一种基于H∞理论的鲁棒预测控制方法

融合H∞控制的鲁棒概念和预测控制的滚动优化原理,提出了一种全新的约束动态对 策预测控制方法.对有状态和控制约束的不确定线性系统,证明了闭环系统的鲁棒稳定性并给 出了鲁棒性条件.该方法同时具有H∞控制和预测控制的优点:鲁棒性和显式处理约束的能力.     

Robust nonlinear dynamic systems — The old question with a new answer

In this paper several upper bounds for parameter variations of a class of nonlinear (feedback) dynamic systems are presented. These sufficient conditions are used iteratively in a computer-aided algorithm to reach to the largest upper bounds or the stability robustness measure of such systems.     

Stability robustness for linear state space models - a Lyapunov mapping approach

Some Pythagorean-like conditions for the existence of a common Lyapunov solution for two given matrices are presented. These conditions are set on the Lyapunov mappings associated with given matrices. The key is the semipositiveness of linear mappings defined on symmetric matrices. From the viewpoint of the existence of a common Lyapunov solution, some known stability robustness results are reviewed and refined.     

具有结构不确定性的输出反馈线性系统的鲁棒稳定性分析

基于向量的幂变换方法，对具有结构不确定性的输出反馈线性系统的鲁棒稳定性问题作了分析。单参数摄动时给出了闭环系统鲁棒稳定的充要条件，多参数摄动时得到了保证系统鲁棒稳定的充分条件，导出了闭环系统鲁棒稳定区域的一种代数表达形式。最后给出了实例。     

PID control for global finite-time regulation of robotic manipulators

This paper addresses the global finite-time regulation problem of robotic manipulators. A simple nonlinear proportional-integral-derivative (PID) control is proposed by adding a nonlinear proportional and derivative term to the commonly used PID controller. Lyapunov's stability theory and geometric homogeneity technique are employed to prove global finite-time stability. Advantages of the proposed control include the absence of modelling information in the control law formulation and the global finite-time stability featuring fast transient and high-precision positioning. Explicit conditions on the controller parameters to ensure global finite-time regulation stability are obtained. Simulations are presented to demonstrate the effectiveness and the improved performances of the proposed approach.     

Robustness of delayed multistable systems with application to droop-controlled inverter-based microgrids

Motivated by the problem of phase-locking in droop-controlled inverter-based microgrids with delays, the recently developed theory of input-to-state stability (ISS) for multistable systems is extended to the case of multistable systems with delayed dynamics. Sufficient conditions for ISS of delayed systems are presented using Lyapunov–Razumikhin functions. It is shown that ISS multistable systems are robust with respect to delays in a feedback. The derived theory is applied to two examples. First, the ISS property is established for the model of a nonlinear pendulum and delay-dependent robustness conditions are derived. Second, it is shown that, under certain assumptions, the problem of phase-locking analysis in droop-controlled inverter-based microgrids with delays can be reduced to the stability investigation of the nonlinear pendulum. For this case, corresponding delay-dependent conditions for asymptotic phase-locking are given.     

Stability of discrete-time linear systems with Markovian jumping parameters

This paper deals with the robustness of a class of discrete-time linear systems with Markovian jumping parameters and unknown but bounded uncertainties. Assuming that the Markovian jump process (disturbance) has finite state space and that there is complete access to the system's state and its mode, we establish necessary and sufficient conditions for stochastic stability of the autonomous nominal model. We also establish sufficient conditions for robust stability for this class of uncertain systems under matching conditions and with bounded uncertainties.The research of the first author was supported by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0036444.     

On robustness of predictor feedback control of linear systems with input delays

This paper is concerned with the robustness of the predictor feedback control of linear systems with input delays. By applying certain equivalent transformations on the characteristic equation associated with the closed-loop system, we first transform the robustness problem of a predictor feedback control system into the stability problem of a neutral time-delay system containing an integral operator in the derivative. The range of the allowable input delay for this neutral time-delay system can be computed by exploring its delay dependent stability conditions. In particular, delay dependent stability conditions for the neutral time-delay system are established by partitioning the delay into segments. The conservatism of this method can be reduced when the number of segments in the partition is increased. Numerical examples are worked out to illustrate the effectiveness of the proposed method.     

Robust stability analysis of systems with real parametric uncertainty: A global optimization approach

This paper presents an optimization framework for the robustness analysis of linear and nonlinear systems with real parameter uncertainty. For linear systems, a nonlinear programming formulation for the exact calculation of the stability margin is presented. The potential of decomposition-based global optimization methods for the solution of this nonconvex problem is discussed. Next the concept of the stability margin is extended to a class of nonlinear systems. A nonlinear stability margin and a uniqueness margin are defined to address the effect of parametric uncertainty on the stability of a particular steady state, as well as on the number of steady states of the system. This analysis allows for the derivation of necessary and sufficient conditions for robust stability and robust uniqueness of the steady state of the system in the presence of parametric uncertainty.     

Temperature control of industrial gas phase polyethylene reactors

The performance of linear and nonlinear temperature control schemes is assessed for an open-loop unstable gas-phase polyethylene reactor (GPPER), based on speed, damping, robustness and the ability to maintain closed-loop stability in different operating regimes. An existing industrial GPPER model is improved by modelling the temperature states in the external heat exchanger using linear and nonlinear driving force models with varying numbers of heat transfer stages. Differences in heat exchanger models do not produce gain mismatch but do result in phase mismatch. It is shown that the nonlinear error trajectory controller (ETC) exhibits significantly superior responses in terms of speed, damping and robustness compared with an optimally-tuned PID controller. Therefore, substantial benefits could be realized using nonlinear controllers because they can provide good disturbance rejection capabilities and ensure closed-loop stability over a wide range of operating conditions. An approach is presented for tuning ETCs for minimum-phase processes of arbitrary relative degree.     

Global uniform asymptotical stability of a class of nonlinear cascaded systems with application to a nonholonomic wheeled mobile robot

In this article, we consider the stability analysis problem for a class of nonlinear cascaded systems by using homogeneous properties. Assume that the driving subsystem and the driven subsystem are both homogeneous and locally uniformly asymptotically stable. If the cascaded term satisfies a given inequality, then the cascaded system is globally uniformly asymptotically stable. Furthermore, in the case that both degrees of homogeneity are negative, the cascaded system is globally uniformly finite-time stable. Compared with the existing methods, the conditions given in this article are much easier to verify. These stability results are applied to the global tracking control problem of a nonholonomic wheeled mobile robot. Simulation results are provided to show the effectiveness of the methods.     

Robustness analysis and distributed control of a networked system with time-varying delays

This paper is concerned with the robustness analysis and distributed output feedback control of a networked system with uncertain time-varying communication delays. This system consists of a collection of linear time-invariant subsystems that are spatially interconnected via an arbitrary directed network. Using a dissipation inequality that incorporates dynamic hard IQCs (integral quadratic constraints) for the delay uncertainties, we derive some sufficient robustness conditions in the form of coupled linear matrix inequalities, in which the coupled parts reflect the interconnection structure of the system. We then provide a procedure to construct a distributed controller to ensure the robust stability of the closed-loop system and to achieve a prescribed $\ell_2$-gain performance. The effectiveness of the proposed approach is demonstrated by some numerical examples.     

输出多采样反馈控制器及系统稳定性

针对由连续被控对象和数字控制器构成的数字控制系统,将现有的线性系统输出多采样线性反馈数字控制器设计方法推广到非线性系统．并相应地研究了非线性输出多采样反馈控制器及摄动非线性系统．给出了这类非线性输出多采样数字控制系统及其摄动系统的稳定性和鲁棒性条件．     

改进的内模控制方法及其在非方系统中的应用

针对工业过程中稳定的含有多时滞和右半平面零点的非方系统,提出一种改进的内模控制方法.通过添加补偿项来消除内模控制器中包含的不可实现因素,并在反馈回路中添加一阶滤波器以增强系统的鲁棒稳定性.同时,针对存在参数不确定性的被控过程,分析了保证控制系统鲁棒稳定的充分必要条件,给出了控制参数调节范围的解析计算式.最后仿真结果验证了该方法的有效性.     

Robust stability analysis for fractional‐order systems with time delay based on finite spectrum assignment

In this paper, the robust stability of a fractional‐order time‐delay system is analyzed in the frequency domain based on finite spectrum assignment (FSA). The FSA algorithm is essentially an extension of the traditional pole assignment method, which can change the undesirable system characteristic equation into a desirable one. Therefore, the presented analysis scheme can also be used as an alternative time‐delay compensation method. However, it is superior to other time‐delay compensation schemes because it can be applied to open‐loop poorly damped or unstable systems. The FSA algorithm is extended to a fractional‐order version for time‐delay systems at first. Then, the robustness of the proposed algorithm for a fractional‐order delay system is analyzed, and the stability conditions are given. Finally, a simulation example is presented to show the superior robustness and delay compensation performance of the proposed algorithm. Moreover, the robust stability conditions and the time‐delay compensation scheme presented can be applied on both integer‐order and fractional‐order systems.     

Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems

This paper considers the robustness of stochastic stability of Markovian jump linear systems in continuous- and discrete-time with respect to their transition rates and probabilities, respectively. The continuous-time (discrete-time) system is described via a continuous-valued state vector and a discrete-valued mode which varies according to a Markov process (chain). By using stochastic Lyapunov function approach and Kronecker product transformation techniques, sufficient conditions are obtained for the robust stochastic stability of the underlying systems, which are in terms of upper bounds on the perturbed transition rates and probabilities. Analytical expressions are derived for scalar systems, which are straightforward to use. Numerical examples are presented to show the potential of the proposed techniques.     

Robust synthesis of a PID controller by uncertain multimodel approach

This paper presents an effective method to design a PID (or PI) controller for nonlinear systems where desirable robustness and performance properties must be maintained across a large range of operating conditions. For this purpose, an uncertain multimodel of the original nonlinear system is used. The uncertainties affecting the system are treated as stochastic matrices. Based on this multimodel representation a robust PID controller can be designed in order to obtain acceptable performance for all operating conditions. Numerical examples show the practical applicability of the proposed method.     

Balanced truncation reduced models of quadratic-bilinear systems in time interval

Accumulative error along with time impedes the application of many computational methods on high-precision simulation; therefore, time-interval methods emerge. In this paper, a new model reduction method of quadratic-bilinear (QB) systems based on time-interval Gramians (TIGs) is presented. The conditions for generalized Lyapunov equations whose solutions are exactly TIGs to be solvable are derived. Lyapunov stability and error bound are discussed to demonstrate the succession and advance of time-interval balanced truncation (TIBT). The accuracy and robustness are improved, as is illustrated in numerical results.     

基于LMI的非线性摄动系统鲁棒绝对稳定性判据

讨论了前馈通道同时存在对象和控制器的范数摄动,而反馈通道存在扇区非线性的摄 动系统的稳定性问题.基于H∞理论和LMI方法,得到了一组由线性矩阵不等式表达的充分性 条件,建立了判断非线性摄动系统鲁棒绝对稳定性的新判据.