具有随机延时的网络控制系统的均方可镇定性分析

针对网络系统的可镇定性问题,研究整数步随机延时离散时间线性系统的均方可镇定性.利用Youla参数化与内外分解方法,结合均方小增益定理得到系统输出反馈均方可镇定的充分必要条件.该条件明确给出系统可镇定性与被控对象特性(不稳定极点、非最小相位零点、相对阶)和信道特性(频域信噪比函数)的关系,其中频域信噪比函数在被控对象不稳定极点的取值对可镇定影响甚大.利用仿真算例量化被控对象的非最小相位零点及相对阶对可镇定性的影响,验证可镇定性条件的正确性.     

A new approach for the design of multivariable feedback systems

A new design technique for multivariable feedback systems is presented. In this approach, n —1 open-loop transfer functions at different inputs of the plant, with all other feedback paths closed, are specified in advance, and are achieved exactly. The nth open-loop transfer function is a by-product of the design process, such that the overall feedback system is stabilized. The design approach is fitted to solve problems in which the plant elements can have non-stable poles and non-minimum phase zeros. The design process is straightforward, no iterations are necessary, and the achieved design copes exactly with the design specifications. The gainbandwidths of the different lis and the overall loop gain l* might be constrained due to non-stable poles and zeros of the plant elements. Based on the obtained different loop gains, any input output matrix T can bo achieved with the aid of an appropriate prefilter matrix F.     

A New Method for Getting Rational Approximation for Fractional Order Differintegrals

In this paper a new algorithm is presented to calculate the poles and zeros to approximate a fractional order (FO) differintegral (s^±α,α∈(0,1)) by a rational function on a finite frequency band ω∈(ω_l,ω_h). The constant phase property of the FO differintegral is the basis for development of the algorithm. Interlacing of real poles and zeros is used to achieve the constant phase. The calculations are done using the asymptotic Bode phase plot. A brief investigation is made to get a good approximation for the Bode phase plot. Two design parameters are introduced to keep the average phase close to the desired phase angle and to keep the error within the allowed bounds. A study is done to empirically understand the relationship between the error and the design parameters. The results thus obtained help in the further calculations. The algorithm is computationally simple and inexpensive, and gives a fairly good approximation of fractance frequency response on the specified frequency band.     

A general frequency stability criterion for multi-input-output,lumped and distributed-parameter feedback systems

The original Nyquist criterion is based on the comparison of the encirclement of the frequency plot of the return ratio function with the number of poles and the number of zeros of the same function to determine the closed-loop stability of a feedback system. The extensions of the return ratio idea to the stability study of multi-variable feedback systems have used the same terminology and followed a similar course. For the multi-input—output case, the use of the Nyquist criterion or its extension is by no means a simple matter. This paper establishes a new frequency stability criterion which converts the Nyquist criterion from a return ratio oriented approach to a return difference oriented one. Instead of examining the encirclement of the return ratio function to a critical point, we examine the phase change of the positive frequency of the return difference function, and the number of zeros of the positive frequency of the return difference function. This result simplifies the stability study of multi-input—output lumped systems tremendously, and covers multi-input-output distributed-parameters systems naturally. For illustration, several typical examples—single-input-output feedback systems with minimum phase or non-minimum phase open-loop transfer functions, multi-input-output feedback systems with stable or unstable open-loop transfer matrices, multi-input-output feedback systems with irrational or transcendental type distributed-parameter open-loop transfer matrices—are included.     

On the design,robustness, implementation and use of quasi-linear feedback compensators

A quasi-linear feedback compensator is one in which its poles depend in an appropriate way on its gain. The reason for introducing this new concept was the desire to remove the limitation to performance imposed by a plant with more than one pole in excess of its zeros. In this article it is shown that this objective is realized for plants with zeros in the left half of the complex plane. The consequences are surprising. In time domain it is possible to track arbitrarily fast a class of reference inputs despite a large class of disturbances and uncertainty in plant parameters. The response is non-oscillatory for high enough compensator gains, which is explained by the automatic adaptation of the closed loop poles to stability and stability margins for such gains. And in frequency domain the phase margin tends to 90° while the gain margin and crossover frequency become unlimited.

Technically the design procedure of quasi-linear compensators presented here is based on our theoretical result concerning the asymptotic behaviour of the roots of certain polynomials in a complex variable which depend also on a large positive parameter.

We also show how to implement such quasi-linear compensators in practical feedback control schemes, and their use at lower gains which is the case of most industrial applications.     

Logarithmic integrals, interpolation bounds, and performancelimitations in MIMO feedback systems

We study performance limitation issues found in linear multivariable feedback systems. Our main contributions include Bode and Poisson type integral inequalities and performance limits for the sensitivity and complementary sensitivity functions. These results characterize and quantify explicitly how open-loop unstable poles and nonminimum phase zeros may impose inherent limitations on feedback design and fundamental limits on the best achievable performance. The role of time delay is also studied in this context. Most notably, we show that the performance and design limitations in multivariable systems intrinsically depend on the locations as well as directions of unstable poles and nonminimum phase zeros, and in particular, on how pole and zero directions are aligned. The latter is characterized by angles measuring the mutual orientation between zero and pole directions, and it is shown to play a crucial role in multivariable system design     

Limitations on maximal tracking accuracy

This paper studies optimal tracking performance issues pertaining to finite-dimensional, linear, time-invariant feedback control systems. The problem under consideration amounts to determining the minimal tracking error between the output and reference signals of a feedback system, attainable by all possible stabilizing compensators. An integral square error criterion is used as a measure for the tracking error, and explicit expressions are derived for this minimal tracking error with respect to step reference signals. It is shown that plant nonminimum phase zeros have a negative effect on a feedback system's ability to reduce the tracking error, and that in a multivariable system this effect results in a way depending on not only the zero locations, but also the zero directions. It is also shown that if unity feedback structure is used for tracking purposes, plant nonminimum phase zeros and unstable poles can together play a particularly detrimental role in the achievable tracking performance, especially when the zeros and poles are nearby and their directions are closely aligned. On the other hand, if a two parameter controller structure is used, the achievable tracking performance depends only on the plant nonminimum phase zeros     

Best tracking and regulation performance under control energy constraint

This paper studies optimal tracking and regulation control problems, in which objective functions of tracking error and regulated response, defined by integral square measures, are to be minimized jointly with the control effort, where the latter is measured by the plant input energy. Our primary objective in this work is to search for fundamental design limitations beyond those known to be imposed by nonminimum phase zeros, unstable poles, and time delays. For this purpose, we solve the problems explicitly by deriving analytical expressions for the best achievable performance. It is found that this performance limit depends not only on the plant nonminimum phase zeros, time delays, and unstable poles-a fact known previously-but also on the plant gain in the entire frequency range. The results thus reveal and quantify another source of fundamental performance limitations beyond those already known, which are nonexistent when only conventional performance objectives such as tracking and regulation are addressed without taking into account the control energy constraint. Among other things, they exhibit how the lightly damped poles, the anti-resonant zeros, as well as the bandwidth of the plant may affect the performance.     

An adaptive learning regulator for uncertain minimum phase systems with undermodeled unknown exosystems

The design of an adaptive learning regulator is addressed for uncertain minimum phase linear systems (with known bounds, known upper bound on system order, known relative degree, known high frequency gain sign) and for unknown exosystems (with unknown order, uncertain frequencies). On the basis of a known bound on system uncertainties and a known bound on the modeled exosystem frequencies, a new adaptive output error feedback control algorithm is proposed which guarantees exponential convergence of both the output and the control input errors into residual bounds which decrease as the exosystem modeling error decreases. Exponential convergence of both errors to zero is obtained when the regulator exactly models all exosystem excited frequencies, while asymptotic convergence of both errors to zero is achieved when the actual exosystem is overmodeled by the regulator. The new algorithm generalizes existing learning controllers since, in the case of periodic references and/or disturbances, the knowledge of the period is not required.     

On H∞-optimal sensitivity theory for SISO feedback systems

This paper deals with the design of feedback controllers which minimize theH^{infty}-norm of the sensitivity function, suitably weighted. This approach to the theory of feedback design was introduced by Zames [1] and developed by Zames and Francis [2]. In this paper the theory of Sarason [3] is applied to the determination of the optimal weighted sensitivity function and an upper bound on its norm. The problem of achieving small sensitivity over a specified frequency band is studied, and the effect of nonminimum phase is elucidated. Finally, a method is introduced for handling plant poles and zeros on the imaginary axis.     

A root-locus technique for linear systems with delay

A new method of plotting the root-loci is developed for the linear control system with delay in control or in state. In case of the system with delay in control, the root-locus plot starts from neighborhoods of the open-loop zeros instead of the open-loop poles and thus the effect of time-delay is easily handled. In case of the system with delay in state, the open-loop poles are firstly found by applying the root-locus method for the system with delay in control and then the desired root-loci are found by starting the root-loci plot from the open-loop poles.     

The synthesis of linear multivariable systems by state-variable feedback

Design procedures are presented for the compensation of linear multivariable-feedback systems. The design objectives which are noninteraction and low-order compensators are obtained by state-variable feedback. Aqth order plant withminputs andmoutputs whereq>mis treated. All the state variables are assumed to be available and measurable. It is shown that it is often possible by state-variable feedback to obtain noninteraction without an increase in system order. When the determinant of the plant transfer-function matrix has right half plane zeros the state-variable feedback method cannot be used to obtain noninteraction since the resulting compensated system would be unstable. It is shown that it is not possible to change these right-half plane zeros by either the well-known transfer-function design methods or by the state-variable feedback method. A combination of both transfer-function and state-variable techniques is discussed and shown to lower the order of the compensators required for the compensation of certain systems.     

Root locus near isolated pole-zero dipoles and a counterintuitive case of digital control compensation

A convenient characterization is given for root loci associated with open-loop pole-zero dipoles. A particular dipole-locus effect is shown to influence the design of a digital PID controller for an oscillatory plant; the design is a counterintuitive one in which zeros of the compensator are placed outside the unit circle in the neighborhood of the plant poles.     

The role of transmission zeros in linear multivariable regulators

The problem is considered of designing compensators to regulate linear multivariable systems. It is shown that the essential mechanism employed by such a compensator is the multivariable analogue of pole-zero cancellation: the compensator supplies transmission zeros to cancel the unstable poles of the disturbance and reference signals. If the compensator is additionally required to function in the presence of small variations in system parameters then it must supply transmission zeros in greater multiplicity. Finally it is shown that the transmission zeros are generated by an ‘ internal model ’, incorporated in the compensator, of the dynamics of the disturbance and reference signals.     

On the order of stable compensators for a class of time-delay system

The stabilization using a stable compensator does not introduce additional unstable zeros into the closed-loop transfer function beyond those of the original plant, so it is a desirable compensator, the price is that the compensator‘s order will go up. This note considered the order of stable compensators for a class of time-delay systems. First, it is shown that for single-loop plants with at most one real fight-half plane zero, a special upper bound for the minimal order of a strongly stabilizing compensator can be obtained in terms of the plant order; Second, it is shown that approximate unstable pole-zero cancellation does not occur,and the distances between distinct unstable zeroes are bounded below by a positive constant, then it is possible to find an upper bound for the minimal order of a strongly stabilizing compensator.     

A lower bound for limiting time delay for closed-loop stability ofan arbitrary SISO plant

This correspondence is concerned with the time delay margin for closed-loop stability of a single-input single-output plant with time delay uncertainty. Since no restriction is placed on the stabilizing controller, the limiting value of time delay depends on the plant transfer function only. The approach, using a modified form of classical Nevanlinna-Pick interpolation theory, provides a lower bound for the limiting time delay given the plant open-loop poles and zeros only     

Regulation performance limitation of networked time-delay systems with incomplete information

In this paper, the regulation performance limitation of networked time-delay systems is studied. The communication network is mainly affected by parameters such as packet dropouts, encoding-decoding, interference signal, and channel noises. Non-minimum phase zeros, unstable poles, and time delay are all considered for a given plant. The corresponding regulation performance expression is derived using coprime factorization and spectral decomposition techniques in the frequency domain. The results indicate that the regulation performance of the system is related to the inherent characteristics of the given plant, including non-minimum phase zeros, unstable poles, and time delay. Additionally, network communication parameters such as white Gaussian noise, packet dropouts, encoding-decoding, and external interference signals all affect the regulation performance of networked time-delay systems. Finally, some simulation examples are provided to demonstrate the effectiveness of the theory.     

Design of multivariable feedback systems with simple unstable plant

This paper proposes a design methodology for distributed linear multivariable feedback systems with simple unstable plants (a simple unstable plant has either first- or second-order unstable poles). The methodology developed provides a global characterization of all realizable compensators which stabilize a given simple unstable plant. A design example is given to show that this methodology can be used to generate, in an appropriate computer-aided design environment, controllers which are optimal with respect to designer-specified criteria. Additionally, it is shown that the nature of the design methodology gives geometric insight into the dynamics of the process whereby an unstable plant is stabilized.     

Achievable performance of multivariable systems with unstable zeros and poles

This paper examines the fundamental limitations imposed by unstable (right half plane; RHP) zeros and poles in multivariable feedback systems. We generalize previously known controller-independent lower bounds on the H     

Robust stabilization of a SISO system with uncertainty in timedelay

Sufficient conditions are developed for the robust stabilization of an unstable strictly proper linear time-invariant (LTI) and single-input-single-output (SISO) plant with uncertainty in the time delay and with arbitrary poles and zeros in the open right half of the complex plane. The technique developed shows that a tradeoff exists between the open-loop gain of the control system and the robust stability with the time delay uncertainty