Optimal Control System Design Research Articles

Optimal control system design of a nuclear reactor by generalized spectral factorization

Optimal feedback control system design of a nuclear power plant has usually been conducted in the time domain by solving the Riccati equation. In this paper, the problem will be treated in the s-domain by means of the MacFarlane extension criterion (MEC). The algorithm is based on generalized spectral factorization (GSF), and the MEC is resolved by the Newton-Raphson method featuring rapid convergence and high precision. Whether the plant is stable or unstable, the initial matrix can be chosen effectively and a general computer code for finding the optimal feedback gain matrix of the multi-input system is presented. The control system design of a boiling water reactor (BWR) shows that the results obtained from the proposed method are consistent with those from solving the conventional Riccati equation. A satisfactory closed-loop multivariable system with a prescribed degree of stability can also be designed in the s-domain. The methodology of this paper can also be generalized to treat similar control sys...

Discrete-time optimal control of systems with unilateral time-delays

Industrial plants which contain unilateral flow of material are considered. First, it is shown that such plants can be represented by finite-dimensional difference equations after sampling. Then, the design of discrete-time optimal control systems is studied based on the difference equations. The main difficulty in this design problem is the high dimensionality resulting from the discretization of long delays. In this paper, a new algorithm to solve the discrete Riccati equation for this class of systems is proposed. An example is given to illustrate how the computational difficulties are effectively reduced.

Orbit and attitude control of a geostationary inertially oriented large flexible plate-like spacecraft

The paper presents design of a near optimal orbit and attitude control system for a very large flexible rectangular flat plate-like spacecraft in geostationary orbit, with its normal kept in the orbital plane in an inertial orientation. First, assuming the plate to be rigid, an optimal control system is designed. Two control systems are needed: one to balance the gravity gradient torque and the other to control the plate's orbit and attitude against disturbances. The interaction of the structural dynamics with the control system is investigated next. It is shown that the structural dynamics destabilizes the control system. The control design is modified to reduce the interactions, by including just a couple of flexural modes into the control logic and by optimally locating the thrusters a little away from the corners. The control structure interaction which is measured by the residual flexural energy after an orbit or attitude correction, is shown to be reduced by several orders of magnitude by the simple modifications. An approach to find an optimal location of actuators and a concept of “associated modes” are also proposed to help the designer evolve a very simple coupled orbit and attitude controllers with minimum control/structure interactions for very large flexible space systems of the future. This configuration considered represents the proposed solar power satellite, solar reflectors, communication platforms, etc.

Optimal design of digital control systems with large plant uncertainty

In this paper, we extend a practical optimal-design procedure that has been presented in our previous work for single-loop digital control systems. The plant transfer function is given with prescribed bounds on its parameters, and a digital controller is to be designed so that the system response to a deterministic input is optimal and lies within permissible bounds. The w-plane method for the discrete design is used so that the design procedure to be presented is still based on frequency-domain concepts.

Optimal design of control systems with large plant uncertainty

This paper presents a practical optimal-design procedure in the fact of a significant and defined plant parameter uncertainty range, using Wiener's least-square optimization with a quadratic constraint in the frequency domain. With a linear time invariant minimum-phase stable plant imbedded, the optimal system to be designed is a two-degree-of-freedom feedback system such that the system response to a deterministic input lies within specified bounds.

Optimal discrete systems with prescribed eigenvalues

This paper deals with the design of optimal discrete control systems with prescribed eigenvalues. Solheim's method for such design is improved and extended to achieve the original design objective. That is the minimization of a quadratic performance index with a prescribed control weighting matrix R and some state weighting matrix Q. A new recursive algorithm is also presented. While this algorithm retains the simplicity provided by Solheim's method, it constructs the resultant state weighting matrix Q as the sum of the recursive state weighting matrices <?(. The algorithm is general and applicable to any system structure. For the sake of completeness, the optimality of Solheim's solution is tested by using a simple necessary condition which is developed in the paper. It is shown that the optimality of Solheim's solution is not. in general, guaranteed.

A case of a linear quadratic optimal design with a weighting matrix which is not non-negative definite

Within the field of optimal design of linear time-invariant control systems according to a quadratic criteria, it is usually assumed that the weighting matrix Q x is non-negative definite. Furthermore, the elements of Q x can generally not. be determined by physical reasoning. Recently, a case has been presented where the weighting matrix is not non-negative definite, and the complete form of the index, including the values of all the coefficients, can be determined physically. It is shown that an optimal solution does exist within certain restrictions that are satisfied for that specific case.

Control system design for an individual signalized junction

The traffic signal settings for a single road junction have been often evaluated by mathematical programming techniques. This paper proposes a new approach to the problem which allows all the regulation variables to be incorporated into a Binary-Mixed-Integer- Linear-Programming model. This general model permits some of the limitative assumptions involved in other formulations of the problem based on the stage matrix to be removed. The model can be easily solved obtaining a fast computation of the globally optimal control system design. A detailed treatment is given for the particular structure of the mathematical programming schemes obtained by considering delay minimization, capacity reserve maximization, or cycle time minimization as the objective.

Optimal design of linear control systems by an interactive optimization method

When designing linear control systems, one of the most difficult problems is that the designer almost has no theoretical basis for the determination of proper parameters in order to obtain a system with desired specifications. Poles and directions of eigenvectors in the pole assignment method or weighting matrices of the quadratic criterion function in the optimal regulator method are such parameters. The designer has to determine them by trial-and-error using computer simulation. The purpose of this paper is to propose an approach to helping determine proper parameters in linear control system design by the state space methods. In the case where the desired specifications are not given explicitly, the approach applies an interactive optimization method called the Interactive Simplex method to search the most suitable parameters directly in the parameter space. But, if the specifications are given explicitly, the design problem can be formulated as a multiobjective optimization problem. In this case, weights which indicate relative importance of different specifications are introduced and the Interactive Simplex method is applied in the weight space to indirectly find the most appropriate parameters. The approach is implemented as part of a CAD system. The designer has only to make pairwise comparisons of response curves which are shown on a graphics display terminal in order to obtain the most preferred control system. Two illustrative examples are demonstrated to indicate the efficiency of the approach.

Interactive computer-aided design of control systems

We describe four computer packages for interactive computer-aided design of control systems. DIGICON (digital control) is a computer aid to the design of digital controls for single-input single-output (SISO) systems using the state-space techniques of pole and zero assignment. CONCON (continuous control) is a similar package for the design of SISO continuous systems using the same techniques. The program DOPTICON (discrete optimal control) is a computer aid for the design of discrete optimal control systems using the linear quadratic Gaussian ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LQG</tex> ) theory and OPTICON (optimal control) is its continuous-time counterpart. All four packages contain algorithms for computation of the poles and zeros of the resulting designs as well as the evaluation of the transient responses.

Matrix factorization and Chandrasekhar equations techniques in the design of linear quadratic optimal control systems

A unified presentation of matrix factorization and Chandrasekhar equations techniques for solving linear quadratic optimal control problems is given in cases of continuous-and discrete-time invariant systems. These techniques are used for designing optimal systems via an augmentation of the system by disturbances and reference models.

The solution of finite‐time optimal control problems with control time delays

AbstractThe design of deterministic LQP optimal control systems is considered for plants with control delays and a finite optimization interval. First, a solution is obtained to the fixed end‐point optimal control problem. An expression for the open‐loop optimal control is derived in the s‐domain. The closed‐loop optimal time‐varying gain matrix is then calculated from the s‐domain results. The open‐loop and closed‐loop solutions to the free end‐point optimal control problem are also given. The constant gain, infinite‐time, feedback control law is obtained as a limiting case of these results.The receding‐horizon optimal control problem for plants with control signal delays is also considered. The solution to this problem yields a constant feedback gain matrix which has obvious advantages for implementation. This gain matrix is not the same as the constant solution to the infinite‐time problem. The receding‐horizon control laws are derived for both the fixed and free end‐point problems, and these are shown to produce asymptotically stable closed‐loop systems.

Economically Optimal Performance Evaluation and Control Systems

The purpose of this paper is to analyze the uses of information in the firm's performance evaluation and control system. From an accounting perspective, we are interested in information. But it is important to acknowledge at the outset that the demand for information in this setting stems from the conjunction of evaluation and control. Thus, our focus is the economically optimal design of performance evaluation and control systems. This focus, in turn, allows us to study the demand for and uses of information in the internal management of the firm. In the most simple (partial equilibrium) setting, a firm might consist of a single owner (principal), the production process owned by the owner, and a single worker (agent). The agent's labor, and possibly knowledge, when combined with the production process and some state realization produce an outcome. If decision making is delegated to the agent, then information may be used in two ways within the firm's performance evaluation and control system. First, information may be gathered after the agent has chosen his action and the outcome has been generated in order to evaluate the agent's action choice and determine his compensation. Here, the information is used for motivational as well as risk-sharing purposes. Demski and Feltham [1976] have termed this use decision influencing. In addition, state information may be supplied to the agent before his action choice in order to improve his action choice. Demski and Feltham [1976] refer to this as information's decision-facilitating role. Notice that with a

Design of stochastic optimal feedback control systems

The design of stochastic, linear, multivaribale feedback systems is considered where the plant is constant and the noise processes are stationary. The plant can be unstable and nonminimum-phase and feedback-system dynamics can be modelled. Approximate methods are described for limiting the effects of plant saturation and for modelling transport delays. The closed-loop system is assumed, to have a coloured process, disturbance and measurement noise inputs and a coloured reference input. The plant disturbance and the closed-loop-system reference inputs are also assumed to contain deterministic components, e.g. step or ramp signals. The design procedure is original and involves two stages. A performance criterion is defined first that is not sensitive to the deterministic signals, and this defines the closed-loop controller. The resulting closed-loop system acts as an optimum regulator to minimise the effects of stochastic disturbances. A second tracking-error performance criterion is then specified that determines the optimal reference input to the closed-loop system. This reference signal is generated by two optimal open-loop controllers. One controller ensures the plant output is following a desired trajectory, and the second acts as a feedforward controller to offset plant disturbances.

Optimal output feedback control with reduced performance index sensitivity

For the design of optimal control systems it is required to know the plant parameters exactly. However, usually those parameters may be varying or uncertain due to ageing, environmental effects and other inaccuracies so that the control systems that are designed to be optimal for a set of nominal values may no longer be optimal for a different set of values. This paper presents an optimal output feedback control with reduced performance index sensitivity. The necessary conditions for an optimal output feedback control are obtained analytically in § 2, and a gradient method for obtaining the numerical solution is presented in § 3. Illustrative examples are given in § 4 and the results in various cases are investigated.

Optimal output feedback control of power systems with high-speed excitation systems

A method of designing a linear, optimal, constant, feedback control system based on quantities easily measurable at the synchronous generator location is presented for power system equipped with fast-acting excitation systems. The method is applied to a single-machine infinite-bus system, and the performance of the system to large disturbances, created by applying three phase faults, is studied. To permit meaningful comparisons between the proposed control scheme and conventionally used schemes, the performance of an 'optimized' supplementary excitation control system is used as a base against which to judge the relative merits of the new scheme. It is found that the proposed control system design, when evaluated over a wide operating range, consistently results in improvements in system behaviour as compared to the conventional control system. To improve system reliability, the optimal control system design is carried out without assuming that the supplementary stabilizer is disconnected. Thus if, for any reason, the new control is not available, the system still has the benefit of stabilizing action provided by the supplementary stabilizer.

Design of Continuous and Discrete Optimal Control Systems with Prescribed Transient Response

The performance index matrices for the optimal control problem are to be chosen so that the closed-loop system would have a prescribed transient response. Two algorithms are developed, the direct algorithm which is based directly on the sensitivity of the closed-loop poles with respect to changes in these matrices, and the associated matrix algorithm which is based on the sensitivity of this special matrix eigenvalues to performance matrix changes. While in the first algorithm one has to solve simultaneously two matrix equations, it is sufficient in the second to solve only one much simpler equation. By applying the direct algorithm to both discrete and continuous cases, it is found that even with R(the control performance index matrix) equal I, the discrete case involves a great deal of computation. On the other hand the associated matrix algorithm yields similar equation for both continuous and discrete cases. The paper also includes a thorough discussion of the existence and uniqueness of both algorithms and for both discrete and continuous control systems.

Design of optimal discrete control systems with prescribed eigenvalues

Abstract A quadratic performance index together with a set of prescribed closed-loop eigenvalues are considered as criteria for designing discrete multi-variable control systems. The design method presented in the paper is an extension of an earlier solution of the equivalent problem for continuous systems.

A new method of optimal digital PID feedback control†

This paper presents a now method of optimal digital PID feedback control for a linear multivariate system by using a, parameter optimization technique. The most difficult points for the design of optimal digital PID feedback control system by the modern control theory are : (1) the control structure of it is specified in advance, (2) unless all the state variables are fed back, the optimal control cannot be obtained by dynamic programming or the maximum principle. However, the optimal digital PID feedback gains are determined by using the parameter optimization technique in this paper. When there are some states which are not fed back in the control system, the optimal feedback gains depend on the initial states. First, the optimal solution is presented in the case where all the initial Btates are known. Next, it is extended to the case where the initial states are random variables and their statistical properties are known,

Design of near-zero sensitivity optimal control systems†

A method for the optimal design of linear time-invariant systems with low sensitivity is proposed. The criterion of optimality is to choose system parameters and the corresponding optimal control so as to obtain zero or near-zero sensitivity of the optimal cost function. The proposed method yields a transient response, not only with faster settling time, but also insensitive to small parameter variations. The procedure is simple and can be extended to the optimal design of multi-parameter systems. It can be easily programmed on a digital computer without excessive increase in computer memory.