Linear Optimal Control Theory Research Articles

The State of the Art in Linear Systems

A review is given of recent developments in the field of linear system theory, covering the topics of external and internal representations of linear systems, variance computation in linear stochastic systems, linear multivaluable system theory, linear (optimal) control theory, realization theory and time-varying systems. The papers to be presented during the session are discussed within the framework of this review.

Application of linear optimal control and filtering theory to the Saturn V launch vehicle

The application of linear optimal control and least square filtering theory to the design of a control system for the Saturn V launch vehicle is described. System performance is evaluated on the basis of the ratio of the standard deviations of structural load, engine deflection, and lateral velocity drift to their design limits. An optimal linear control is derived from a quadratic performance index in ratios of these critical variables to their design limits. It is shown that this essentially eliminates trial and error search for suitable quadratic index weighting coefficients. It is also shown that the standard deviations are only slightly degraded when feedback gains on actuator states and bending and slosh modes are eliminated, leaving feedback gains on only the three rigid-body states and feed-forward gains on the wind-induced angle of attack and wind-shear velocity. A new method of reducing the state estimation filter dimension to yield suboptimal estimation of the three rigid-body states and two wind model states is applied and shown to cause only a slight additional increase in the standard deviations of the critical system variables.

New Jacobi-type necessary and sufficient conditions for singular optimization problems

Jacobi-type conditions for singular optimization problems obtained by transformation to nonsingular form adaptable to linear quadratic optimal control theory

On the linear optimal servo problem†

Some methods of handling command inputs via the linear optimal control theory are compared, and the convergence of the associated Riccati matrix differential equation is investigated.

Dynamic control of a two-stand cold mill

The design of a control system for a two-stand tandem cold rolling mill producing thin brass sheet is developed. The control objective is to minimize output thickness variations resulting from three process disturbances while observing a number of physical constraints. Three manipulated variables are available, and five process measurements can be made if desired. A linearized mathematical model, valid for fluctuations about the steady-state operating point, is derived. The model is multivariable, fully interacting, and contains a time delay representing the travel time of the metal between stands. Linear optimal control theory combined with digital simulation is used to derive the control. The control proposed has a novel structure. In addition to providing acceptable dynamic performance, the control is insensitive to steady-state errors in the process model, and may offer significant advantages over more conventional controls.

Dual-system methods in dynamical analysis. Part 1: Variational principles and their application to nonlinear-network theory

The feedback connection of a dynamical system and its dual, through nonlinear coupling elements, is shown to generate a pair of fundamental stationary principles. These provide a unified basis for both the classical Lagrangian and Hamiltonian treatments of dynamical systems aud modern work on nonlinear network theory and linear optimal-control theory.

A theory of modal control

Although considerable progress has been made in various aspects of control theory, there still appears to be no adequate theory for the control of large-scale linear time-invariant multivariable systems. If the engineering specifications required of the controlled system can be effectively summarized in a quadratic performance measure, then linear optimal control theory, in principle, provides a linear feedback controller which would perform the required task. Even under these circumstances the computational problems may be insurmountable. In an effort to circumvent these difficulties Rosenbrock suggested the use of modal control as a design aid. Modal control may be defined as control which changes the modes (i.e., the eigenvalues of the system matrix) to achieve the desired control objectives. This paper presents a complete and rigorous theory of modal control as well as recursive algorithms which permit modal control to be realized.

Computer Control of a Paper Machine—an Application of Linear Stochastic Control Theory

This paper describes an attempt to apply linear optimal control theory to computer control of an industrial process. The applicability of the theory is discussed. Particular attention is given to the problem of obtaining a mathematical model of process dynamics and disturbances. Results of actual measurements as well as results from on-line control experience are presented.

An application of the quadratic penalty function criterion to the determination of a linear control for a flexible vehicle

Optimal linear control theory to develop quadratic cost-criterion control law for flexible rocket vehicle

The characteristics of model-following systems as synthesized by optimal control

Synthesis through linear optimal-control theory is applied to two types of model-following systems. Although the two system concepts are fundamentally different, the optimal-control theory in both cases generates constant feedback gains which modify the plant dynamics so that the resultant system response approaches that of the model. Each synthesis method produces an optimal-control law that has a closed-form solution and minimizes an integral quadratic performance index involving both system errors and control motions. The first type of model-following system is generated by incorporating the model only in the performance index. The integral square error between the model and the system is minimized by one term in the performance index. The basic idea in this system is to alter, by the feedback, the coefficients in the equations of motion for the plant so that these coefficients approach those of the model. The feedback control obtained from this method depends on the solution of the matrix Riccati equation, and also on a product of constant matrices. For an infinite weight on the error term in the performance index, the solution of the Riccati equation approaches zero. The second type of model-following system incorporates the model as part of the control system, and places it ahead of the plant as a prefilter. The difference between the model output and the plant output is minimized in the performance index. The resulting system has not only feedback gains for the plant state variables but also feedforward gains for the model state variables. Evaluation shows that the feedback gains are independent of the model, and are exactly those which would be obtained for the normal regulator problem. The feedforward gains depend on both plant and model.