feedback systems. We find exact measures of the extent of permissible perturbations in the plant and/or the compensator that maintain feedback stability

Control Strategies for Complex Systems for Use in Aerospace Avionics

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryAir Force Office of Scientific Research (AFSC) / AF-AFOSR 78-363

Observer synthesis for the T-S fuzzy system with uncertainty and output disturbance

[[abstract]]The paper proposes a novel fuzzy observer synthesis for the Takagi-Sugeno (T-S) fuzzy system with uncertainty and output disturbance. First, an augmented fuzzy model is built by integrating the system state and the output disturbance into a new variable. Then, based on Lyapunov theory and LMIs tools, two main theorems are derived for particular and general cases of fuzzy systems, respectively. In each main theorem, three key conditions are proposed, under which the fuzzy observer is synthesized to estimate the system state and the output disturbance simultaneously. According to the main theorems, a methodical procedure for the fuzzy observer synthesis is also provided. Finally, the effectiveness of the observer is demonstrated by a numerical example.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙

Performance-Driven Robust Identification and Control of Uncertain Dynamical Systems

The grant DEFG02-97ER13939 from the Department of Energy has supported our research program on robust identification and control of uncertain dynamical systems, initially for the three-year period June 15, 1997-June 14, 2000, which was then extended on a no-cost basis for another year until June 14, 2001. This final report provides an overview of our research conducted during this period, along with a complete list of publications supported by the Grant. Within the scope of this project, we have studied fundamental issues that arise in modeling, identification, filtering, control, stabilization, control-based model reduction, decomposition and aggregation, and optimization of uncertain systems. The mathematical framework we have worked in has allowed the system dynamics to be only partially known (with the uncertainties being of both parametric or structural nature), and further the dynamics to be perturbed by unknown dynamic disturbances. Our research over these four years has generated a substantial body of new knowledge, and has led to new major developments in theory, applications, and computational algorithms. These have all been documented in various journal articles and book chapters, and have been presented at leading conferences, as to be described. A brief description of the results we have obtained within the scope of this project can be found in Section 3. To set the stage for the material of that section, we first provide in the next section (Section 2) a brief description of the issues that arise in the control of uncertain systems, and introduce several criteria under which optimality will lead to robustness and stability. Section 4 contains a list of references cited in these two sections. A list of our publications supported by the DOE Grant (covering the period June 15, 1997-June 14, 2001) comprises Section 5 of the report

Two dimensional agonistic control

The conventional method of precise multiple-axis motion control entails use of a multiple axis positioning system with each axis carrying not only the workpiece but also the positioning system of the remaining axes. The resultant structure is heavy, sluggish, and expensive. An alternative positioning technique is being investigated in which the motion of the workpiece is controlled by pulling it with tendons, each of which has its own actuator. Since the actuators can be mounted on the base of the structure instead of being carried by motion system of the other axes, they can be relatively large and powerful without the need for a massive structure such as is found in a conventional motion control system. This method of control is given the appellation agonistic, based on the usages of the word suggesting tension or a contest. Agonistic control system can be used for low cost accurate positioning of workpiece. The control task can be moving the workpiece from one point to another point and kept there or tracking a given trajectory. While the workpiece moves, the tendons should be always kept in tension. In this thesis, the model of two dimensional agonistic control (in the case of tendons of infinite elastic modulus) is established. It leads to a nonlinear multi-variable control problem. Based on this nonlinear model, a full-state feedback control law is synthesized. It is composed of two parts. The first part is a feedforward control to cancel the nonlinear dynamics. The second part is a PD control term which requires velocity information. In the practice, velocity measurement may be contaminated by noise. In order of only using position measurement in the control law, a nonlinear observer is designed to provide the velocity information. Numerical simulation is performed to verify the ability of the proposed control law. In reality, the tendon has some elasticity. This finite elasticity, if not accounted for, can render the closed-loop system unstable. The investigation shows that the effect of elastic tendons can be compensated for by appropriately modifying the control law designed for inelastic tendons. In particular, the control law is synthesized using the singular perturbation method. It consists of a fast control and a slow control. The fast control is used to stablize the oscillations incurred by the finite elasticity of the tendon. The slow control drives the system to track the desired trajectory. Robustness of the controller is enhanced by using sliding mode control. In the chapter 4, the design of observer in the elastic case is addressed. Linear uncertain system theory is used. The observer is globally stable. The use of decentralized control scheme makes very simple the controller design and reduces the computational complexity. It is very useful for real time agonistic control. A design approach is presented for the decentralized control scheme. A simple linear second order model is used instead of complex nonlinear model used in centralized version. In this approach, the tension in each tendon is treated as disturbance, estimated by an observer, to be compensated