Linear Quadratic Gaussian Regulator Research Articles

Stochastic robustness synthesis applied to a benchmark control problem

AbstractStochastic robustness synthesis is used to find compensators that solve a benchmark problem. The synthesis minimizes a robustness cost function that is the weighted quadratic sum of stochastic robustness metrics. These metrics — probability of instability, probability of actuator saturation, and probability of settling time violation — are estimated using Monte Carlo analysis. A simple search method minimizes the robustness cost by selecting values for the design parameters of a linear quadratic Gaussian regulator. The resulting compensators are robust, require low actuator authority, and compare well with previous designs.

Polynomial LQG regulator design for general system configurations

A polynomial-equation approach to the linear quadratic Gaussian (LQG) regulation problem for a general system configuration is presented. The solution is given in terms of a left-spectral factorization plus a pair of bilateral Diophantine equations. The resulting control-design procedure is based on an innovations representation of the system. This can be obtained from a physical description by solving, via polynomial equations, a minimum mean-square error filtering problem. The use in cascade of the above two procedures allows one to generalize previous polynomial design results to general system configurations. >

Structure/control design synthesis of active flutter suppression system by goal programming

The simultaneous design of the structure and control for a typical wing section with a trailing control surface is considered. Since the original structure usually has inadequate dynamic characteristics for active control, design parameters must be optimally modified. Full-state feedback control gains are designed using the linear quadratic Gaussian regulator theory at the design airspeed; this is the only control design parameter. A typical wing section with a trailing control surface is examined as a design example, and then both structure and control design parameters are optimized in accordance with the following prioritized design requirements: 1) the flutter speed of an initial open-loop system is maintained, 2) the stability characteristics of a closed-loop system are obtained over a wide range of flight speed, 3) the control surface deflection angle is restrained, and 4) the degree of structural design changes is minimized. The sequential goal programming method is successfully applied to optimize these multidisciplinary design requirements.

An experiment in state space control of a simply supported plate excited by steady disturbances

Experimental results of an active vibration control experiment on a simply supported plate are presented. A linear quadratic Gaussian (LQG) regulator control design is implemented to reject steady disturbances of the plate's fundamental mode. A discussion of the control law is provided. Performance of a four-mode controller is demonstrated for harmonic, narrow-band, and broadband point-force disturbances. Typical reductions in the fundamental mode amplitude were up to 60 dB at the disturbance center frequencies. Results are presented in both time domain and frequency domain format. The digital controller was implemented on a transputer-based parallel processing system for enhanced computational performance. The initial sample speeds obtained with this system were up to eight times faster than the controller hardware previously available. [Work supported by DARPA/ONR.]

The LQG optimal regulation problem for systems with perfect measurements: explicit solution, properties, and application to practical designs

The continuous-time stationary linear-quadratic-Gaussian (LQG) optimal regulation problem is considered where the measurements are free of white noise components. A simple direct solution in the s-domain is derived for the optimal controller for general linear, time-variant right-invertible or left-invertible systems. The explicit expressions that are found for the controller transference and for the regulator return-ratio matrix can be used to obtain a practical suboptimal design in the s-domain. These expressions are applied to derive simple conditions for the precise recovery of the return-ratio matrix of the LQG regulator.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the influence of noise on jump linear systems

Jump linear systems are considered in a random environment where they are subject to additive and multiplicative noises. Stochastic notions of stabilizability and detectability are introduced to characterize the asymptotic behavior of the optimal jump linear quadratic Gaussian regulator and a dual Kalman filter.

The multiple linear quadratic gaussian problem

In this paper we define and solve the multiple linear quadratic gaussian (LQG) problem for discrete-time systems using Salukvadze's ideal point method which treats dynamic, but deterministic, multicriteria optimization problems. The solution consists in designing a scalar regulator where the weighting matrices are replaced by the sums of their counterparts in the individual criteria. The resulting control is optimal, in the sense that it minimizes the difference between the cost of the implemented policy from the cost that would occur if we optimized each criterion separately and added the outcomes. All the nice properties of the scalar LQG regulator are enjoyed by the multicriteria regulator as well. Extension to the continuous-time case is straightforward, yielding identical results.

Time-domain stability robustness measures for linear regulators

The stability robustness aspect of linear systems is analyzed in the time domain. A bound on the perturbation of an asymptotically stable linear system is obtained to maintain stability using Liapunov matrix equation solution. The resulting bound is shown to be an improved upper bound over the ones recently reported in the literature. The proposed methodology is then extended to Linear Quadratic (LQ) and Linear Quadratic Gaussian (LQG) regulators. Examples given include comparison with an aircraft control problem previously analyzed.

A Globally Convergent Recursive Adaptive LQG Regulator

Time-varying recursive Riccati equations are exploited for a globally convergent discrete-time adaptive regulator for a fixed but unknown plant. With the addition of sufficiently rich perturbations for consistent parameter estimation, the controller is asymptotically the optimal regulator in a linear, quadratic Gaussian (LQG) sense with external perturbation signals.The scheme has advantages over globally convergent minimum variance based schemes in that there is a more direct trade-off between control energy and tracking error. For nonminimum phase plants, the scheme has an advantage of computational simplicity over globally convergent schemes based on solving Bezoutian equations for pole assignment, in that the Riccati equation is easier to update at each iteration than the solution of a Bezout equation.

Pitch control system for large-scale wind turbines

The purpose of this analysis is to study the design of a pitching blade segment control system for the NASA-DOE MOD 0 wind turbine to alleviate some of the problems associated with shear, tower shadow, and gravity phenomena, such as shortened lifetime and noise generation. The classical linear quadratic Gaussian optimal regulator approach is used in the control formulation. A quasisteady aerodynamic analysis incorporating wind shear and tower shadow is utilized. An equivalent hinge model describes the turbine structural dynamics. The study shows that the proposed control system can provide significant vibration and noise reduction as well as a cleaner power signal, better gust response, and increased annual energy output.

Optimal feedback slewing of flexible spacecraft

A method is presented for maneuvering a flexible spacecraft from one position to another while leaving an arbitrary number of bending modes inactive at the end of the maneuver. The method combines standard fixedtime linear quadratic Gaussian regulator control theory with a modal decomposition of a flexible body. Further features of the method are that it uses minimum control effort and it can be converted to a feedback form to deal with random disturbances and parameter uncertainties. Several examples are given to demonstrate the efficacy of the method, and results from a hardware experiment are presented.