Closed-loop balancing for a class of non-linear singularly perturbed systems

The aim of this article is to investigate the closed-loop balancing reduction method for a class of non-linear singularly perturbed systems. We show that the well-known two-stage strategy involved commonly within the singular perturbation theory can be used to derive an approximate closed-loop balancing. The proposed two-stage method avoids the difficult task of solving high dimensional and ill conditioned non-linear Hamilton–Jacobi equation due to the presence of the small perturbation parameter.     

Two-time scale sliding-mode control for a class of nonlinear systems

The paper deals with the robust asymptotic stabilization of a class of nonlinear singularly perturbed systems using sliding-mode control techniques. The approach consists of decomposing the original system into two reduced order systems, for which stabilizing sliding-mode controllers are applied and combined in a two-time scale sliding-mode control for the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. An example illustrates the design procedure and performance of the proposed control scheme. © 1997 by John Wiley & Sons, Ltd.     

挠性航天器的非线性PID和PI姿态控制器设计

针对存在模型不确性和常值干扰的挠性航天器, 提出一种不依赖于模型参数的非线性PID姿态控制器. 该控制器在小姿态偏差的情况下近似经典的线性PID控制器. 另外, 考虑到航天器上陀螺失效情况, 设计了一种仅需姿态测量信息的非线性PI控制器. 这两种控制器在局部均对常值干扰有抑制作用, 并能使无干扰作用的姿态控制系统半全局渐近稳定. 闭环系统的稳定性证明采用了奇异扰动理论, 以解决积分项的存在带来的稳定性分析问题. 文章最后用数学仿真验证了控制器的性能.     

基于PI 控制器的线性系统的鲁棒耗散控制

针对参数具有确定性及不确定性的连续系统,给出两种严格耗散PI控制器的设计方法.首先,系统参数确定时,采用线性矩阵不等式方法,导出了类状态反馈和静态输出反馈严格耗散PI控制器存在的充要条件,并由线性矩阵不等式的可行解构造出严格耗散PI控制器增益的显式表达式;然后,考虑系数矩阵均具有范数有界不确定性时的鲁棒严格耗散控制问题,得到相似的结果;最后,通过数值算例表明了所给方法的有效性.     

Robust regulation of a class of partially observed nonlinear continuous bioreactors

We propose a design of robust dynamic output feedback for the global partial stabilization of a class of continuous stirred bioreactors. Our approach is robust with respect to exogenous disturbances and functional uncertainties of the kinetics, considered as bounded unknown inputs. The method is based on a design of dynamic guaranteed bounds on the unmeasured variables, conditioned to past measurements and given bounds on the initial condition. This approach is suitable to systems which are not detectable for unknown inputs. The flexibility in the design of the parameters allows the consideration of saturation constraints on the control variable.     

Nonlinear performance of a PI controlled missile: an explanation

The primary aim of this paper is to investigate the practical interest of the incremental norm approach for analysing (realistic) nonlinear dynamical systems. In this framework indeed, incremental stability, a stronger notion than ℒ︁₂-gain stability, ensures suitable qualitative and quantitative properties. On the one hand, the qualitative properties essentially correspond to (steady-state) input/output properties, which are not necessarily obtained when ensuring only ℒ︁₂-gain stability. On the other hand, it is possible to analyse quantitative robustness performance properties using the notion of (nonlinear) incremental performance, the latter being defined in the continuity of the (linear) H_∞ performance (i.e. through the use of a weighting function). As testing incremental properties is a difficult problem, stronger, but computationally more attractive, notions are introduced, namely quadratic incremental stability and performance. Testing these properties reduces indeed to solving convex optimization problems over Linear Matrix Inequalities (LMIs). As an illustration, we consider a classical missile problem, which was already treated using several (linear and nonlinear) approaches. We focus here on the analysis of the nonlinear behavior of this PI controlled missile: using the notions of quadratic incremental stability and performance, the closed loop nonlinear missile is proved to meet desirable control specifications. Copyright © 1999 John Wiley & Sons, Ltd.     

模糊逻辑补偿的网络PI控制系统及稳定性分析

针对现代工业过程中常用的网络PI控制系统, 分析了网络所诱导的时滞对PI控制系统性能的影响, 设计了一个模糊逻辑补偿器来实现对网络所诱导的时滞的补偿. 利用Hermite-Biehler引理在准多项式稳定性问题上的推广, 研究了具有模糊逻辑补偿的网络PI控制系统的稳定性问题, 给出了使闭环系统稳定的模糊逻辑调节参数的取值范围. 仿真结果验证了理论分析结果的有效性.     

一类线性切换系统具有H∞性能指标的二次稳定

研究了一类线性切换系统具有H_∞扰动衰减度二次稳定问题.这类线性切换系统由两个子系统组成,并且每个子系统都不是具有H_∞扰动衰减度二次稳定的.利用单Lyapunov函数方法,得到了线性切换系统具有H_∞扰动衰减度二次稳定的充分条件,同时由凸组合系统设计出确保线性切换系统二次稳定且具有H_∞扰动衰减度的切换律.进一步,还给出了线性切换系统具有H_∞扰动衰减度二次稳定的必要条件.最后的仿真实例表明了结论的有效性.     

PID regulation of robot manipulators: stability and performance

Position control of robot manipulators using a novel PID control configuration derived from modeling error compensation ideas is introduced. The PID control law stability depends only on the inertial parameters of the robot. A simple proof of semiglobal PID stabilization of robot manipulators is provided. It is shown that the performance of the inverse dynamics control can be recovered by the PID control in the high-gain limit. Simple tuning guidelines derived from the proposed PID control configuration and closed-loop stability analysis are presented.     

An extremum seeking approach via variable-structure control for fed-batch bioreactors with uncertain growth rate

In this paper, we present an extremum-seeking scheme based on an approach to variable structure control for fed-batch bioreactors. The proposed scheme deals with uncertainty on the specific growth rate without assuming an explicit mathematical expression. The control approach exploits the inhibitory effect of the substrate concentration on the growth rate, in such a manner that the closed-loop system reaches the sliding regime on an optimal switching manifold, which is defined by maximizing biomass production. The control scheme comprises an estimation scheme consisting of a high-gain observer and a discrete gradient estimator which computes the unknown terms. The practical stabilizability for the closed-loop system around an unknown optimal set-point is analyzed. Numerical experiments illustrate the effectiveness of the proposed approach.     

A general analysis and control framework for process systems with inventory recycling

In this work, we generalize our previous results concerning the impact of material recycling and energy recovery on plant dynamics and control. We define a generic class of integrated process systems, in which an extensive quantity that obeys conservation laws is recovered from the process output and recycled to the process feed; the operation of the system is assumed to be subject to time‐varying, measurable disturbances. We establish, in this general case, that integration is conducive to the emergence of a two‐time‐scale dynamic behavior and derive reduced‐order models for the dynamics in each time scale. Subsequently, we postulate a hierarchical control framework that exploits these dynamics results in the design of coordinated fast and slow feedback/feedforward controllers and formulate a stability result for the closed‐loop system. We demonstrate these concepts on a case study concerning an energy‐integrated process. Copyright © 2013 John Wiley & Sons, Ltd.     

Improved PI controller based on predictive functional control for liquid level regulation in a coke fractionation tower

Due to limitations of hardware, cost and so on, the application of proportional-integral-derivative (PID) control is more convenient than predictive control. However, predictive control usually has better performance than traditional PID control, thus it is important to combine the advantages of these two control algorithms. A novel PI controller optimized by predictive functional control (PFC) is proposed and tested on liquid level in the industrial coke fractionation tower in this paper. Since this kind of process always shows the integrating behavior, a P controller is first used for it to generate a self-balancing generalized process, then the PFC based PI control is designed for the generalized process. The resulting controller displays the performance of both PFC and PI control with easy implementation in practice. The performance of the proposed PI controller is compared with traditional PI controller in terms of regulatory/servo set-point tracking, disturbance rejection and measurement noise issues, from which results show that the proposed PI controller provides better performance than traditional PI controller.     

Semi-global robust output regulation for a class of singular nonlinear systems via nonlinear internal model

Most of existing results on robust output regulation problem of singular nonlinear systems are limited to local solutions. In this paper, the semi-global robust output regulation problem for a class of singular nonlinear systems is investigated by using a nonlinear internal model. Attaching a nonlinear internal model to the singular nonlinear system yields an augmented singular nonlinear system whose semi-global robust stabilisation solution leads to the solution of the semi-global robust output regulation problem of the original singular nonlinear system. The solvability conditions of the semi-global output regulation problem are established by addressing the solvability of the robust stabilisation problem of augmented singular nonlinear system. Finally, a numerical simulation example is used to illustrate the design of the semi-global regulator for the singular nonlinear systems.     

Robust stability of a class of polynomial families under nonlinearly correlated perturbations

Kharitonov-like result and edge result are established for robust stability of a class of polynomial families with nonlinearly correlated perturbations - some composite functions of the numerator and denominator of interval plants or polytopic plants. These results are useful in robust stability analysis of feedback control systems as well as uncertain polynomial matrices. Illustrative examples are presented.     

一类广义不确定时滞系统的鲁棒容错控制

为了保证系统的稳定性和解决系统执行器失效的问题,针对一类线性广义时滞不确定系统,研究了在有记忆状态反馈作用下和执行器失效情况下的鲁棒容错控制问题。在采用具有更广泛意义的执行器故障模型下,给出了线性不确定时滞广义系统对执行器故障保持渐近稳定并且满足给定干扰衰减指标的鲁棒控制器的存在条件和设计方法。仿真结果验证了该方法的可行性和正确性。     

Design of decentralized PI control systems based on Nyquist stability analysis

This paper presents a simple, but effective, design method for decentralized PI control systems with guaranteed closed-loop stability. Nyquist stability conditions are used to derive the stability region for each PI controller in terms of the controller parameters. A detuning factor for each loop is specified based on a diagonal dominance index. Then appropriate controller settings are determined using this index and the stability region. Simulation results for a variety of 2 × 2, 3 × 3, and 4 × 4 systems demonstrate that the proposed design method guarantees closed-loop stability and provides good set-point and load responses.     

二阶线性系统全维PI观测器的参数化设计

基于一类广义Sylvester矩阵方程的解．提出了二阶线性系统的全维PI观测器设计参数化方法．给出了该类观测器的增益矩阵和左特征向量矩阵的参数化表达式．该观测器设计的参数化方法直接基于二阶线性系统的参数矩阵,不涉及系统的变换或增广．数值例子表明了所提方法的简单有效性．     

A robust PI passivity‐based control of nonlinear systems and its application to temperature regulation

This paper deals with the problem of control of partially known nonlinear systems, which have an open‐loop stable equilibrium, but we would like to add a PI controller to regulate its behavior around another operating point. Our main contribution is the identification of a class of systems for which a globally stable PI can be designed knowing only the systems input matrix and measuring only the actuated coordinates. The construction of the PI is carried out invoking passivity theory. The difficulties encountered in the design of adaptive PI controllers with the existing theoretical tools are also discussed. As an illustration of the theory, we consider a class of thermal processes. Copyright © 2015 John Wiley & Sons, Ltd.     

New stability criteria for singular systems with time-varying delay and nonlinear perturbations

This paper concerns the stability analysis for singular systems with time-varying delay and nonlinear perturbations. Two cases of time-varying delay, which is differentiable (Case 1) or not differentiable (Case 2), are considered. The considered nonlinear perturbations includes the norm-bounded uncertainties as a special case. Some delay-dependent stability criteria are derived by using a delay decomposition approach. In the delay decomposition approach, the entire delay interval is divided into multiple sub-intervals for which different energy functions are defined for building new Lyapunov–Krasovskii functional. Some numerical and practical examples are given to show the effectiveness and significant improvement of the proposed method.     

Asymptotic stability of nonlinear singularly perturbed systems using higher order corrections

This paper examines a methodology for investigating the asymptotic stability properties of nonlinear singularly perturbed systems. This is achieved by constructing the so-called zeroth order model (uncorrected model). Based on this model a weighted scalar sum of the Lyapunov functions for two lower order subsystems is obtained. The estimates of the region of attraction and the upper bound on the perturbed parameter are established. It is shown that by extending this methodology to higher order corrected models, less conservative results are obtained. These considerable improvements are facilitated by introducing a new fast variable in both uncorrected and corrected models.