Optimal LQG Research Articles

Control of asynchronous sampled data systems

This paper is concerned with the problem of controller design in the case of asynchronous sampled data systems. Optimal LQG controllers are obtained for the class of two-rate systems where all the control inputs are held at a rate which is asynchronously related to the rate with which all of the outputs are sampled. Furthermore for this class, a parameterization of all stabilizing controllers is provided.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Control of an industrial spray drying unit

The development of a dynamic mechanistic model and an optimal sampled-data LQG controller for industrial detergent spray drying processes are considered. A model-order reduction procedure which preserves the identity of the variables was shown to lead to poor closed-loop behavior. The optimal controller takes account of the dynamic behavior of the process between the sampling instants, and has been extended to incorporate sampled-data integral action. The state estimator has been modified in order to correct for offset disturbances that corrupt the output measurements. Production runs have proved both the applicability of the controller, and that it removes some of the shortcomings of conventional control schemes.

Stable LQG controllers

The optimal LQG controller is known to stabilize the closed loop if certain mild conditions are satisfied. The controller itself, however, may be unstable. The paper presents a method of selecting the weighting and covariance matrices such that the optimal controller is internally asymptotically stable. The method is very easy to apply and for stable open-loop system involves the solution of a single Lyapunov equation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Innovations system representation in the optimal LQG regulation problem

New insights on the role of the innovations system representation in the context of the optimal LQG (H/sub 2/) 'standard' problem are provided. The optimal controller is derived by using polynomial matrix techniques based on an innovations representation of the system. This can be obtained from the physical description by solving an appropriate minimum mean-square error filtering problem. The key result is that both the descriptions share the same optimal controller. A quite general cascade control structure is revisited in the present setting and the appropriate filtering problem is solved. The optimal controller is further obtained and the overall design procedure is compared with the one based on the physical system description. As a result, both a generalisation of the solution for the proposed cascade control problem and a better understanding of the role of the innovations system representation are provided. >

A Comparison of Adaptive LQG and Nonlinear Controllers for Vehicle Suspension Systems

Abstract A design feature of many computer-controlled suspension systems, is their ability to adapt control law parameters to suit prevailing road conditions. Here, for systems employing high bandwidth actuators and state variable feedback control, the benefits of such adaptation are shown to be at best marginal. An optimal adaptive LQG system is compared with a fixed structure nonlinear feedback controller in the context of a simple quarter-vehicle suspension model. Performance comparisons are made, and trends considered under more realistic conditions. In consequence the overall usefulness of this type of adaptation is called into question.

Optimal hold functions for sampled data regulation

This paper investigates the use of Generalized Sampled Data Hold Function Control (GSHF) to optimize quadratic measures of performance in sampled data control loops. The idea of GSHF control is to use sampled data feedback, but consider the hold function as a design parameter. Explicit solutions are given for the GSHF versions of the optimal LQ and LQG regulators. The questions of existence, uniqueness and computation of optimal hold functions are treated. An example is presented.

The optimal LQG digital shape and orientation control of an orbiting shallow spherical shell system

The analysis and design of the optimal LQG digital shape and orientation control of an orbiting shallow spherical shell system are presented. In this paper the emphasis is placed on the mathematical models of the dynamics and observation, and the analysis and design of LQG optimal digital controllers and observers. The problem of determining the number and locations of the actuators is also studied by means of the concept of the degree of controllability and related simulations. The analysis and design of the optimal LQG digital control system for the shell has been certified by simulations. Typical figures showing the transient responses of LQG control are included here to show the influence of the different combinations of the controller and observer pole locations on the estimate and control process; also studied here are the influence of different numbers of actuators and for a fixed number of actuators, the effect of varying the actuator locations on the LQG control process.

Two-degrees of freedom feedback and feedforward optimal control of multivariable stochastic systems

A polynomial matrix solution is obtained to the optimal LQG output regulator problem for a system with both input and output disturbances, dynamic feedback element and a cost-function with dynamic weighting terms. The cost-function can include both the usual LQG output and control terms and sensitivity/complementary sensitivity terms. The solution of this regulating problem is also shown to provide a two-degrees of freedom controller when a reference input is used for a tracking problem. Similarly a feedforward controller can also be derived from the results when a disturbance is measurable. Since in practice disturbances cannot usually be measured accurately provision is made for corrupting the measured spectrum and allowance is made for a measurement noise on this signal. The results are obtained for a general multivariable plant.

Optimal multivariable LQG control using a single diophantine equation

The general solution of the optimal LQG problem using the polynomial equation approach involves the solution of a couple of two-sided matrix polynomial equations. The conditions under which a single one-sided equation which is related to the original two (the ‘implied’ diophantine equation) yields the unique optimal controller are derived in this paper. The result has considerable relevance to aspects such as computation and self-tuning control applications.

One-step Optimal Correction for Input Saturation in Discrete Model-based Controllers

A one-step optimal method for compensating for any form of input saturation in discrete linear controllers is developed. The algorithm is straightforward to implement as an analytical correction operating on the difference between the past calculated control inputs and the inputs actually implemented. A further correction for multivariate controllers is necessary to simultaneously adjust the remaining control inputs if some inputs saturate The correction is valid for minimum variance and one-step optimal LQG controllers It can also be applied to Internal Model or Dahlin controllers. The algorithm is illustrated by simulation on several SISO and MIMO examples.

Optimal adaptive LQG control for systems with finite state process parameters

The situation where a totally observed process y t is generated by a stochastic differential equation whose parameters evolve on a finite set {1, ... N} according to a stochastic differential equation is considered. The optimal control law is sought with respect to quadratic loss functions on y t and the control u t . The auxiliary P.D.E. technique of Hijab [6] is used together with a nonlinear filter to obtain the solution whose existence depends upon that of a smooth solution to the auxiliary P.D.E. and strong solutions to the system S.D.E. under the given control inputs.

Controller reduction by component cost analysis

Component cost analysis [1] is used to develop a method for controller reduction. The reduction of the controller is based upon the participation of the controller states in the value of a quadratic performance metric. The controller states which have the smallest contribution to the performance metric are truncated to produce the reduced controllers. An error index is defined to evaluate the reduced controller compared to the optimal LQG controller, and bounds on this index are derived. A numerical example is included to illustrate the procedure.

System models for optimal self-tuning control

In most self-tuning control systems measurement noise and disturbance spectra are combined into one effective noise model. In cases where a priori information is available regarding one of these models the separate subsystems can be identified. It is shown that the optimal LQG controller for this case may then give an improved performance relative to an LQG controller based upon a single noise source model.

Matrix Quadratic Solutions

Matrix quadratic equation solution derivation applied in finding steady state solutions of Riccati differential equations with constant coefficients