用时变控制器消除分散控制系统的固定模

众所周知,在分散控制系统的设计中,不稳定的固定模的存在使得我们不能用分散化的、定常的局部控制器去稳定系统。本文应用一种采样和具有指数衰减保持的时变控制器来消除系统的固定模,由此而得到的定常可稳定的系统可以用局部输出反馈来稳定并进而可以实现最优控制。     

Time-varying feedback laws for decentralized control

Decentralized control schemes are considered for time-invariant, finite dimensional, linear systems with know state equations. It is assumed that the systems are reachable and observable at a fictitious centralized control station, and that there is strong connectivity between the decentralized control stations via the system where necessary. It is shown that whether or not there are decentralized fixed modes in the open-loop system, periodically varying feedback gains at all but one of the control stations permit the remaining control station to observe and control the system given knowledge of the control laws implemented at the other control stations. Certain time-invariant systems which cannot be stabilized by decentralized time-invariant controllers, namely those with unstable decentralized fixed modes, can thus be stabilized by decentralized time-varying controllers.     

Coupling measures between modes and state variables in power-system dynamics

A new method for model reduction called Selective Modal Analysis uses the eigenvectors and reciprocal eigenvectors of the system matrix A to calculate participation factors associating modes to certain state variables. This paper investigates the idea in depth. The novel aspect of this paper is the use of MacFarlane's concept that the system matrix A represents an energy transformation map to show that the participation factors are actually modal energies. This interpretation has some advantage because of its direct link to stability. It is shown that the participation factors, or modal energies, can be taken to be coupling measures between modes and state variables. An application to a single-machine infinite-busbar system with and without controllers is given. The properties and limitations of these coupling measures are investigated.     

On the mixed sensitivity minimization for systems with infinitely many unstable modes

In this note we consider a class of linear time invariant systems with infinitely many unstable modes. By using the parameterization of all stabilizing controllers and a data transformation, we show that controllers for such systems can be computed using the techniques developed earlier for infinite dimensional plants with finitely many unstable modes.     

基于模态空间的海洋平台冰致振动的 H∞ 控制

通过在海洋平台顶部安装主动调谐质量阻尼器（AMD）,研究了平台在冰荷载作用下的主导模态H∞控制．首先采用H∞方法与模态空间的平衡降阶法进行控制设计,然后基于虚拟激励法得到了系统冰致振动的解答,并应用此解答进行了广泛的参数研究,确定了平台减振效果最佳时的H∞控制器最优参数．通过该应用特例,以评价H∞控制器的有效性．结果表明如果H∞控制器的参数选择合适,则可以显著减小平台的冰致振动响应．     

Designing fuzzy controllers from a variable structures standpoint

A procedure is presented for designing fuzzy controllers based upon variable structures techniques. Three such controllers are presented: the fuzzy equivalents of sliding-mode controllers, saturating controllers, and tanh controllers. By using an approach based upon variables structures (VSS) techniques, the stability of each of these controllers is assured. By using a sliding surface, the order of the rule base is reduced to size r×m, where r is the number of inputs and m is the number of fuzzification levels. This combination makes the proposed design procedure able to generate simple controllers with guaranteed stability properties. To illustrate the proposed design procedure, fuzzy controllers are designed for a ball-and-beam system. It is demonstrated that in spite of this system being a fourth-order unstable system, the proposed design procedure results in simple stable fuzzy controllers     

Recursive identification of modal participation in substructuring applications

The utility of modal models in substructuring applications is well known. A recursive scheme for identifying the contributions of subsystem modes to the coupled system is presented. The modal contributions are characterised by evaluating an index based on the difference in the frequency response functions (FRFs), at arbitrarily selected frequencies of interest, between the coupled system containing all available modes and a series of coupled systems with reduced modes. It is shown that the contribution of the subsystem modes can be quantified by eliminating one mode at a time, performing coupling, and evaluating the FRFs at the frequencies of interest.     

导弹控制系统稳定性研究

导弹控制系统是一个非线性的时变系统；传统的控制器设计是将总的飞行时间分为几段，然后对于不同的时间段设计不同的控制器；由于在同一时间段内系统参数不断变化，而控制器参数不变，这样就造成在时间段内控制系统性能变差；为了解决在每一个时间段内系统性能变差问题和在时间段之间切换控制器时系统性能的突变及发动机工作的不稳定的问题，提出了采用对各个控制器相对时间进行单点模糊化、乘积推理和平均加权反模糊化的方法，实现在整个时间段控制系统的平稳工作。克服动态性能的跳变和发动机工作不稳定的问题，提高了导弹的可靠性。仿真实验证明了此方法的有效性。     

On the notion of strong stabilizability

A system is called strongly stabilizable (SS) if it can be stabilized using a stable controller. Observer state feedback can be used to design a controller of the same order as the system, but the designs may lead to unstable controllers. The implementation of an unstable controller should be done with care and with a well-designed safety net. One implementation could use a stable observer fed with actual input in addition to the measured output. Several examples are discussed, and how unstable controllers might be required for good closed-loop performance, even if they are not required for stability is shown     

Model reduction tools for nonlinear structural dynamics

Three mode types are proposed for reducing nonlinear dynamical system equations, resulting from finite element discretizations: tangent modes, modal derivatives, and newly added static modes. Tangent modes are obtained from an eigenvalue problem with a momentary tangent stiffness matrix. Their derivatives with respect to modal coordinates contain much beneficial reduction information. Three approaches to obtain modal derivatives are presented, including a newly introduced numerical way. Direct and reduced integration results of truss examples show that tangent modes do not describe the nonlinear system sufficiently well, whereas combining tangent modes with modal derivatives and/or static modes provides much better reduction results.     

DIRECT ADAPTIVE CONTROL FOR NONLINEAR MATRIX SECOND‐ORDER SYSTEMS WITH TIME‐VARYING AND SIGN‐INDEFINITE DAMPING AND STIFFNESS OPERATORS

A direct adaptive control framework for a class of nonlinear matrix second‐order systems with time‐varying and sign‐indefinite damping and stiffness operators is developed. The proposed framework guarantees global asymptotic stability of the closed‐loop system states associated with the plant dynamics without requiring any knowledge of the system nonlinearities other than the assumption that they are continuous and bounded. The proposed adaptive control approach is used to design adaptive controllers for suppressing thermoacoustic oscillations in combustion chambers.     

Fixed zeros of decentralized control systems

Considers the notion of decentralized fixed zeros for linear, time-invariant, finite-dimensional systems. For an N-channel plant that is free of unstable decentralized fixed modes, an unstable decentralized fixed zero of channel i (1⩽i⩽N) is defined as an element of the closed right half-plane, which remains as a blocking zero of that channel under the application of every set of N-1 controllers around the other channels, which make the resulting single-channel system stabilizable and detectable. The paper gives a complete characterization of unstable decentralized fixed zeros in terms of system-invariant zeros     

Stabilisation of unstable FOPDT processes with a single zero by fractional-order controllers

In this article, stabilisation of unstable first-order-plus-dead-time (FOPDT) processes with a single zero by fractional-order (FO) controllers is investigated. A Nyquist stability criterion-based approach is adopted to derive the conditions for stability. Sufficient stabilisability conditions by FO [proportional integral] controllers and FO-lead–lag controllers are established. In addition, robust stability of the system with these FO controllers is investigated. To illustrate the results, some examples are provided.     

An enhanced velocity-based algorithm for safe implementations of gain-scheduled controllers

This paper presents an enhanced velocity-based algorithm to implement gain-scheduled controllers for nonlinear and parameter-dependent systems. A new scheme including pre- and post-filtering is proposed with the assumption that the time-derivative of the controller inputs is not available for feedback control. It is shown that the proposed control structure can preserve the input–output properties of the linearised closed-loop system in the neighbourhood of each equilibrium point, avoiding the emergence of the so-called hidden coupling terms. Moreover, it is guaranteed that this implementation will not introduce unobservable or uncontrollable unstable modes, and hence the internal stability will not be affected. A case study dealing with the design of a pitch-axis missile autopilot is carried out and the numerical simulation results confirm the validity of the proposed approach.     

Parametric output feedback control with response insensitivity

A recent parameterization of the class of linear output-feedback controllers that assign a set of desired self-conjugate eigenvalues to the closed-loop system is used to formulate and solve a fundamental response insensitivity problem. It is established to what extent output-feedback control can be used to render the closed-loop system response insensitive to possibly many not necessarily small parameter variations in the open-loop state space model. A non-conservative sequential design procedure is developed for making as many of the closed-loop system eigenmodes as possible totally insensitive while retaining arbitrary assignment of the maximum number of closed-loop eigenvalues. The main result is a class of desensitizing fixed-gain output-feedback controllers explicitly specified by a set of free parameters which may be chosen to satisfy additional design requirements. Conditions are given for total modal decoupling insensitivity to possibly many not necessarily small parameter variations in the open-loop state model. The mechanism of modal decoupling insensitivity for a given mode is interpreted in terms of the insensitivity of the corresponding left eigenmode. A parametric approach to output feedback design for modal decoupling insensitivity is discussed.     

线性离散时间大系统次优分散控制器设计

在大系统分散控制器设计中,如果完全忽略各子系统之间的联系,控制性能往往较差,有 时甚至整个系统都不能稳定;如果完全考虑各子系统之间的联系,则通常需要求解一个高维问 题(其维数等于系统总阶数).为此,本文提出了一种简化设计方法,在求解某个子系统控制器 时,将该子系统以外的系统其余部分降阶,得到一个低阶近似系统,再求解由它们构成的分散 控制器设计问题,从而得到该子系统的控制器.该方法可以大大降低分散控制器设计问题的 复杂性,且控制性能甚好.     

Stabilisability analysis of high-order unstable processes by fractional-order controllers

In this article, the sufficient stabilisability criteria for unstable time-delay processes by fractional-order controllers are investigated. The process is a high-order system with a single unstable pole, which also has a stable zero. The adopted approach to derive the sufficient conditions for stability is based on the well-known Nyquist stability criterion. Stabilisability is studied by applying fractional-order proportional integral and proportional derivative controllers and the results are given in terms of the maximum allowable value of time delay. Additionally, limitations on the parameters of the controllers which must be taken into account in the controller design are proposed.     

PI-Fuzzy controllers for integral plants to ensure robust stability

New PI-fuzzy controllers comprising Takagi-Sugeno and Mamdani fuzzy systems to control a class of integral plants specific to servo systems are proposed in this paper. Linear PI controllers are designed in the first phase. They are tuned using the Extended Symmetrical Optimum method to ensure the desired overshoot and settling time with respect to step setpoint modifications and three types of load disturbance inputs. This type of PI controller design guarantees robust stability of the closed-loop system in response to parametric variations in a controlled plant. Following this, based on the results from the linear case and the modal equivalence principle, an original development method for PI-fuzzy controllers is proposed. Some experimental results are included to illustrate the effectiveness of the design process.     

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.     

A simple method of tuning series cascade controllers for unstable systems

A simple method is proposed to design P/PI controllers for a series cascade control system for unstable first order plus time-delay （FOPTD） systems. In this paper, the controller design for unstable FOPTD systems cascaded in series with stable/unstable FOPTD systems is considered. The proposed method is based on equating the coefficients of corresponding powers of s and s2 in the numerator to α1 and α2 times those of the denominator of the closed-loop transfer function for a servo problem. The open loop system consists of an unstable FOPTD system cascaded in series with a stable/unstable FOPTD system. Only two tuning parameters （α1 and α2） are required for the design of controllers. The closed-loop performances are evaluated for both the servo and regulatory problems and the performances are found to be better than that of the well established synthesis method. The robustness for uncertainty in the model parameters is studied and compared with that of the controllers designed by the synthesis method.