Robust controls with structured perturbations

This final report summarizes the recent results obtained by the principal investigator and his coworkers on the robust stability and control of systems containing parametric uncertainty. The starting point is a generalization of Kharitonov's theorem obtained in 1989, and its generalization to the multilinear case, the singling out of extremal stability subsets, and other ramifications now constitutes an extensive and coherent theory of robust parametric stability that is summarized in the results contained here

Robust control of systems with real parameter uncertainty and unmodelled dynamics

During this research period we have made significant progress in the four proposed areas: (1) design of robust controllers via H infinity optimization; (2) design of robust controllers via mixed H2/H infinity optimization; (3) M-delta structure and robust stability analysis for structured uncertainties; and (4) a study on controllability and observability of perturbed plant. It is well known now that the two-Riccati-equation solution to the H infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H infinity controllers if the optimal H infinity norm or gamma, an upper bound of a suboptimal H infinity norm, is given. In this research, we discovered some useful properties of these H infinity Riccati solutions. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H infinity norm. We also set up a detailed procedure for applying the H infinity theory to robust control systems design. The desire to design controllers with H infinity robustness but H(exp 2) performance has recently resulted in mixed H(exp 2) and H infinity control problem formulation. The mixed H(exp 2)/H infinity problem have drawn the attention of many investigators. However, solution is only available for special cases of this problem. We formulated a relatively realistic control problem with H(exp 2) performance index and H infinity robustness constraint into a more general mixed H(exp 2)/H infinity problem. No optimal solution yet is available for this more general mixed H(exp 2)/H infinity problem. Although the optimal solution for this mixed H(exp 2)/H infinity control has not yet been found, we proposed a design approach which can be used through proper choice of the available design parameters to influence both robustness and performance. For a large class of linear time-invariant systems with real parametric perturbations, the coefficient vector of the characteristic polynomial is a multilinear function of the real parameter vector. Based on this multilinear mapping relationship together with the recent developments for polytopic polynomials and parameter domain partition technique, we proposed an iterative algorithm for coupling the real structured singular value

Linear quadratic control for systems with structured uncertainty

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1991.Includes bibliographical references (leaves 93-96).by Joel S. Douglas.M.S

Asymmetric Stability Robustness Bounds for Uncertain Linear Systems with Arst-order Lyapunov Method

Mechanical Engineerin

Stability analysis of a phase plane control system

Many aerospace attitude control systems utilize a phase plane control scheme which includes nonlinear elements such as dead zone and ideal relay. Nonlinear control techniques such as pulse width modulation (PWM), describing functions, and absolute stability are implemented to determine stability. To evaluate phase plane control robustness, stability margin prediction methods must be developed. While PWM has been used to predict stability margins, in this research, describing functions and absolute stability are extended to predict stability margins. Time domain simulations demonstrate all techniques yield conservative gain margin results. A constrained optimization approach is also used to design flex filters for roll control. The design goal is to optimize vehicle tracking performance while maintaining adequate stability margins. Two filters are designed in this thesis; one meets PWM stability margin specifications and the other holds for Popov stability

Effects of torsional dynamics on nonlinear generator control

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1995.Includes bibliographical references (p. 146-147).by Eric H. Allen.M.S

Robust stability analysis of active voltage control for high-power IGBT switching by Kharitonov's theorem

The main idea of active voltage control (AVC) is to employ classic feedback-control methods forcing the IGBT collector voltage transient to follow a predefined trajectory. This feedback control of IGBTs has great advantages in guaranteeing that IGBTs remain in safe operating area (SOA), restricting EMI, mitigating the voltage/current stress, minimizing/predicting their power losses, and balancing voltages of IGBTs in series. Inevitably, however, AVC introduces stability issues. Based on the assumption that accurate IGBT small-signal model parameters are available, an analogue proportional-derivative and multiloop feedback control was proposed to achieve stable performance in previous work. Due to nonlinearities and uncertainties in IGBT parameters, previous stability analysis methods have important limitations. This work uses Kharitonov's theorem during the IGBT controlled turn-off to assess the system's stability and guide the AVC design to account for model uncertainties and varying parameters. We conducted experiments to investigate the system's robust stability due to these uncertainties in the IGBT parameters, which confirm the validity of the proposed theoretical analysis. With the use of wide bandwidth op-amps, it is shown that the feedback design may be simplified

Robust control with structured perturbations

Two important problems in the area of control systems design and analysis are discussed. The first is the robust stability using characteristic polynomial, which is treated first in characteristic polynomial coefficient space with respect to perturbations in the coefficients of the characteristic polynomial, and then for a control system containing perturbed parameters in the transfer function description of the plant. In coefficient space, a simple expression is first given for the l(sup 2) stability margin for both monic and non-monic cases. Following this, a method is extended to reveal much larger stability region. This result has been extended to the parameter space so that one can determine the stability margin, in terms of ranges of parameter variations, of the closed loop system when the nominal stabilizing controller is given. The stability margin can be enlarged by a choice of better stabilizing controller. The second problem describes the lower order stabilization problem, the motivation of the problem is as follows. Even though the wide range of stabilizing controller design methodologies is available in both the state space and transfer function domains, all of these methods produce unnecessarily high order controllers. In practice, the stabilization is only one of many requirements to be satisfied. Therefore, if the order of a stabilizing controller is excessively high, one can normally expect to have a even higher order controller on the completion of design such as inclusion of dynamic response requirements, etc. Therefore, it is reasonable to have a lowest possible order stabilizing controller first and then adjust the controller to meet additional requirements. The algorithm for designing a lower order stabilizing controller is given. The algorithm does not necessarily produce the minimum order controller; however, the algorithm is theoretically logical and some simulation results show that the algorithm works in general

Robust control design with real parameter uncertainty using absolute stability theory

The purpose of this thesis is to investigate an extension of mu theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed mu and absolute stability theory. In particular, it is shown that the upper bounds for mixed mu are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed for several nonlinearities and stability multipliers using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. For controller synthesis, these stability conditions are used to form an overbound of the H2 performance objective. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered. A numerical algorithm is developed to design robust controllers that minimize the bound on an H2 cost functional and satisfy an analysis test based on the Popov stability multiplier. The controller and multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K procedure of mu synthesis. Several benchmark problems and experiments on the Middeck Active Control Experiment at M.I.T. demonstrate that these controllers achieve good robust performance and guaranteed stability bounds