一类时变系统中补偿器的功能和设计

PID控制器由于其结构简单和参数整定容易,具有良好的控制功能,被广泛应用在工程上的线性确定性系统中.但是,在非线性系统和不确定性系统中, PID控制器由于其固定的控制参数和结构限制,很难克服系统中内外干扰的影响,控制器鲁棒性能较差.本文按照被控对象中的标称模型设计常规PID控制器优化参数,对非线性系统中多个线性化模型和不确定性系统中的不同工作点模型,设计了一类补偿器,使得整个闭环系统具有与标称模型下相同的控制品质.工程应用例子论证了本文提出的补偿器能提高不确定与非线性系统的控制品质和鲁棒性能.     

多变量控制系统频域分析和设计的综述

本文介绍了多变量系统频域分析和设计方法的一些最新发展。在系统分析方面,主要介绍特征轨迹(CL)方法和主增益、主相位的方法。在系统综合方面,主要介绍方向排列(alignment)技术,鲁棒性准则和逆结构正则化(RFN)补偿器,最后作者们对多变量系统分析和设计中的频域法的研究前景进行了展望。     

Design of rate and amplitude saturation compensators using three degrees of freedom controllers

This paper proposes two frequency-domain design techniques for rate and amplitude saturation compensators formulated as three degrees of freedom controllers. For single constraint systems, it shows an equivalence between the a posteriori compensator design and the a priori controller synthesis proposed by Horowitz. For rate and amplitude constrained systems, the three degrees of freedom controller is a special case of the general saturation compensator. Through multivariable frequency domain analysis of the compensators, hidden properties of the three degrees of freedom controller are revealed. These inherent properties are utilized in compensator designs by techniques shaping the characteristic loci and specification of singular values. Simulated examples illustrate the success of the design methods.     

Methods to reduce non-linear mechanical systems for instability computation

Summary Non-linear dynamical structures depending on control parameters are encountered in many areas of science and engineering. In the study of non-linear dynamical systems depending on a given control parameter, the stability analysis and the associated non-linear behaviour in a near-critical steady-state equilibrium point are two of the most important points; they make it possible to validate and characterize the non-linear structures. Stability is investigated by determining eigenvalues of the linearized perturbation equations about each steady-state operating point, or by calculating the Jacobian of the system at the equilibrium points. While the conditions and the values of the parameters which cause instability can be investigated by using linearized equations of motion studies of the non-linear behaviour of vibration problems, on the other hand, require the complete non-linear expressions of systems. Due to the complexity of non-linear systems and to save time, simplifications and reductions in the mathematical complexity of the non-linear equations are usually required. The principal idea for these non-linear methods is to reduce the order of the system and eliminate as many non-linearities as possible in the system of equations. In this paper, a study devoted to evaluating the instability phenomena in non-linear models is presented. It outlines stability analysis and gives a non-linear strategy by constructing a reduced order model and simplifying the non-linearities, based on three non-linear methods: the centre manifold concept, the rational approximants and the Alternating Frequency/Time domain method. The computational procedures to determine the reduced and simplified system via the centre manifold approach and the fractional approximants, as well as the approximation of the responses as a Fourier series via the harmonic balance method, are presented and discussed. These non-linear methods for calculating the dynamical behaviour of non-linear systems with several degrees-of-freedom and non-linearities are tested in the case of mechanical systems with many degrees-of-freedom possessing polynomial non-linearities. Results obtained are compared with those estimated by a classical Runge-Kutta integration procedure. Moreover, an extension of the centre manifold approach using rational approximants is proposed and used to explore the dynamics of non-linear systems, by extending the domain of convergence of the non-linear reduced system and evaluating its performance and suitability.     

Absolute stability results for non-linear systems using logarithmic plots

Absolute stability of non-linear systems is examined using the conventional techniques, and a representation of Popov line in the logarithmic gain and phase versus frequency plane. A grapho-analytical procedure is advanced for the Popov line transference to the Bode plane. The technique may be used either as an analytical tool for investigating absolute stability of systems with specified non-linearity sector, or as a synthesis technique for compensator design. The application of the proposed method for substantiating compensator design results is illustrated by two examples.     

Synthesis of an internal model for non-linear output regulation

Given a plant described by non-linear differential equations, it is known that a compensator which solves the regulator problem contains an internal model of the disturbance generator. In this paper, conditions for the existence of an internal model yielding asymptotic disturbance compensation are given in terms of the existence of a suitable controlled invariant distribution. The synthesis of the internal model is also discussed.     

Optimal directionality compensation in processes with input saturation non-linearities

A notion of process directionality in input-constrained processes is defined, and the class of processes that do not exhibit the process directionality is characterized. An optimal directionality compensator for non-linear processes with actuator saturation non-linearities is presented. Given an unconstrained controller output and the characteristic (decoupling) matrix of the process under consideration, the compensator calculates an optimal constrained (feasible) process input that results in a process response as 'close' as possible to the response of the same process to the unconstrained controller output. The compensator can be used for both linear and non-linear processes, irrespective of the type of controller being used. For processes whose non-singular characteristic matrix can be made diagonal by row or column rearrangements, the optimal directionality compensator is identical to a series of limiters (clippers); this class of processes does not exhibit the process directionality over a short time horizon. The performance of the optimal directionality compensator is shown and compared with those of clipping and direction preservation, by numerical simulation of a linear example under decentralized proportional-integral control, a linear example under model-based control, and a non-linear bioreactor under input-output linearizing control.     

Compensation method for non-linear systems having jump and hysteresis properties†

The paper introduces a novel method for describing non-linear systems. The method, which uses non-integer calculus provides greater insight into the physical aspects of jump and hysteresis phenomena in systems with single-valued non-linear characteristics. The method is well suited to non-linear systems having minimum phase-shift linear parts. A non-integer-order compensator is developed for singularities arising from non-linearities. To illustrate the scheme, saturation is considered. Numerical design of a compensator for jump and hysteresis is also described.     

EVOLUTIONARY SEARCH FOR LIMIT CYCLE AND CONTROLLER DESIGN IN MULTIVARIABLE NONLINEAR SYSTEMS

A feature of many practical control systems is a Multi‐Input Multi‐Output (MIMO) interactive structure with one or more gross nonlinearities. A primary controller design task in such circumstances is to predict and ensure the avoidance of limit cycling conditions followed by achieving other design objectives. This paper outlines how such a system may be investigated using the Sinusoidal Input Describing Function (SIDF) philosophy quantifying magnitude, frequency and phase of any possible limit cycle operation. While Sinusoidal Input Describing function is a suitable linearization technique in the frequency domain for assessment of stability and limit cycle operation, it can not be employed in time domain. In order to be able to incorporate the time domain requirements in an overall controller design technique, the appropriate linearization technique suggested here is the Exponential Input Describing Function (EIDF). First, an evolutionary search based on a multi‐objective formulation is employed for the direct solution of the harmonic balance system matrix equation. The search is based on Multi‐Objective Genetic Algorithms (MOGA) and is capable of predicting specified modes of theoretically possible limit cycle operation. Second, the design requirements in time as well as frequency domain are formulated by a set of constraint inequalities. A numerical synthesis procedure also based on Multi‐Objective Genetic Algorithm is employed to adjust the initial compensator parameters to meet the imposed constraints. Robust stability and robust performance are investigated with respect to linearization uncertainty within the context of multiobjective formulation. In order to make the Genetic Algorithm (GA) search more amenable to design trade‐off between different and often contradictory specifications, a weighted sum of the functions is introduced. This criterion is subsequently optimized subject to the nonlinear system dynamics and a set of design requirements. Examples of use are given to illustrate the effectiveness of the proposed approach.     

A method for the design of phase-lead demodulating compensators for use in carrier control systems

A fairly new type of compensator for carrier control systems consists of a passive electric network that contains one or more periodically-conducting branches. This type of compensator (referred to as a demodulating compensating network) is superior to other types, used previously, in terms of size, weight, cost, and sensitivity to variations in carrier frequency. Although a detailed analysis of the operation of a demodulating compensating network is usually very tedious, it is possible to describe the effect of such a network in a feedback control system very simply by the use of an equivalent time-invariant passive electric network. A procedure for designing a phase-lead demodulating compensating network to meet specifications on system performance is presented in this paper. In essence, this procedure consists of the following steps. First, the uncompensated frequency response of the system is examined. Then an acceptable and realizable phase and/or gain characteristic is selected. Finally, by the use of design curves, the parameters of the demodulating compensator required to provide the desired frequency response are determined. Numerical examples are included to illustrate the application of the design procedure, and experimental results are reported to reveal the value of the procedure.     

基于系统输出的嵌套饱和系统抗饱和补偿器设计

针对嵌套输入饱和系统的吸引域扩大问题,本文提出了一种基于系统输出的抗饱和补偿器激发策略,将被控系统输出信号经性能补偿器馈入到抗饱和补偿器激发环节中,形成蕴含系统实时性能信息的抗饱和激发新机制,克服了传统抗饱和激发机制无法直接反映系统性能的缺点.基于上述抗饱和控制新框架,本文建立了抗饱和补偿器及性能补偿器存在的充分条件,并依此构建了优化问题求解最优补偿器增益以实现扩大闭环系统吸引域的目的.仿真结果表明本文方法的有效性.     

Discrete time subharmonic modelling and analysis

Traditionally the Volterra time and frequency domain analysis tools cannot be applied to severely non-linear systems. In this paper, a new method of building a time-domain NARX MISO model for a class of severely SISO non-linear systems that exhibit subharmonics is introduced and it is shown how this allows the Volterra time and frequency domain analysis to be extended to this class of non-linear systems. The new approach is based on decomposing the original single input based on a Fourier analysis to provide a set of modified input signals which have the same period as the output signal. A MISO NARX model can then be constructed from the decomposed multiple inputs and the single output signal. The resulting MISO model is shown to meet the basic requirement for the existence of a Volterra series representation from which important frequency domain properties can be derived, explained and discussed. This is done by first introducing the derivation of generalized frequency response functions (GFRFs) from time domain MISO NARX models. The steady state response synthesis problem using the input spectrum and the MISO GFRFs is then investigated in order to verify the effectiveness and accuracy of the MISO modelling approach for severely non-linear systems. Finally a new frequency domain analysis method is introduced for systems that exhibit subharmonic oscillations.     

A geometric framework for pole assignment algorithms

The problem of pole assignment by gain output feedback or by low-order dynamical compensator is considered from a geometric point of view. This makes it possible to unify, in a general framework, most of the existing pole assignment methods formulated in a state-space context, such as the minimal-order observers, the Brasch-Pearson compensator, and the methods proposed by H. Kimura, and to simplify their presentation. Moreover, new pole assignment algorithms may be derived from this general formulation     

Structural classification of non-linear systems by input and output measurements

It is desirable to know the internal structure of a non-linear system that is regarded as a 'black box'. The structural classification of the 'black box' is made from input and output relations. In this paper, the necessary conditions of structural classification are developed by the Volterra and Wiener theories and correlation analysis. A class of non-linear models in cascade is described by cross-correlation functions and Volterra and Wiener kernels. These conditions are first discussed in the frequency domain. Then the formulae of the conditions for structural identification in the time domain are obtained. Further, relations between structural information and the kernels are developed. Simulations are carried out that verify the authors' methods of structural testing. Next, some formulae for discriminating the feedback non-linear system's structure are newly developed. Furthermore, it is shown that the linear subsystem transfer functions and the non-linear subsystem parameters for these feedback non-linear systems can be estimated. Finally, the validity and sufficiency of the conditions for structural testing are discussed.     

Global stabilization with almost disturbance decoupling of a class of uncertain non-linear systems

In this paper we study the global stabilization of a class of non-linear uncertain systems while decoupling the output from external disturbances to any specified degree of accuracy. The class of non-linear systems considered could be viewed as a generalization of uniform rank multivariable linear systems which have the property that all their infinite zeros are of the same order. Although the plants considered are non-linear, the compensator developed here is linear. Our compensator which achieves global exponential stability and almost disturbance decoupling of the output requires only output feedback rather than full state feedback. Model uncertainty is dealt with either by restricting the uncertain elements to particular subspaces satisfying the so-called ‘matching conditions’ and/or by treating a family of plants  for which a single controller simultaneously globally exponentially stabilizes all the plants in  while achieving almost disturbance decoupling of the output.     

Compensation-based control for lossy communication networks

In this paper, we are concerned with the stability analysis and the design of stabilising compensation-based control algorithms for networked control systems (NCSs) that exhibit packet dropouts. In order to increase the robustness against packet dropouts for such NCSs, we propose a new type of model-based dropout compensator, which depends on the local dropout history. Moreover, we provide linear matrix inequality based synthesis conditions for such compensators guaranteeing robust stability. The analysis and design framework includes both worst-case-bound and stochastic models to describe the packet-dropout behaviour in both the sensor-to-controller and the controller-to-actuator channels. Numerical examples demonstrate the significantly improved robustness with respect to packet dropouts using the proposed dropout compensator, compared to using the existing zero strategy and the hold strategy.     

An investigation into the characteristics of non-linear frequency response functions. Part 1: Understanding the higher dimensional frequency spaces

The characteristics of generalized frequency response functions (GFRFs) of non-linear systems in higher dimensional space are investigated using a combination of graphical and symbolic decomposition techniques. It is shown how a systematic analysis can be achieved for a wide class of non-linear systems in the frequency domain using the proposed methods. The paper is divided into two parts. In Part 1, the concepts of input and output frequency subdomains are introduced to give insight into the relationship between one dimensional and multi-dimensional frequency spaces. The visualization of both magnitude and phase responses of third order generalized frequency response functions is presented for the first time. In Part 2 symbolic expansion techniques are introduced and new methods are developed to analyse the properties of generalized frequency response functions of non-linear systems described by the NARMAX class of models. Case studies are included in Part 2 to illustrate the application of the new methods.     

数字DC/DC开关电源环路补偿器设计

建立了数字控制DC/DC开关电源闭环系统的s域小信号模型,采用数字重设计法针对给定的系统参数设计了数字补偿器。应用SISO Design Tool仿真平台,在伯德图分析和根轨迹法的基础上设计了连续域的模拟补偿器,并进行了离散化处理。在建立系统s域模型时引入了模数转换器和数字脉宽调制发生器产生的延迟效应,使补偿器的设计考虑了采样速率对系统的影响,改善了传统离散设计的误差。基于数字重设计法构建的数字补偿器实现了对脉宽调制信号的可编程精确控制,保证了变换器闭环工作良好的动态特性。仿真实验结果验证了所设计的数字补偿器的性能。     

Fuzzy control of an electrodynamic shaker for automotive and aerospace vibration testing

A fuzzy logic based digital time domain sinusoidal acceleration waveform amplitude controller for an electrodynamic shaker is presented. The purpose of Fuzzy Logic Control (FLC) is to reproduce a pre-defined sinusoidal acceleration amplitude profile (in amplitude, frequency and time) at the shaker table. Sinusoidal vibration profiles (sine and logarithmic sine sweep) are considered for a controlled vibration generation in typical automotive and aerospace testing. The difficulty in sine sweep testing is that the non-rigid load dynamics are unknown and it can severely modify the shaker’s performance during sweep test. Since a logarithmic frequency sweep is normally used, a controller needs to be robust to un-modeled dynamics and also fast enough to hold the desired acceleration amplitude within predefined limits throughout the sweep test. The controller structure is developed based on the usual power amplifier technology. The control action is implemented on a waveform-by-waveform basis and a FLC is developed in the LabVIEW environment on a PXI platform for real time control of the shaker. To attenuate the shaker suspension mode resonance a compensator based on electromechanical model of the shaker is designed and cascaded to FLC. The shaker model, suspension mode compensator design, FLC synthesis and experimental implementation results are presented in this paper.     

On decentralised control of non-linear interconnected systems

The asymptotic stabilisation problem of a class of large-scale interconnected systems is considered, where the non-linear interconnections between subsystems satisfy quadratic constraints that are functions of the whole system's state vector. A decentralised combined observer-controller compensator is proposed and analysed, where the subsystems’ state vectors are estimated using local sliding mode observers. The closed-loop system driven by the proposed decentralised compensator is guaranteed to be asymptotically stable subject to two conditions that are easily verifiable. Simulation results illustrate the effectiveness of the proposed decentralised combined observer-controller compensator.