Cevat Gokcek

An LQR/LQG theory for systems with saturating actuators

An extension of the LQR/LQG methodology to systems with saturating actuators, referred to as SLQR/SLQG, where S stands for saturating, is obtained. The development is based on the method of stochastic linearization, whereby the saturation is replaced by a gain, calculated as a function of the variance of the signal at its input. Using the stochastically linearized system and the Lagrange multiplier technique, solutions of the SLQR/SLQG problems are derived. These solutions are given by standard Riccati and Lyapunov equations coupled with two transcendental equations, which characterize both the variance of the signal at the saturation input and the Lagrange multiplier associated with the constrained minimization problem. It is shown that, under standard stabilizability and detectability conditions, these equations have a unique solution, which can be found by a simple bisection algorithm. When the level of saturation tends to infinity, these equations reduce to their standard LQR/LQG counterparts. In addition, the paper investigates the properties of closed-loop systems with SLQR/SLQG controllers and saturating actuators. In this regard, it is shown that SLQR/SLQG controllers ensure semi-global stability by appropriate choice of a parameter in the performance criterion. Finally, the paper illustrates the techniques developed by a ship roll damping problem.

An LQG approach to systems with saturating actuators and anti-windup implementation

This paper extends the LQG design methodology to systems with saturating actuators and shows that resulting linear controllers do not require an anti-windup implementation.

SLQR/SLQG: an LQR/LQG theory for systems with saturating actuators

An extension of the LQR/LQG methodology to systems with saturating actuators, referred to as SLQR/SLQG, is obtained. The development is based on the method of stochastic linearization. Using this method and the Lagrange multiplier technique, solutions to the SLQR and SLQG problems are derived. These solutions are given by Riccati and Lyapunov equations coupled with two transcendental equations. It is shown that, under standard stabilizability and detectability conditions, these equations have a unique solution, which can be found by a simple bisection algorithm. When the level of saturation tends to infinity, these equations reduce to their standard LQR/LQG counterparts.

Disturbance rejection in control systems with saturating actuators

Addresses the disturbance rejection problem in control systems with saturating actuators by using the method of stochastic linearization. The disturbance is assumed to be white noise and the performance measure considered is the output variance. Both analysis and synthesis problems are investigated. In the analysis part, a method is developed to predict disturbance rejection quality of a given control system. In the synthesis part, a systematic controller design method that achieves suboptimal disturbance rejection is presented.

Analysis of H/sub 2/ performance robustness with respect to disturbance model uncertainty

A method for evaluating the H/sub 2/ performance robustness of an LTI SISO feedback system with respect to parametric uncertainties in the disturbance model is developed. The disturbance is assumed to be colored noise obtained by passing standard white noise through a linear finite-dimensional filter with uncertain coefficients. The method is based on the converse of a spectral factorization problem. The main result obtained is an explicit formula for the output variance in terms of the uncertain parameters of the coloring filter. This result is illustrated on a ship roll stabilization problem.

Damping of idle engine speed oscillations using a reversible alternator

We consider the problem of damping the speed oscillations of an automotive engine crankshaft, using a reversible alternator, with a focus on the design of the controller. The reversible alternator is used to apply a control torque to the crankshaft that will improve the uniformity of its speed. One would then potentially use a lighter flywheel, or remove it altogether, thereby reducing engine size and weight. We have characterized the controllers that meet a variety of possibly competing performance specifications, leading to design charts. These charts are level curves of various controller performance metrics in a two-dimensional plane of controller design parameters. Simulation results suggest that engine speed oscillations can be substantially reduced by this method.

AN LQG APPROACH TO SYSTEMS WITH SATURATING ACTUATORS AND ANTI-WINDUP IMPLEMENTATION

Abstract This paper extends the LQG design methodology to systems with saturating actuators and shows that resulting linear controllers do not require an anti-windup implementation.

Robustness of control systems with respect to disturbance model uncertainty

Abstract The problem of control system performance robustness with respect to disturbance model uncertainty is addressed. The performance index considered is the output variance. The disturbance model is assumed to be a linear filter with uncertain parameters driven by standard white noise. Both analysis and synthesis problems are investigated. In the analysis part, an analytical method for investigating performance robustness is presented. In the synthesis part, several methods for designing controllers with guaranteed robustness are proposed. The development is motivated and illustrated by an aircraft example.

A method for evaluating H/sub 2/-performance robustness with respect to disturbance model uncertainty

A method for evaluating H/sub 2/-performance robustness of a linear time-invariant feedback system with respect to parametric uncertainties in disturbance model is developed.