Relationships between Recent Developments in Linear Control Theory and Classical Design Techniques (Part 1)

The root-locus-approximation procedure is extended to provide for the complex-plane analysis of equations which contain a term quadratic in the variable parameter in addition to the usual linear term. Such an extension will have many applications; in the paper, a discussion is given concerning the design of linear time-invariant multivariable feedback systems. It is shown that, particularly for 2-input/2-output problems, where the algebra involved in obtaining the equations to be analysed remains fairly simple, much useful information is available by straightforward hand calculation. Brief suggestions are given for further generalisations of the techniques (inclusion of a cubic gain term etc.)

This paper presents an algebraic theory for analysis and design of linear multivariable feedback systems. The theory is developed in an algebraic setting sufficiently general to include, as special cases, continuous and discrete time systems, both lumped and distributed. Designs are implemented by construction of a controller with two vector inputs and one vector output. Use of controllers of this type is shown to generate convenient stability results, and convenient global parametrizations of all I/O maps and all disturbance-to-output maps achievable, for a given plant, by a stabilizing compensator. These parametrizations are then used to show that any such I/O map and any such disturbance-to-output map may be simultaneously realized by choice of an appropriate controller. In the special case of lumped systems, it is shown that the design theory. can be reduced to manipulations involving polynomial matrices only. The resulting design procedure is thus shown to be more efficient computationally. Finally, the problem of asymptotically tracking a class of input signals is considered in the general algebraic setting. It is shown that the classical results on asymptotic tracking can be generalized to this setting. Additionally, sufficient conditions for robustness of asymptotic tracking, and robustness of stability are developed.

Relationships between Recent Developments in Linear Control Theory and Classical Design Techniques (Part 5: Conclusion)

In this paper a basis is developed for the systematic design of linear multivariable continuous-time tracking systems for plants with inaccessible states which thus extends the results for continuous-time plants with accessible states previously obtained by Porter and Bradshaw (1974). The design method is illustrated by the presentation of the results of computer simulation studies.

In this paper a basis is developed for the systematic design of linear multivariable discrete-time tracking systems for plants with inaccessible states, which thus extends the results for discrete-time plants with accessible states previously obtained by Bradshaw and Porter (1975). The design method is illustrated by the presentation of the results of computer simulation studies.

In the transform analysis of linear systems the two classical approaches use complex functions to study gain as a function of frequency (the Nyquist—Bode approach)and to study frequency as a function of gain (the Evans root locus approach)The central feature of any transform approach to the analysis of linear multivariable systems is the use of transfer-function matrices, and it. is the primary purpose of this paper to explain how the ideas of studying gain as a function of frequency, and frequency as a function of gain, can be extended to the multivariable case by associating with transfer-function matrices characteristic gain functions and characteristic frequency functions The characteristic gain function and characteristic frequency function are algebraic functions, each of which is defined on an appropriate Riemann surface. Considering the Riemann surface domain for the characteristic frequency function, a stability criterion for linear multivariable feedback systems is established which doe...

The paper is concerned with the derivation of useful results that complement the linearisation-based analysis and design of multivariable systems with measurement nonlinearity. The approach is based on the closed-loop linearised system descriptions and certain nonlinearity related parameters representing sector and/or incremental sector properties, and also enables the consideration of nonlinearities with discontinuities at the origin. Nonlinear-system stability and performance is assessed on the basis of the stability and performance of the corresponding linearised system and certain easily computable sufficient conditions representing BIBO and asymptotic stability conditions, as well as absolute and derivative performance bounds. The results depend on useful linearised system descriptions such as the L∞ operator norm, thus offering the advantages of meaningful assessments and overall computational simplicity.

A new designing method of multivariable linear time-varying tracking systems with stochastic disturbances for polynomial command inputs is proposed. It has been shown that it is possible to choose the matrices of gain elements placed in feedbacks and parallel paths of the closed-loop system so that the output y(t) tracks the polynomial command input v(t) with (E expectation operator).

SOME UNIFYING CONCEPTS IN MULTIVARIABLE FEEDBACK DESIGN

The paper presents a method of engineering analysis and design for complex control systems, the time-domain infinite-matrix method. The formulation of the infinite matrix follows from the convolution summation of sampled-data systems. The mathematical basis of the time-domain matrix formulation is related to the applicable concepts of infinite matrices and sequence spaces. The method is applicable to both continuous-data and sampled-data systems. For continuous systems it is necessary to introduce a fictitious sampler and `hold? of sufficient sampling rate to effect an accurate approximation. The time-domain-matrix method is presented and illustrated as a method of analysis and design of linear, non-linear, and time-varying systems of the continuous-data or sampled-data class. The investigation of non-linear systems is greatly simplified by the time-domain approach. Multi-loop systems may be investigated, and the signals at intermediate points throughout the loops are readily available. Also, systems with multiple non-linearities may be investigated. Two methods of design of a discrete compensator for a sampled-data system are presented. These methods are accomplished directly in the time domain and allow for a compromise of specifications in the time domain. In one design procedure the response between sampling instants is also accounted for. The time-domain-matrix method may be readily programmed on a digital computer, and therefore provides a rapid analysis and design technique.

In this paper, the class of linear multivariable continuous-time plants which are amenable to high-gain error-actuated control is characterized in terms of the relatively prime polynomial matrix factors of the transfer function matrices of such plants. It is shown that this characterization greatly facilitates the design of high-gain error-actuated controllers, and the resulting synthesis technique is illustrated by designing such a controller for a third-order plant with two inputs and two outputs.

This paper presents a method for the analysis and control design of linear systems in the presence of actuator saturation and L/sub 2/-disturbances. A simple condition is derived under which trajectories starting from an ellipsoid will remain inside an outer ellipsoid. The stability and disturbance tolerance/rejection ability of the closed-loop system under a given feedback law is measured by the size of these two ellipsoids and the difference between them. Based on the above mentioned condition, the problem of estimating the largest inner ellipsoid and/or the smallest difference between the two ellipsoid is then formulated as a constrained optimization problem. All the constraints are shown to be equivalent to LMIs. In addition, disturbance rejection ability in terms of L/sub 2/ gain is also determined by the solution of an LMI optimization problem. By viewing the feedback gain as an additional free parameter, the optimization problem can easily be adapted for controller design. Numerical examples show that the proposed analysis and design methods significantly improve recent results on the same problems.

A unique design technique of power line filter is being proposed. It is based on the conventional technique of composite low pass filter. The equivalent circuit of the composite low pass filter is being presented in the two different modes by considering the modal propagation of noise. The consideration of composite LPF is taken into account in the design technique of power line filter. In order to accurately predict the insertion loss of the filter the effects of non-ideal behaviour of the passive lumped components are considered. It is based on the parasitic effect of the passive lumped elements. The filter is then characterized using S-parameters. The response of the filter's circuits is simulated using advanced design software (ADS). Keywords: Conducted emission, Composite filter, electromagnetic compatibility, lumped elements, and power line filter. I. Introduction Switching and modulation techniques are used for efficient use of electrical power. Widely used Switched mode power supplies (SMPS) for powering today's electronics loads is a most common example. Unfortunately, all the power control techniques deliberately distort sinusoidal wave form of power frequency and generate unwanted interfering signals. Obviously, they all are often cited as one of the main source of conducted emission (CE). Usually the power supplies which are using controlling techniques cannot comply with the strict electromagnetic compatibility (EMC) regulations. In order to meet the limit set for conducted EMI, power supplies require a filter at its input. Conducted EMI generated through particular equipment gets coupled into other equipments mostly through power line cables. CE can be controlled by using filters and increasing line impedance. Conducted EMI has two components: The common mode (CM) interference and differential mode (DM) interference. The coupling mechanisms of these interferences are different (4). The difference in the direction of propagation of these coupling currents along the phase and neutral line, leads to differential mode ( ) current and common mode ( ) current. Therefore design of EMI filters demand decoupling of these two modes (2). This paper attempts to describe a design technique for Power Line filter using classical design technique. 1.1 Characterization of common mode & differential mode currents

A design methodology for linear multivariable feedback systems is formulated which utilizes modern algebraic control theory and does not require manipulation of polynomial or rational matrices. The methodology uses direct measurements of the plant in obtaining designs.

An analytical method is described for the design of linear time-invariant SISO feedback systems to meet specified performance criteria in the presence of structured and unstructured uncertainty. The design framework also provides for control over the degree of the compensator.