Normalized Coprime Factorization Research Articles

正規化既約分解法に基づくΗ<sub>∞</sub>制御を用いた高速移相器のロバスト周波数動揺安定化制御系の設計手法

Nowadays, the power industry is in transition to a fully competitive scenario. Under this situation, some power system controls such as frequency control will be served as ancillary services. Then, it is important to consider how the system frequency should be controlled. In this paper, a robust frequency stabilization controller design method of solid-state phase shifter is proposed. The frequency controller of phase shifter located in series with a tie line between two areas, is designed based on the idea of enhancing the damping of inter-area oscillation mode. The method of Overlapping Decompositions for system reduction and the Η∞ control via Normalized Coprime Factorization (NCP) approach are used to achieve the proposed design idea. By NCF approach, the weighting selection in Η∞ control design is simplified. Simulation results confirm the performance and robustness of the proposed control against load disturbance and system uncertainties.

Robust Stabilization of Nonlinear Systems via Normalized Coprime Factor Representations

A reasonably complete theory for the synthesis of robust controllers for a broad class of nonlinear systems is now available. We use this theory to generalize the linear theory of normalized coprime factor robustness optimization to the case of affine input nonlinear systems. In particular, we show that the equilibrium controller may be characterized in terms of the stabilizing and destabilizing solutions of the Hamilton–Jacobi equation used to calculate the normalized (right) coprime factors of the plant. We also show that the optimal robustness margin of √ 1− M N 2 H generalizes to the nonlinear case. In preparation for the nonlinear analysis, we review the linear case in a way which motivates our approach to the nonlinear case and highlights the parallels with it.

H∞ Control of a Flying Vehicle in Ground Effect

The purpose of this study is to design a stabilizing controller of the longitudinal motion of a flying vehicle in ground effect and validate it's properties by experiments. The aerodynamic coefficients are nonlinear to height, which results in a substantial change of the dynamic characteristics. Nonlinear simulations and a stabilizing experiment in ground effect are carried out. These results demonstrate that H∞ controller based on the normalized coprime factorization is effective to control vehicles in ground effect.

98/02239 Case study of the conversion of tangential- and wall-fired units to low-NOx combustion: Impact on fly ash quality

The paper presents the bacterial foraging optimization algorithm (BFOA) and particle swarm optimization (PSO) algorithm based robust controllers for voltage deviations due to the variation of reactive power in an isolated wind-diesel hybrid power system. The isolated wind-diesel system consists of wind energy conversion system (WECS) utilizing a permanent magnet induction generator (PMIG). Further, a synchronous generator (SG) is used with the diesel engine set for power generation. The mismatch between generated and consumed reactive power in the system causes voltage fluctuations, which will occur at generator terminals. These oscillations further causes reduction in the stability and quality of the power supply. The static synchronous compensator (STATCOM) and an automatic voltage regulator (AVR) are used to suppress voltage fluctuations in an isolated wind-diesel hybrid power system. The STATCOM is used as a reactive power compensator and the AVR is used to keep the terminal voltage constant for the synchronous generator. Both STATCOM and AVR are having proportional and integral (PI) controllers with single input. In modeling for the system, a normalized co-prime factorization is applied to show the possible unstructured uncertainties in the power system such as variation of system parameters and generating and loading conditions. The performance and robust stability conditions of the control system are formulated as the optimization problem, which is based on the Hα loop shaping. BFOA and PSO algorithms are implemented to solve this optimization problem and to achieve PI control parameters of STATCOM and AVR simultaneously. In order to show the efficiency of the proposed controllers, the performance of the proposed controllers is compared with the performance of the conventional controller and genetic algorithm (GA) based PI controllers for the same wind-diesel system. The dynamic responses of the system for four different small-disturbance case studies has been carried out in MATLAB environment.

Robust controller design for a nuclear power plant using H/sub /spl infin// optimization

This paper presents an application of H/sub /spl infin//-optimal control to a nuclear power plant. Data from a pressurized heavy water reactor as well as actuator models incorporating nonlinearities were provided for this study by a nuclear agency. Starting with the identification about the nominal operating point to the final controller validation by studying responses for set point changes and disturbance rejection, a detailed description is presented. The normalized coprime factorization approach is adopted to synthesize the H/sub /spl infin// controller.

Computation of normalized coprime factorizations of rational matrices

We propose a new computational approach based on descriptor state space algorithms for computing normalized coprime factorizations of arbitrary rational matrices. The proposed approach applies to both continuous- and discrete-time rational transfer-function matrices and shows that each rational matrix possesses a normalized coprime factorization with proper factors. The new method is conceptually very simple, essentially reducing the original factorization problem to one for proper systems. The main computation consists in solving an appropriate generalized algebraic Riccati equation.

System identification using balanced parametrizations

Some general issues in the black-box identification of multivariable systems are first discussed. It is then suggested that balanced parametrizations can be used to give identifiable forms. A particular advantage is that balanced parametrizations are known for several useful classes of linear dynamic models, including stable minimal models, minimum-phase models, positive-real models, and normalized coprime factor models. Before optimizing the parameters of balanced parametrizations, an initial model must be found. We use realization-based methods and so-called subspace methods for this purpose. These methods are very effective at finding accurate initial models without preliminary estimation of various structural indexes. The paper ends with two simulation examples, which compare the use of balanced parametrizations with more traditional ones, and three real examples based on practical problems: a distillation column, an industrial dryer, and the (irrational) spectrum or sea waves.

On robust stabilization regions of unstructured uncertainties

Relations on the robust stabilization regions of four main forms of unstructured uncertainties are investigated. The robust stabilization regions represented by three other perturbations are derived from coprime factor perturbation and additive perturbation, respectively. Furthermore, it is shown that the normalized coprime factor H ∞ robust controller can also be explained in additive and multiplicative perturbations.

Normalized coprime factorizations for sampled-data systems

The notion of normalized coprime factorization (NCF) for sampled-data systems is studied. The problem is approached by the study of linear systems with discrete jumps at periodic time instants. These systems arise in the study of linear systems with sampled-data control and filtering problems. It is shown that the NCF can be obtained through the solution to Riccati equations with jumps. The properties of the Riccati equations and the corresponding properties of the NCF are studied.

Robust high-gain loop-shapingH ∞ control of servomechanisms

Loop-shapingH ∞ control with normalized coprime factorization is applied to a servo motor-driven precision positioning system. A high-gain controller is designed to attenuate the position errors caused by friction. The analysis of the controller shows that no limit cycle is introduced by the presence of actuator saturation. The designedH ∞ control system is experimentally tested on a rotary index table which requires a high-accuracy position control. The results show that the suggested control scheme improves the positional accuracy and its robustness to the model perturbation and external disturbances without any compensation scheme for friction.

Intelligent Material and Fluid Systems. Large Scale Active Microvibration Control System Using Piezoelectric Actuators Applied to Semiconductor Manufacturing Equipment.

This paper verifies the performance of the active microvibration control system using piezoelectric actuators with a table length of 3 m, a width of 1.8 m and a weight of 4000kg applied to large-scale semiconductor manufacturing equipment whose microlithographic accuracy was actually degraded due to the constant vibration. The mounted equipment was the integral-design semiconductor manufacturing equipment weighting 2600 kg. The controller was designed by a method dependent on the normalized coprime factor plant model in the preceding study used to prevent the elastic vibration of the equipment and table from causing the spillover phenomena of the control system. For the frequency-forming algorithm, the model matching method and the H∞ method were employed. As a result of this system's application, the microlithographic accuracy of the manufacturing equipment could be improved from about 2μm (before application) to an intrinsic value of nearly 0.1 μm.

Study on Non-Contact Hold and Transfer Control by One-Pole-Type Magnetic Robot Hand System. Design and Experiments of Control System Using H.INF. Control Based on the Normalized Coprime Factorization Method and Disturbance Observer.

Study on Non-Contact Hold and Transfer Control by One-Pole-Type Magnetic Robot Hand System. Design and Experiments of Control System Using H.INF. Control Based on the Normalized Coprime Factorization Method and Disturbance Observer.

Normalized coprime factorizations in continuous and discrete time - a joint state-space approach

Based on state-space formulas for coprime factorizations over ... and an algebraic characterization of J-inner functions, normalized doubly-coprime factorizations for different classes of continuous- and discrete-time transfer functions are derived by using a single general construction method. The parametrization of the factors is in terms of the stabilizing solutions of general degenerate continuous- respectively discrete-time Riccati equations, which are obtained by examining state-space representations of J-normalized factor matrices.

Robust control of positioning systems with a multi-step bang-bang actuator

A nonlinear control scheme for preventing the limit cycle due to the nonlinearity of the multi-step bang-bang actuator in mechanical position control systems is proposed. A linearized model, sinusoidal input describing function (SIDF), for a multi-step bang-bang actuator is introduced to compensate the nonlinearity of the multi-step bang-bang actuator. Using that model, an H ∞ robust controller for position control systems with a bang-bang actuator is proposed by loop shaping techniques with normalized coprime factorization stabilization to address the robustness. The proposed scheme requires a smaller deadband as a result of compensating the nonlinearity of the bang-bang actuator. A single-axis servo system is implemented in order to verify the proposed control scheme experimentally. Experimental results show that the controller can satisfy the special interest, silent contact switching of the actuator.

On balanced realizations of bounded real and positive real functions

Based on normalized coprime factorizations with respect to indefinite metrics and the construction of suitable characteristic functions, the Ober balanced canonical forms for the classes of bounded real and positive real functions are derived. This uses a matrix representation of the shift realization with respect to a basis related to sets of orthogonal polynomials.

Riccati equations and normalized coprime factorizations for strongly stabilizable infinite-dimensional systems

The first part of the paper concerns the existence of strongly stabilizing solutions to the standard algebraic Riccati equation for a class of infinite-dimensional systems of the form Σ( A,B,S −1/2 B *, D), where A is dissipative and all the other operators are bounded. These systems are not exponentially stabilizable and so the standard theory is not applicable. The second part uses the Riccati equation results to give formulas for normalized coprime factorizations over H ∞ for positive real transfer functions of the form D+ S −1/2 B *( author− A) −1, B.

Full Range Autopilot Design for an Unmanned Underwater Vehicle

This paper presents results from an investigation into advanced Unmanned Underwater Vehicle (UUV) control functionality to meet mission trajectory requirements. The study's overall aim was to address the multivariable control design strategy across the entire operating envelope for a multi-configured UUV and optimise the transfer between controllers The study has shown that the Hanus bumpless transfer approach can be modified for use in association with linear designs from the H-Infinity loop-shaping approach, and the technique successfully applied to bumpless transfer between different control strategies for a multi-configured UUV. It is also shown that H-Infinity controllers from the normalised coprime factor form can be scheduled using its unique observer structure. In particular this form of gain scheduling is addressed for changing operating point within a selected control strategy.

Active Vibration Control of 2-bed Pendulum.

This paper presents active vibration control of a 2-bed pendulum using H∞ andμ controllers. This paper is a first step to the study of the active control of a suspension bridge tower under construction. Since the suspension bridge tower is flexible, the undesirable wind-indused vibration arises. Thus it is necessary to reduce the vibration to an allowable level. The 2-bed pendulum, which has almost same natural frequency and damping as those of the suspension bridge tower, is adopted as a simple example of this problem. The mathematical model of the 2-bed pendulum is obtained by mechanical laws, and a nominal model is obtained by the reduction of this model. For the designing of a controller, we use both the H∞ theorem based on the "normalized coprime factorization" and μ synthesis. From the experimental results obtained for two types of 2-bed pendulums, the H∞ and μ controllers are proved to be effective for reducing vibration.

H∞ Identification with Truncated Model

In this paper we study identification of discrete time systems using normalized coprime factorization. Robust identifications which agree with robust control theory have been actively investigated in frequency domain and time domain. We have proposed several new identification methods using normalized coprime factorization for time domain identification problems, in which the evaluated functions are given to have relation to the graph topology. In these methods, unknown terms of the identified rational functions, which are caused by I/O data finiteness, are optimally interpolated so that the evaluated functions are minimized. On the other hand, we can show other methods in which the unknown coefficients are approximately equal to 0. According to this idea, we propose some new identification methods using truncated model in this paper. Their algorithms contain iteration of some processes, to solve a linear matrix inequality or the 2-block problem of H∞-norm condition. We also give numerical examples and discuss the effectiveness and the problems of these methods.

Gain-Scheduled Positioning Control for Varying Rope Length in Travelling Cranes.

In this paper we report a design method for controlling a travelling crane mounted on a flexible structure. In order to control the position of the crane cart, the sway of the crane rope and the vibration of the flexible structure, a robust servosystem is designed using the normalized coprime factor H∞ robust stabilization approach. We consider varying the lenght of the crane rope in positioning control and schedule the H∞ compensator in accordance with varying the natural frequency of the crane rope. By numerical calculation the settling performance of the gain-scheduled H∞ compensator is compared with that of a switching H∞ compensator. We verify the efficiency of the gain-scheduled H∞ compensator.