29 research outputs found
STABILIZATION BY ADAPTIVE FEEDBACK CONTROL FOR POSITIVE DIFFERENCE EQUATIONS WITH APPLICATIONS IN PEST MANAGEMENT
An adaptive feedback control scheme is proposed for stabilizing a class of forced nonlinear positive difference equations. The adaptive scheme is based on so-called high-gain adaptive controllers and contains substantial robustness with respect to model uncertainty as well as with respect to persistent forcing signals, including measurement errors. Our results take advantage of the underlying positive systems structure and ideas from input-to-state stability from nonlinear control theory. Our motivating application is to pest or weed control, and in this context the present work substantially strengthens previous work by the authors. The theory is illustrated with examples
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
Parameter-Dependent Lyapunov Functions and the Popov Criterion in Robust Analysis and Synthesis
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57842/1/ParDepPopovTAC1995.pd
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