Entire Eigenstructure Assignment Research Articles

Design and Simulation of Three Degrees-of-Freedom Tracking Systems for Capsule Endoscope

Wireless capsule endoscopes (WCE) are a new technology for inspection of the intestines, which offer many advantages over conventional endoscopes, while devices currently in use are passive and can only follow the natural transit of the intestines. There is a considerable interest in methods of controlled actuation for these devices. In this paper, an actuation system based on magnetic levitation is proposed, utilizing a small permanent magnet within the capsule and an arrangement of digitally controlled electromagnet placed on a movable frame. The objective of this paper is to design a multi-input multi-output (MIMO), three degrees-of-freedom (3DOF) tracking system for capsule endoscope. Two techniques, entire eigenstructure assignment (EEA) and linear quadratic regulator (LQR), are presented to design the controller of the system. The performance of the EEA and LQR controllers was compared based on the stability parameters to validate the proposed actuation system. Finally, simulation results suggest that the LQR approach can be used to synthesize a suitable and simple controller for this application.

Explicit Determination of State Feedback Matrices

Methods which calculate state feedback matrices explicitly for uncontrollable systems are considered in this paper. They are based on the well-known method of the entire eigenstructure assignment. The use of a particular similarity transformation exposes certain intrinsic properties of the closed loop w-eigenvectors together with their companion z-vectors. The methods are extended further to deal with multi-input control systems. Existence of eigenvectors solution is established. A differentiation property of the z-vectors is proved for the repeated eigenvalues assignment case. Two examples are worked out in detail.

Optimal entire eigenstructure assignment of discrete-time linear systems

An improved method which assigns the closed-loop eigenvalues of a discrete-time linear system in desired preselected stable locations and which simultaneously selects those eigenvectors which satisfy a quadratic cost criterion with suitable weighting matrices is presented. The optimal feedback gain-matrix is determined without solving the algebraic matrix Riccati equation. The proposed explicit solution of the Riccati equation is feasible for both real and complex closed-loop stable eigenvalues.

A new control design for multiterminal HVDC systems using optimal entire eigenstructure assignment

This paper presents a new method of control design for multiterminal HVDC systems. The proposed design approach applies the optimal entire eignestructure assignment technique developed for optimal state feedback controls of multi-input linear systems in order to achieve predetermined response characteristics. The feedback-gains are computed to assign the closed-loop eigenvalues of the HVDC system at any specified distinct modes and simultaneously minimize an appropriate linear quadratic (LQ) performance index. Therefore, the controller design takes into account the dynamics of the DC transmission system, making possible the regulation of the current at the remote terminals, and at the same time assures both stability with predetermined duration of transient response and minimum system effort. A computer simulation of an integrated ac/dc power system is used to demonstrate the effectiveness of the proposed design since in all simulated cases the transient response for typical disturbances appears desirable, showing fast damping characteristics without significant overshoots or oscillations.

Optimal modal controller design by entire eigenstructure assignment

A computationally simple sequential algorithm for designing an optimal modal controller is presented. The approach is capable of systematically calculating a set of appropriate weighting matrices for the cost functional in the quadratic performance index, so that the resulting optimal control law would not only minimise the cost functional, but also place the eigenspectrum of the closed-loop system at some predefined locations.

Variable Structure Model Reference Adaptive Control System with Application in Robots

The oaoer use the theory of Variable Structure System (VSS) to design a Model Reference Adaptive Control (MRAC) system for a industrial robot. In error state space, the entire eigenstructure assignment method is used to synthesize the hypersurfaces. The control vectors are so decided that the sliding mode is ensured to occur on the hypersurfaces and the sliding motion is both stable and robust to the change of system parameters. A simple equation is used to approximate the equivalent control so the on-line computer control is easier to realize. Digital simulation is done to compare with MRAC, the results show that Variable Structure Model Reference Adaptive Control (VSMRAC) is more adequate to calculate and statisfactory in control performance.

Eigenvalue-generalized eigenvector assignment by output feedback

This note generalizes the previous results of the closed-loop eigenstructure assignment via output feedback in linear multivariable systems. Necessary and sufficient conditions for the closed-loop eigenstructure assignment by output feedback are presented. Some known results on entire eigenstructure assignment are deduced from this result.

Some necessary and sufficient conditions for eigenstructure assignment

Abstract Some necessary and sufficient conditions for closed-loop eigenstructure assignment by output feedback in time-invariant linear multivariable control systems are presented. A simple condition on a square matrix necessary and sufficient for it to be the closed-loop plant matrix of a given system with some output feedback is the basis of the paper. Some known results on entire eigenstructure assignment are deduced from this. The concept of an inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigenstructure consisting of the eigenvalues and a mixture of left and right eigenvectors.

Computer-Aided Design of Dynamic Compensators for Linear Multivariable Continuous-Time Systems

In view of the fundamental new insights into the structure of linear multivariable continuous-time systems provided by the method of entire eigenstructure assignment, the design of dynamic compensators is equivalent to the selection of pairwise-orthogonal eigenvectors and reciprocal eigenvectors from two families of well-defined subspaces which are parametrised by associated self-conjugate eigenvalue spectra. This selection is effected by the use of a powerful new algorithm which requires the performance of restricted elementary row and column operations on matrices formed from the spanning vectors of these subspaces. The digital computer implementation of the resulting procedure incorporating this algorithm is described and is illustrated by the design of an error-actuated dynamic compensator for a linear multivariable plant.

Minimum settling-time control policies for cascaded production-inventory systems

In this paper, the technique of entire eigenstructure assignment is used to derive minimum settling-time control policies for a class of production—inventory systems which can be described by linear multivariate discrete-time state equations. It is shown that this technique can be readily used to derive minimum settling-time control policies for production-inventory systems which consist of a set of production-inventory sub-systems connected in cascade. The advantage obtained by using control policies derived in this way, compared with control policies derived by consideration of each sub-system in isolation, is clearly demonstrated.

Design of linear multivariable continuous-time tracking systems incorporating error-actuated dynamic controllers

In this paper the method of entire eigenstructure assignment (Porter and Bradshaw 1978) is applied to the design of linear multivariable continuous-time tracking systems incorporating error-actuated dynamic controllers. The method is illustrated by designing an error-actuated dynamic controller which causes the output of a second-order continuous-time plant to track a constant command input in the presence of an unmeaaurable constant disturbance input.

Design of linear multivariable continuous-time output-feedback regulators

In this paper, the method of entire eigenstructure assignment (Kimura 1975, Moore 1976, Porter and D'Azzo 1917) is applied to the design of linear multivariable continuous-time output-feedback regulators. It is shown that, in the case of self-conjugate distinct eigenvalue spectra, the closed-loop eigenstructure assignable by output feedback is constrained by the requirement that the eigenvectors and reciprocal eigenvectors lie in well-defined subspaces. The method is illustrated by designing an output-feedback regulator for a third-order continuous-time system.

Design of high-gain state-feedback controllers for linear multivariable systems

It is shown that recent results in the theory of entire eigen-structure assignment greatly facilitate the design of high-gain state-feedback controllers. The design of such controllers is reduced to the separate computation of well-defined subspaces associated with the `slow´ and `fast´ modes of closed-loop systems incorporating high-gain controllers.

Algorithm for the synthesis of state-feedback regulators by entire eigenstructure assignment

The algorithm for the computation of a basis for ker (A−λoIn, B) presented greatly facilitates the synthesis of state-feedback regulators by entire eigenstructure assignment. It is ideally suited for digital-computer implementation and can be readily dualised for use in the synthesis of full-order observers by entire eigenstructure assignment.