Extended howze-pearson compensators in block decoupling problems.

A simple method is presented on how to generate the state feedback which makes the closed-loop transfer matrix the inverse of the interactor matrix. This can be regarded as a generalization of decoupling control using state feedback. An arbitrary pole assignment which preserves the lower left triangular form of the inverse of the interactor matrix is also considered. >

The pole assignment problems of linear systems by decentralized static output feed-back are considered in this paper. A compactification of decentralized static feedback space, product Grassmannians, is introduced in this paper. Its degree under Plücker–Segre embedding is computed. Sufficient conditions for arbitrary and almost arbitrary pole assignability are given. It is also proved that the generic $m \times p$ system of McMillan degree n has arbitrary pole assignability by r-channel decentralized static output with $m_i $ inputs and $p_i $ outputs on the ith channel if $\sum_{i = 1}^r {m_i p_i } \geq n$ when the degree of the product Grassmannians is odd, or if a $\sum_{i = 1}^r {m_i p_i } > n$ and the local channels have either the same numbers of inputs or the same numbers of outputs when the degree of the product Grassmannians is even.

In this study, we propose a class of dynamic compensators based on linear function observers which achieve arbitrary pole assignment of the closed loop. The construction procedure directly utilizes Wang's algorithm (1992, 1996) for the static output feedback pole assignment problem, and the same technique can be applied to dual observers also. As a result, assuming the structure of either observer, the sufficient condition of the compensator's order is naturally derived. The condition is more transparent than the one proposed by Rosenthal and Wang (1996), and it is shown that both give the same minimal order under some mild assumptions.

It is important to know how far non-dominant poles can be located away from the dominant poles since the closed-loop system transient response may not be as expected, if the non-dominant poles are not placed far enough from the dominant pole pair. Even if the arbitrary pole assignment is possible with a full state feedback or an output feedback controller with the order of plant order minus one, low order controllers and especially PID controllers are used in most practical applications. Therefore, the farthest possible non-dominant pole locations with PID controllers are found for all pole systems in this study. Proposed calculation method is demonstrated on two different examples and the closed-loop system performance is investigated with the designed PID controllers.

The problem of block decoupling of singular systems via state feedback and regular input transformation is solved by following an approach based on the matrix fraction description (MFD) of the system. The solvability condition is obtained from the 'numerator' matrix of a coprime and column reduced MFD of the given system. The characterization of the fixed poles is given and it is shown that all the non-fixed poles can be arbitrarily assigned.

This short paper deals with the problem of pole assignment with incomplete state observation. It is shown that if the system is controllable and observable, and if n \leq r + m - 1 , an almost arbitrary set of distinct closed-loop poles is assignable by gain output feedback, where n, r , and m are the numbers of state variables, inputs and outputs, respectively. This result improves considerably the ones obtained so far about this problem. Different from the conventional approach using the characteristic equation, an approach based on the properties of the eigenspaces of the closed-loop dynamics is used in this short paper, which gives a new light on the various problems in the linear system theory. It is also shown, as a direct consequence of this result, that the minimum order of the dynamic compensator required for almost arbitrary pole assignment of overall closed-loop system is not greater than n - m - r + 1 .

Based on the method of inequalities, we propose a systematic design method for SISO unity feedback systems. Using this method, we can take account of the influence of pole-zero cancellations. First, we derive a simple pole-zero placement algorithm which can achieve specified pole-zero cancellations, ensuring the steady state characteristics with the order of the controller fixed. Then we show how to modify the search algorithm by considering the properties of the tuning parameters. To illustrate the effectiveness of our method, we present a design example where the proposed design method is compared with another approach.

A new pole-placement algorithm for multi-input controllable systems is presented. The algorithm can be used to obtain real-valued feedback gains for arbitrarily specified real and complex, distinct or multiple eigenvalues. The multi-input controllable time-invariant system is converted to a single-input system. Pole assignment is achieved by making use of certain properties of the equation TF - AT = D , where A is the open-loop system matrix and F represents a matrix having the desired closed-loop eigenvalues.

A sufficient rank condition for arbitrary pole assignability by static output feedback of m-input, p-output linear systems of McMillan degree n<mp is given. This condition is easy to check and is satisfied by the generic system. An effective computational method to compute the feedback laws assigning any self-conjugate set of closed-loop poles is also given.

The problem of trim point transitions is investigated for 6DOF quadrotors, using I/O decoupling controllers. The linear approximant of the quadrotor is derived in parametric form with respect to the physical parameters of the nonlinear model and the trim points. Based upon the linear approximant, a static state feedback control law achieving I/O decoupling, command following and arbitrary pole assignment for the linear approximant of the closed loop system, is derived. The controller is expressed in terms of the physical parameters and the closed loop characteristic polynomial arbitrary coefficients. To increase the range of accurate transition among different trim points of the nonlinear model, appropriate cost criteria are used and a trim point transition algorithm is proposed. The performance of the overall scheme is demonstrated through simulation results.

This article investigates region stabilization issue of switched neural networks (SNNs) with multiple modes (MMs) and multiple equilibria (ME) via a pole assignment method. In such an SNN, every neuron is observed with more than one mode and unstable equilibrium point. First, SNNs with MMs and ME are modeled in terms of switched systems with unstable subsystems and ME. Second, a necessary and sufficient condition and a sufficient condition are, respectively, proposed for arbitrary switching paths pole assignment and arbitrary periodic/quasi-periodic switching paths (PSPs/QSPs) asymptotically region stabilizing pole assignment of switched linear time-invariant (LTI) systems with ME. It is shown that to stabilize a switched LTI system, some/all poles of all/some linear subsystems can be assigned to suitable locations of the right-half side of the complex plane. Third, based on the obtained pole assignment results, an asymptotical-region-stabilizing-control law observed as distributed state feedback controllers of MMs, asymptotical-region-stabilizing PSPs/QSPs, and a corresponding algorithm are all designed for asymptotical region stabilization of switched linear/nonlinear neural networks with MMs and ME. Finally, a numeral example is given to illustrate the effectiveness and practicality of the new results.

This paper presents a new technique to analyze dynamic behaviour of a sucker rod string used in the oil well industry. The main concept of the proposed approach is to replace the actual complicated system by a simpler one. This needs the output or one-time accurate solutions of the actual system. This problem is solved using D‘Alembert's solution of systems equation and the adaptive filter matrix method developed by the authors. The developed computer program performs the calculations in very short real time with reasonable accuracy, and without extensive hardware and software requirements. It has been proven that it is possible to use the transfer matrix to calculate load-displacement relations a hundred or more times in one stroke. This could be very advantageous in building new well-head controllers and other tools to control the oil wells. Introduction Rod pumping is the oldest and still the most common method of artificial lift used extensively in the oil well industry(1,2). The literature devoted to the analysis of this system is very extensive. There are different computer programs aimed at the analysis and troubleshooting of rod pumping systems(3–5), however, they require fully equipped computer hardware to perform the calculations. These calculations usually take an amount of time that is longer than the period of pumping (one stroke) and cannot be directly used to control the well in real time. In this paper, a transfer matrix method has been proposed to model the dynamic behaviour of the rod of the sucker string. The main concept of the method is to replace the solution of the mathematical model by a simple matrix operation in which the bottomhole force-displacement values are obtained as the product of the vector of the data at the polished rod end by a transfer matrix. This is an extremely fast mathematical operation, which can be performed hundreds of times during the period of one stroke and does not require any sophisticated software. The system transfer matrix for any given oil well is defined only once in advance using the filter matrix method(6–8). The matrix does not change with time and replaces the mathematical model of the analyzed system. Using this technique, the calculations of the bottomhole values can be performed very fast and in a very simple way. These calculations are easy to implement in one microprocessor. In the studies presented here, we found that to create the system transfer matrix, it is enough to replace the real system by a two-segment rod. The simplified model is solved using D‘Alembert's method(9). Using the equivalent model, the transfer matrix is created. Mathematical Modelling To analyze the performance of the oil well, the force and displacement at the polished rod are measured using a dynamometer. Then these data are used as the boundary conditions for the calculation of forces and displacements at the bottom of the rod string that defines the conditions of the pump, effectiveness of pumping, production rate, etc.

Internal-inertial image stabilization (IIIS) is a new form of image (or beam) stabilization. One of the components of an image-forming system is directly attached to a gyroscope to provide an inertial reference, thereby eliminating the usual vibration sensor/feedback/control subsystem, ordinarily required to produce vibration-free imaging. This paper discusses two basic optical configurations utilizing IIIS: that for the image surface mechanically coupled to the instrument, as in photographic applications, and that for a mechanically uncoupled image surface, such as an eye. Basic stabilization relations are derived, and a definition of stabilization factor is presented. Kinematic transfer matrix approaches are constructed which allow the effect on image stability of any system element to be determined. A method of deriving the coordinate transformation matrix corresponding to a given reflection matrix is presented.

Continuous time and discrete space Another form of lattice-gauge theory that is very intuitively appealing is the theory's Hamiltonian form. In many problems it is very instructive to make energyestimates, look at wavefunctions, and estimate the masses, sizes, and shapes of bound states etc. that a quantum-mechanical formulation with a Hamiltonian gives. Sometimes these simple things are hard to extract from a path-integral formulation. Mechanisms of confinement, flux-tube dynamics, and chiral-symmetry breaking are also amenable to Hamiltonian analysis. Decon-finement at finite T and transitions as functions of chemical potential will also be discussed in this formulation below. Since there is much more pioneering physics to be done in QCD in extreme environments, it is important to have many approaches available. In the Hamiltonian formulation one uses a spatial lattice and leaves the time variable continuous, as we have illustrated in several 1 + 1 examples above. The Hamiltonian is the generator of time evolution and acts on quantized states. The Hamiltonian could be obtained methodically from the path-integral formulation by calculating the system's transfer matrix and then taking the time continuum limit [9]. It is more instructive, however, to construct the Hamiltonian from scratch. In fact, we can think about just two spatial points, write the Hamiltonian for that system, and then consider a full three-dimensional spatial lattice. As in the Euclidean formulation, the key to the construction is the requirement that local color-gauge invariance be an exact symmetry for any lattice spacing a . Let there be two sites with the link between them.

This paper presents the application of multivariable identification methods to obtain models for commercial road vehicles from measured stress responses arising in certain structural elements due to stochastic road excitation. The elementary subystem representation of the system transfer matrix allowing an effective structure and parameter estimation is used to model the vehicle and noise dynamics. Measurements were carried out on a laminated spring suspension bus, and models were indentified atvarious road profile variances and speed levels of the vehicle.