Single-input Case Research Articles

Function based hybrid-fuzzy genetic controller for VSI based STATCOM

In this paper a variable structure fuzzy PI-genetic control scheme is proposed for a Voltage Source Inverter based STATCOM in damping the electro-mechanical oscillations of a power system. The function based Takagi-Sugeno-Kang (TSK) fuzzy controller uses two rules and generates the proportional action which, by one-to-two mapping, gives a variable gain PI controller. This single-input, function based fuzzy controller, dispenses the gain dependency of the proportional or integral gains and generates independent controls. To demonstrate the application of the proposed controller, a case study is done with a single and multimachine power system operating with STATCOM. Further, Genetic Algorithm (GA) is used to tune the parameters of the analytical fuzzy PI controller for optimal damping performance. Computer simulation results clearly reveal the superior performance of the proposed controller. A comparison is also made with a two-input fuzzy controller using four rules instead of just two as in the single input case.

Using data envelopment analysis to solve unconstrained two-objective binary integer linear programming

A subset of projects, from a set of feasible projects, is treated as a portfolio.The problem of selecting and evaluating all possible collective projects is modeled as unconstrained binary integer linear programming (BILP). Data envelopment analysis (DEA) is an effective method for classifying all portfolios into efficient and inefficient subgroups. In this paper, we focus on the single input and output case and use DEA as a tool to solve the two-objective BILP. The inherent relationships between output-input ratios of projects, and DEA portfolio efficiencies are presented in this paper. These findings enable the efficient and inefficient portfolios to be identified by ratio analysis. Moreover, if project with non-positive input and/or output is included in the decision set, our method is also valid through changing variables from the original model.

On positivity and stability of a class of time-delay systems

In this paper, the properties of positivity and stability dependent on and independent of the delays as well as the closed-loop stabilization under linear feedback of continuous-time linear time-invariant multi-input multi-output dynamic systems subject to point constant delays are discussed. A main attention is paid to provide joint stability and positivity results which are shown to be conflictive objectives in the general case. Links with positive realness are given for the single-input single-output case. Illustrative examples are also given.

Formula omitted] control of preview systems

The H 2 -optimal controller for systems with preview, in which the knowledge of external input is available in advance for the controller, is derived. The single input case is first considered and solved by transforming the problem into a non-standard LQR problem. Based on the single input result, the multiple inputs case and the multiple preview times case are treated. In every case considered, the controller consists of a static state feedback plus a finite impulse response block. The paper also provides a formula for the optimal H 2 -norm that clearly shows how the performance gain owing to the previewed input varies as the preview time increases.

Exponential /spl epsiv/-regulation for multi-input nonlinear systems using neural networks

This paper considers the problem of robust exponential epsilon-regulation for a class of multi-input nonlinear systems with uncertainties. The uncertainties appear not only in the feedback channel but also in the control channel. Under some mild assumptions, an adaptive neural network control scheme is developed such that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded and, under the control scheme with initial data starting in some compact set, the states of the closed-loop system is guaranteed to exponentially converge to an arbitrarily specified epsilon-neighborhood about the origin. The important contributions of the present work are that a new exponential uniformly ultimately bounded performance is proposed and that the design parameters and initial condition set can be determined easily. The development generalizes and improves earlier results for the single-input case.

H2 CONTROL OF PREVIEW SYSTEMS Agoes

The H2-optimal controller for systems with preview, in which the knowledge of external input is available in advance for the controller, is derived. The single input case is first considered and solved by transforming the problem into a non-standard LQR problem. It turns out that the extensions to multiple inputs and multiple preview times cases are straightforward. In every case considered, the controller consists of a static state feedback plus a finite impulse response block.

Feedback Classification of Multi-Input Nonlinear Control Systems

We study the feedback group action on multi-input nonlinear control systems with uncontrollable mode. We follow slightly an approach proposed in Kang and Krener [W. Kang and A. J. Krener, SIAM J. Control. Optim., 30 (1992), pp. 1319--1337] which consists of analyzing the system and the feedback group step by step. We construct a normal form which generalizes, on one hand, the results obtained in the single-input case and, on the other hand, those recently obtained by the same author in the controllable case. We illustrate our results by studying the Caltech Multi-Vehicle Wireless Testbed (MVWT) and the prototype of Planar Vertical TakeOff and Landing aircraft {(PVTOL)}. We also study the notion of bifurcation of controllability for systems with one nonzero uncontrollable mode. We first show that the equilibria for those systems is a p-dimensional submanifold (p equals number of inputs). Provided that one term in their normal form is nonzero, we show that these systems are linearly controllable, hence stabilizable, at any nearby equilibrium point of the origin.

Insensitivity of a class of LQ regulators of neutral systems

It is well known that the linear quadratic regulators of finite dimensional linear systems have the insensitivity property. In this paper, as a particular class of infinite dimensional systems, a neutral delay-differential system is considered as a plant. A class of linear quadratic regulators is constructed for the plant using a simple feedback law, which does not require real-time either integral or derivative operations. The feedback gain is calculated by solving a finite dimensional linear matrix inequality. First, it is shown that the regulator satisfies the circle condition. Then, its sensitivity against the parameter variations is evaluated. In the single-input case, it is done by calculating the absolute value of the sensitivity function. In the multi-input case, it is done by the so-called “comparison sensitivity” method where the sensitivities of the closed-loop system and the open-loop system are compared based on certain sensitivity indices. Procedures used for the investigation of the regulator's properties are based on natural extension of methods proposed by Perkins and Cruz for the finite dimensional case. As a result, it is found that the class of linear quadratic regulators of neutral systems, similarly to finite dimensional systems, has the insensitivity property. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 150(2): 28–34, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20013

On the tightness of a recent set invariance condition under actuator saturation

A sufficient condition for an ellipsoid to be invariant was obtained recently and an LMI approach was developed to find the largest ellipsoid satisfying the condition. This condition was later shown to be necessary for the single input case. This paper is dedicated to the multi-input case. We will examine the conservatism of the condition for multi-input systems. Our investigation is conducted by studying the optimal solution to a related LMI problem. A criterion is presented to determine when the condition is not conservative and when the largest invariant ellipsoid has been obtained by using the LMI method.

New results on doubly coprime fractional representations of generalized dynamical systems

This note first points out that the main results by Wang and Balas regarding the doubly coprime fractional representations for generalized dynamical systems have severe limitation in their applications, that is, the doubly coprime factorization obtained by Wang and Balas cannot characterize the parameterization of all properly stabilizing controllers when a system is singular, therefore, truly generalized. To remedy those results, two new doubly coprime factorizations have been developed that will parameterize all properly stabilizing controllers for single-input or single-output cases. In addition, the new results can characterize the parameterization of all corresponding causal properly stabilizing controllers. Finally, the extension to the multiple-input-multiple-output case is presented.

Insensitivity of a Class of LQ Regulators of Neutral Systems

It is well known that the linear quadratic regulator of finite dimensional linear systems has the insensitivity property. In this paper, as a particular class of infinite dimensional linear systems, a neutral delay-differential system is considered as a plant. A class of linear quadratic regulators is constructed for the plant via a simple feedback law without real-time integral nor derivative operation. The feedback gain is calculated with a solution of a finite dimensional linear matrix inequality. First, it is shown that the regulator satisfies the circle condition. Then, its sensitivity against the parameter variation is evaluated. In the single-input case, it is done by calculating the absolute value of the sensitivity function. In the multi-input case, it is done by the method so called “comparison sensitivity”, where the sensitivities of the closed loop system and the open loop system are compared by some sensitivity indices.The procedure to investigate the property is a natural extension of one by Perkins and Cruz, where the finite dimensional case was treated. As a result, it is shown that the class of linear quadratic regulators of neutral systems has the insensitivity property as well as that of finite dimensional systems.

Configuration Controllability of Mechanical Systems Underactuated by One Control

We investigate local configuration controllability for mechanical control systems within the affine connection formalism. We rely on previous results on controllability and series expansions for the evolution of mechanical systems starting from rest. Extending the work by Lewis for the single-input case, we are able to characterize local configuration controllability for systems with n degrees of freedom and n-1 input forces.

An algorithm for the multi-input complex eigenvalue assignment problem

In this paper, a simple, efficient and accurate method for complex eigenvalue assignment in the multi-input linear system is presented. The method considers both cases: all eigenvalues need to assign are complex (with their complex conjugates). The other case is the arbitrary eigenvalues need to assign are mixed (some are real and the others are complex which are closed under complex conjugations). The algorithm proposed in this method is a modification to the one proposed by Arnold and Datta [IEEE Trans. Automat. Contr. 35 (10) (1986) 1149] which considers the case where all the eigenvalues need to assign are only real. Also, it is a kind of extension to the algorithms suggested by Ramadan [in press] and Ramadan and El-Shazly [in press] where arbitrary preassigned complex and mixed eigenvalues are assigned for single-input case respectively. The method first transforms the problem to block-Hessenberg form, of needed form, using orthogonal reduction, then a simple linear recursion is carried out to find the feedback matrix so that the closed-loop matrix has the prescribed eigenvalues. The main advantages of the algorithm, besides being simple and has recursive nature it avoids complex arithmetic and easy to program on computer. Numerical examples are given to illustrate the reduction process, the algorithm performance and the accuracy of the method.

How Not to Measure the Efficiency of Public Services (and How One Might)

SummaryThe single-input case of the ‘technical efficiency’ theory of M. J. Farrell is reformulated geometrically and algebraically. Its linear programming developments as ‘data envelopment analysis’ are critically reviewed, as are the related techniques of ‘stochastic frontier analysis’. The sense and realism of using data envelopment analysis or stochastic frontier analysis techniques, rather than some value-based method, for the assessment of police force efficiency are questioned with reference to the Spottiswoode report and related studies.

STABILIZING CONTROL FOR DISCRETE TIME MULTI-INPUT BILINEAR SYSTEMS

This paper presents two stabilizing control methods for discrete time bilinear systems. One is a stabilizing controller for single input systems, and the other is a generalized stabilizing control method for discrete time multi-input bilinear systems. The proposed control methods guarantee the stability for each closed loop systems with single-input case and multi-input case, respectively. This paper introduces a lemma used to extend the stabilizing control method which is useful to represent any bilinear systems as pure differential (difference) matrix equations. The proposed algorithms are verified by a numerical example.

Stability of Planar Switched Systems: The Linear Single Input Case

We study the stability of the origin for the dynamical system $\dot x(t)=u(t)Ax(t)+(1-u(t))Bx(t),$ where A and B are two 2 × 2 real matrices with eigenvalues having strictly negative real part, $x\in {\mbox{{\bf R}}}^2$, and $u(.):[0,\infty[\to[0,1]$ is a completely random measurable function. More precisely, we find a (coordinates invariant) necessary and sufficient condition on A and B for the origin to be asymptotically stable for each function u(.). The result is obtained without looking for a common Lyapunov function but studying the locus in which the two vector fields Ax and Bx are collinear. There are only three relevant parameters: the first depends only on the eigenvalues of A, the second depends only on the eigenvalues of B, and the third contains the interrelation among the two systems, and it is the cross ratio of the four eigenvectors of A and B in the projective line CP1. In the space of these parameters, the shape and the convexity of the region in which there is stability are studied. This bidimensional problem assumes particular interest since linear systems of higher dimensions can be reduced to our situation.

Resonance phenomenon of interspike intervals from a spiking oscillator with two periodic inputs

We consider a spiking oscillator to which two periodic and synchronized inputs can be applied. As either input is applied, typical phenomena from the oscillator are phase locking and quasi-periodic behaviors. Applying both inputs and adjusting their parameters appropriately, the system behavior approaches a resonance point characterized by: (1) The state is quasi-periodic; (2) the output pulse-train is periodic; and (3) they are not synchronized with the periodic inputs. Generating such resonance phenomena is impossible in the single input case. We present a simple implementation method of the spiking oscillator and verify the typical phenomena in the laboratory.

Banded matrix fraction representation of triangular input normal pairs

An input pair (A, B) is triangular input normal if and only if A is triangular and AA* + BB* = I/sub n/, where I/sub n/ is the identity matrix. Input normal pairs generate an orthonormal basis for the impulse response. Every input pair may be transformed to a triangular input normal pair. A new system representation is given: (A, B) is triangular normal and A is a matrix fraction, A = M/sup -1/ N, where M and N are triangular matrices of low bandwidth. For single input pairs, M and N are bidiagonal and an explicit parameterization is given in terms of the eigenvalues of A. This band fraction structure allows for fast updates of state space systems and fast system identification. When A has only real eigenvalues, one state advance requires 3n multiplications for the single input case.

Flexible Structure Control by Eigenstructure Assignment

Abstract This paper presents a generalization to multi input of a technique used for designing control laws of single input flexible structures. The objective consists of assigning the eigenvalue motions due to (scalar) loop gain variations. In the single input case, phase is changed at some frequencies. In the proposed generalization, phase lead and lag is replaced by eigenvector “assignment” which consists of designing a dynamic feedforward having ad hoc eigenstructure. It remains to tune the scalar loop gain. The design problem considered is shown to reduce to solving a set of linear equalities and/or inequalities. A quadratic criterion which enables to minimize energy involved in assignment is also proposed.

Reliability assessment of structure subjected to horizontal-vertical random earthquake excitations

Statistical analysis of the response spectra due to both horizontal and vertical ground excitations is conducted. A method is presented for generating a uniform hazard response spectrum making use of the seismic hazard curve expressing annual probability of exceedance as a function of peak ground acceleration (PGA), a set of normalized mean response spectra, and a coefficient-of-variation function for the random normalized spectral values in terms of period T. The response spectra of the system are calculated by considering both horizontal and vertical excitations simultaneously. Comparison on the uniform hazard response spectrum for case of single input (horizontal excitation only) and for case of multiple inputs (horizontal and vertical excitations) are made. It is important to note that the effect of load ratio ( Mg / P cr) as well as the PGA ratio between horizontal and vertical ground accelerations are two important parameters in the analysis of structural systems subjected to both horizontal and vertical ground motions.