Suboptimal Regulator Research Articles

Relationship between discrete polynomial and state-space solutions of the H∞ optimal regulator problem

A relationship is established between the discrete state-space and polynomial matrix solutions of the H∞ state-feedback sub-optimal regulator problem. The solution of polynomial matrix diophantine equations is related to the solution of the discrete H ∞ Riccati equation. The links between DGKF state-space and the polynomial system solutions provide insights into the structure of the controller that may be helpful for calculations and implementation.

An alternative digital redesign of continuous-time suboptimal regulators for input time-delay systems

In this paper, an alternative digital redesign approach dealing with the digital-controller-based input time-delay system is proposed. It directly converts the original continuous-time quadratic cost function into the discretized form and solves the optimization problem in the discrete-time domain. This method reveals an essentially different approach of digital redesign from the traditional ones. The main goal of approximation of the system performance of the discretized system to the original continuous-time one is achieved. Illustrative examples are presented to demonstrate the effectiveness of the proposed procedure.

Complete decomposition of sub-optimal regulators for singularly perturbed systems

The linear regulator problem is studied for systems with slow and fast modes. Using the descriptor variable method, the design of sub-optimal regulators for such systems is completely decomposed. It is shown that the sub-optimal regulator is composed of fast and slow regulators, and that both of these, mutually decoupled, can be designed independently. A relevant computational procedure is also presented. The procedure is applicable to designs of sub-optimal regulators with either finite or infinite terminal time, and for both singular and normal singularly perturbed systems.

Suboptimal design of hydroturbine governors

A state space method for the design of turbine governors in hydro power plants with Kaplan turbines is presented. The design is based on the suboptimal regulator problem solved by the use of projective controls. A design procedure that permits the design of multivariable static and low order dynamic hydroturbine governors is proposed. It provides an organized way of choosing the governor structure and the tuning of its parameters. A case study is presented to illustrate the proposed design method and to demonstrate the extensive applicability of the suboptimal solution and its merits as compared to conventional governors. >

Two-stage suboptimal discrete-time regulators for continuous-time stiff dynamic systems

A two-stage design method is developed for design of linear quadratic regulators (LQRS) with regional pole assignment for a large-scale continuous-time stiff dynamic system and its observer, which do not exhibit a two-time scale structure explicitly. The method also provides a procedure to convert the designed analog LQR and observer to an equivalent digital LQR and observer, respectively, for digital implementations. First, the large-scale stiff dynamic system is block-decomposed into two block-decoupled subsystems according to their own characteristics via the fast and stable matrix sign algorithm. Next, a sequential design procedure is used to design a LQR with regional pole placement for each subsystem. The same procedure is then carried out to design an optimal observer. For implementation of the designed analog LQR using a digital LQR, the designed analog LQR and observer are converted into an equivalent digital LQR and observer, respectively, via a digital redesigned method. A practical stiff system is used as an illustrative example to demonstrate the effectiveness of the proposed method.

Some new results on optimal and suboptimal regulators of the LQ problem with output feedback

The LQ (linear quadratic) regulator problem with output feedback is considered. In the problem studies an output feedback control is determined such that the cost is J*, the optimal cost for the LQ problem with state feedback, or beta j* with some constant beta >1. A set of sufficient conditions is given for determining such optimal and suboptimal output feedback control laws.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Flight-test maneuver modeling and control

The use of automated flight test schemes decrease the aircraft flight testing time and pilot work load while enhancing the data quality. Two major elements involved in developing such an automated technique are maneuver modeling to generate command histories from the maneuver specifications and the synthesis of control systems to track these command histories. This paper describes the maneuver modeling for eight flight test trajectories. The control system synthesis with Kosut's suboptimal minimum error excitation linear quadratic regulator approach is presented. The closed-loop simulation results are given.

Power System Stabilizers Design for Suboptimal Performance of Multimachine Power System

The paper presents a state space method for the design of power system stabilisers (PSSs) in multimachine power systems. The design is based on the suboptimal output regulator problem solved by use of projective controls. A sequential design procedure is proposed, which provides an organized way of choosing the stabilisers′ structure and tuning its parameters. A numerical example of a multimachine power system is presented to illustrate the proposed design method.

Projective Control Design Procedures for Power Plant/Power System Control

This paper presents an approach, illustrated through a case study, to designing a multivariable control system for large process models. The case study involves the development of a preliminary multivariable control design for load following and frequency regulation on an Advanced Boiling Water Reactor (ABWR). The design procedure is based on the suboptimal output feedback regulator problem solved by use of projective controls. The procedure is applicable to design of controls for any power plant. In designing static controllers the selection of the projective control is based on eigenvalue sensitivity criteria developed to single out eigenvalues in the reference system most sensitive to perturbations in the control. These eignevalues are then retained by the use of projective controls, and the gains are adjusted, if necessary, to meet additional criteria, such as bumpless transfer in this particular case study.

Design of a Proportional-Integral Power System Stabilizer

Stabilization of power systems is investigated using a proportional-integral (PI) power system stabilizer. Digital (sampled-data) PI stabilizers as well as analog (continuous-time) PI stabilizers are examined in this paper. Two approaches, viz., the root-locus method and the suboptimal regulator method, are presented for determining the optimal stabilizer gains of the proposed PI stabilizer. The dynamic responses following a step disturbance by digital simulation are obtained by means of three types of stabilizers: the conventional power system stabilizer, the optimal stabilizer and the PI stabilizer. Simulation results show that the proposed PI stabilizer yields better system dynamic performance than the others in the sense of having greater damping in response to a step disturbance. A characteristic feature of the proposed PI stabilizer is that it is very simple for practical implementation, especially in the digital case, as commercial PI controllers have been widely employed by the industry for years.

Computer Aided Design of Suboptimal Linear Regulators

A CAD program package has been developed for the design of suboptimal linear regulators. Various controller configuration and performance index options are available and the package adopts a common numerical approach to the solution of these problems. Recent numerical improvements and enhancements are described including the study of sampled-data systems. Three design applications are included. For a helicopter regulation problem output feedback and dynamic compensation techniques are employed with a model-following approach to attempt to match new designs to a desired model response resulting from a linear optimal regulator design. Sensitivity reduction is realized in a gas turbine engine example using output feedback and is further reduced by dynamic compensation. The third example deals with a sampled-data system and involves the design of an output feedback controller for a gas turbine engine with significant time-delay components.

CAD of Control Systems: Application of Nonlinear Programming to a Linear-Quadratic Formulation

The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a CAD package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, modelfollowing errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.

Control design for a wind turbine-generator using output feedback

The modeling and approach to control design for a large horizontal axis wind turbine (WT) generator are presented. The control design is based on a suboptimal output regulator which allows coordinated control of WT blade pitch angle and field voltage for the purposes of regulating electrical power and terminal voltage. Results detailed nonlinear simulation tests of this controller are shown.

Suboptimal Control of Large Scale Systems by Chained Aggregation

A new procedure to evaluate chained aggregation matrix has been developed using Pouth Canonical form. This method is simple compared to generalized Hessenberg representation. The structural properties of Routh Canonial realizations are very useful in obtaining a closed form chained aggregation matrix. This new approach gives better results when compared to the suboptimal regulators derived using Routh approximant reduced order models.

Output feedback pole placement in the design of suboptimal linear quadratic regulators†

A design oriented methodology is presented for the construction of low-order, suboptimal, output feedback compensators. The design is suboptimal in the sense that it retains an l-dimensional eigenspace from a reference optimal state-feedback linear quadratic regulator problem. If r is the number of outputs, then for fixed l > r, it is known that the design requires a dynamic compensator of dimension l — r. The parameters of the compensator are determined by the solution of an associated output feedback pole placement problem. Using iterative, dyadic pole placement, a procedure is given which determines the solution of this problem, without a priori assumptions on the dimension of the compensator. The design is also extended to the class of stabilizable systems, and the resulting compensator is shown to possess a separation property.

Robustness of suboptimal control: Gain and phase margin

The purpose of this paper is to introduce the gain and phase margin as measures of robustness of suboptimal linear-quadratic regulators. It will be shown that the suboptimal control retains the infinite gain margin of the corresponding optimal system, but that the phase margin and gain reduction tolerance depend on the degree of suboptimality of the nominal optimal control law. This establishes the degree of suboptimality as an index of both the system performance regarding the optimality criterion and the robustness to plant parameter uncertainties and distortions of the optimal control law. It will also be shown that the suboptimal closed-loop systems remain stable despite insertion of memoryless nonlinear gains inside individual feedback loops, thus raising further the confidence in suboptimal designs of linear-quadratic regulators.

A CAD Program for Suboptimal Linear Regulators

A number of suboptimal linear regulator design strategies is discussed and it is shown that they may be incorporated within a general problem formulation. It is therefore possible to adopt a common numerical approach to the solution of these problems and a gradient minimization technique is selected as the solution method following a study of four alternative schemes. This method requires the solution of a pair of Liapunov matrix equations during each iterative step and it is found that these equations are best solved by application of the Bartels-Stewart algorithm. An interactive CAD program has been developed and it functions both as a design tool and as a research aid. As a design tool it offers access to a number of existing design strategies, provides added flexibility in the choice of controller configuration and enables different strategies to be merged to form an effective overall design procedure. As a research aid the program is easily modified to include new controller configurations or test new performance index specifications; it may also be extended to handle linear discrete-time systems and linear stochastic systems.

Suboptimal regulator design of linear systems with quantized controls

This short paper presents a design technique for determining a suboptimal feedback control law for linear systems actuated by the quantized control signals. This control law is easily implemented in the form of the switching hyperplanes characterized by a nonlinear matrix difference equation for discrete-time systems or by a differential equation for continuous-time systems. The properties of this control law are investigated in detail.

Improvement of dynamic stability of parallel AC‐DC power system by suboptimal control

One of the advantages of dc power transmission over ac transmission is that the dynamic stability of the ac system can be improved greatly by connecting a dc transmission system in parallel to the ac system and controlling the dc power in the case of disturbance. The suboptimal feedback coefficient matrix for the parallel ac-dc system usign a linear model is derived. The suboptimal gain of the automatic voltage regulator (AVR) is derived and the effect of AVR gain on the control performance of the suboptimal regulator is analyzed. It is shown that the proposed suboptimal control, in which only two output variables (magnitude of generator terminal voltage and time derivative of terminal voltage phase angle) are used as feedback signals, is as effective as the optimal control in which all state variables are used as feedback signals.

Design algorithms for a sensitivity constrained suboptimal regulator

The problem of finding the linear feedback control comprised of state and trajectory sensitivity terms which minimizes an infinite-time quadratic cost functional containing sensitivity variables is discussed. Since trajectory sensitivity cannot be accurately modelled in a closed-loop formulation the control feeds back approximate sensitivity terms. As the minimizing control is dependent on initial conditions, necessary conditions for a minimum are derived which satisfy various alternative sets of initial condition criteria. An efficient computer algorithm, based on a gradient search technique, is proposed for finding the feedback gains. By means of a numerical example it is shown that it is possible to reduce trajectory sensitivity while retaining certain desirable features of the linear optimal regulator design. Finally an algorithm is suggested for finding the linear feedback control comprised of state terms alone which minimizes the augmented cost functional.