ANALYSIS AND DESIGN OF FEEDBACK CONTROL SYSTEMS WITH TRACKING ERRORS SQUARE

In this study, a command tracking error square control scheme is first proposed for analysis and design of feedback control systems. One of the tracking errors is low‐pass filtered and used in the feedback loop for gain adaptation; the other is used in the forward loop for command tracking control. The overall systems are nonlinear feedback systems, and can be reconfigured to an automatic gain control (AGC) loop with command tracking error input. The stability and robustness of the controlled systems are verified by time response, frequency response, and large parameter variation testing with a simple illustrating example and are finally applied to a complicated electro‐hydraulic velocity servo system with large load disturbance.     

柴油发电机组非线性H2/H∞调速器的研究

船舶电力系统频率的稳定性主要取决于船舶电站柴油机调速系统的转速响应特性. 船舶电站柴油机调速系统是一个非线性控制系统, 为了分析系统的动态特性, 首先建立柴油机调速系统的非线性数学模型, 然后以此为基础设计非线性H2/H∞速器. 将直接反馈线性化和混合H2/H∞控制理论相结合应用于柴油发电机组调速器的设计,把系统的性能要求转化为标准H2/H∞控制问题, 获得了柴油机非线性H2/H∞转速控制律. 计算机仿真结果表明, 设计的非线性H2/H∞调速器有效地提高了系统的动态精度和抑制扰动的能力, 改善了船舶电力系统频率的稳定性.     

继电反馈多模型控制及应用

作为简单、鲁棒的设计方法,基于继电反馈的PID控制器巳广泛应用于工业过程控制。它可以由继电反馈引起的振荡近似估计过程临界信息进行控制器的设计。多模型控制是解决系统时变、非线性、参数不确定性等复杂问题得一种有效方法。该文将继电反馈控制与多模型控制相结合,对时变、非线性的电厂主汽温系统过进行控制。首先在各个工况点应用继电反馈方法设计子控制器。然后在系统整个运行区间进行多模型自适应控制以克服非线性、时变对系统的影响。仿真表明本方法所建立的控制系统具有良好的控制品质及较强的自适应能力。     

参数激励系统的主共振分岔控制

设计了非线性参数控制器来改变参数激励系统的稳态响应,消除了系统主共振时的鞍结分岔和减小了系统稳态响应的幅值.从而消除了系统特有的跳跃和滞后现象.首先由多尺度法得到系统的近似频响方程,再由奇异性理论来分析分岔特性,从而实现非线性控制的目标.由数值模拟来确定了非线性参数控制器的有效性和可行性.     

铰支柔性梁主参数共振的时滞反馈控制

研究了时滞反馈控制作用下铰支柔性梁主参数共振问题.采用多尺度法,从理论上推导了时滞位移反馈控制作用下铰支柔性梁非线性主参数共振,分析了时滞、反馈控制增益,非线性系数等系统参数对系统非线性主参数振动的影响,分析了主参数动力响应随参数变化的规律.结果表明:随着反馈增益的增大,系统响应幅值得到明显抑制,合理地控制系统参数选取可提高振动控制的效率.     

含时滞轨道吸振器的建筑结构的动力学分析

本文研究了具有时滞轨道非线性吸振器的建筑结构的动力响应及其控制效果.采用谐波平衡法和弧长延拓法给出了简谐激励作用下主结构的幅频响应曲线,并与龙格库塔法的结果进行了对比.考察了不同参数情况下幅频曲线的变化情况,揭示了系统的复杂运动现象.结果表明,轨道非线性会导致幅频曲线向左偏转.时滞反馈控制能够降低主结构的位移幅值,并可抑制混沌响应.     

Transient performance for discrete‐time singular systems with actuators saturation via composite nonlinear feedback control

This paper is concerned with the transient performance improvement in tracking control problems for linear multivariable discrete‐time singular systems subject to actuators saturation. A composite nonlinear feedback control strategy is considered, and the resulting controller consists of a linear feedback law and a nonlinear feedback law without any switching element. The nonlinear term leads to a varying damping ratio of the closed‐loop system and yields a small overshoot as the output approaches the target reference, whereas the linear component is designed to achieve a quick response of the closed‐loop system. Two composite nonlinear feedback control laws by both state feedback and measurement output feedback are addressed. An illustrative example is included to show the validity of the obtained results. Copyright © 2012 John Wiley & Sons, Ltd.     

Semi-global output regulation for linear systems with input saturation by composite nonlinear feedback control

To improve transient performance of output response, this paper applies composite nonlinear feedback (CNF) control technique to investigate semi-global output regulation problems for linear systems with input saturation. Based on a linear state feedback control law for a semi-global output regulation problem, a state feedback CNF control law is constructed by adding a nonlinear feedback part. The extra nonlinear feedback part can be applied to improve the transient performance of the closed-loop system. Moreover, an observer is designed to construct an output feedback CNF control law that also solves the semi-global output regulation problem. The sufficient solvability condition of the semi-global output regulation problem by CNF control is the same as that by linear control, but the CNF control technique can improve the transient performance. The effectiveness of the proposed method is illustrated by a disturbance rejection problem of a translational oscillator with rotational actuator system.     

Improving transient performance in tracking control for linear multivariable discrete-time systems with input saturation

In this paper, we present a composite nonlinear feedback (CNF) control technique for linear discrete-time multivariable systems with actuator saturation. The CNF control law serves to improve the transient performance of the closed-loop system by adding an additional nonlinear feedback. The linear feedback can be designed to yield a quick response at the initial stage, then the nonlinear feedback is introduced to smooth out overshoots when the system output approaches the target reference. As such, the resulting closed-loop system typically has very fast transient response and small overshoots. The goal of this work is to complete the theory for general discrete-time systems. The technique is applied to a magnetic-tape-drive servo system design and yields a huge improvement in settling time compared to that of a purely linear controller.     

Composite nonlinear feedback control for strict-feedback nonlinear systems with input saturation

This paper focuses on composite nonlinear feedback (CNF) controller design for tracking control problem of strict-feedback nonlinear systems with input saturation to address the improvement of transient performance. First, without considering the input saturation, a stabilisation control law is designed by using standard backstepping technique for the nonlinear system, then a feedforward control law is added to the backstepping-based stabilisation control law to construct a tracking control law. The tracking control law is tuned to drive the output of the closed-loop system to track a command input with quick response. Then, an additional nonlinear feedback law is constructed and combined with the tracking control law to obtain a CNF control law. The role of this additional nonlinear feedback law is to smoothly change the damping ratio of the closed-loop system while the system output approaches the command input, and to reduce overshoot caused by the tracking control law. It is shown that the extra-adding nonlinear feedback part does not cause the loss of stability of the closed-loop system in its attractive basin.     

On improvement of transient performance in tracking control for a class of nonlinear systems with input saturation

This paper studies the technique of the composite nonlinear feedback (CNF) control for a class of cascade nonlinear systems with input saturation. The objective of this paper is to improve the transient performance of the closed-loop system by designing a CNF control law such that the output of the system tracks a step input rapidly with small overshoot and at the same time maintains the stability of the whole cascade system. The CNF control law consists of a linear feedback control law and a nonlinear feedback control law. The linear feedback law is designed to yield a closed-loop system with a small damping ratio for a quick response, while the nonlinear feedback law is used to increase the damping ratio of the closed-loop system when the system output approaches the target reference to reduce the overshoot. The result has been successfully demonstrated by numerical and application examples including a flight control system for a fighter aircraft.     

A note on the inverse optimal control of nonlinear systems

A procedure for the selection of a nonlinear feedback law has been suggested by Thau as a part of his study on the inverse optimal control problem of nonlinear systems. In this note we suggest an alternative feedback law which turns out to be better, in the sense that the transient response improved and at the same time the control energy requirement is reduced.     

基于伪谱法的自由采样实时最优反馈控制及应用

利用高斯伪谱法收敛速率快、精度高的特点,基于通用伪谱优化软件包在线求解非线性系统的最优控制问题.将伪谱反馈控制理论与非线性最优控制理论结合起来,给出了一种自由采样实时最优反馈控制算法,该算法通过连续在线生成开环最优控制的方式提供闭环反馈.考虑计算误差、模型参数不确定性和干扰的作用,假定系统状态方程右侧的非线性向量函数关于状态、控制和系统参数是Lipschitz连续的,利用Bellman最优性原理对闭环控制系统的有界稳定性进行了分析和理论证明.最后,以高超声速再入飞行器为应用对象,研究了其再入制导问题,仿真结果验证了该算法的可行性和有效性.     

Nonlinear robust state feedback control system design for nonlinear uncertain systems

This paper presents a systematic approach to the design of a nonlinear robust dynamic state feedback controller for nonlinear uncertain systems using copies of the plant nonlinearities. The technique is based on the use of integral quadratic constraints and minimax linear quadratic regulator control, and uses a structured uncertainty representation. The approach combines a linear state feedback guaranteed cost controller and copies of the plant nonlinearities to form a robust nonlinear controller with a novel control architecture. A nonlinear state feedback controller is designed for a synchronous machine using the proposed method. The design provides improved stability and transient response in the presence of uncertainty and nonlinearity in the system and also provides a guaranteed bound on the cost function. An automatic voltage regulator to track reference terminal voltage is also provided by a state feedback equivalent robust nonlinear proportional integral controller. Copyright © 2016 John Wiley & Sons, Ltd.     

Nonlinear sampled-data output feedback receding horizon control

In this paper, we present an output feedback receding horizon control for a class of SISO nonlinear systems. A globally stabilizing state feedback receding horizon control scheme is combined with a discretized high gain observer. This is motivated by the fact that measurable system’s outputs are only available at specific sampling intervals. Our result follows from the application of a separation principle applicable to a class of sampled-data nonlinear systems. It is shown that the output-feedback scheme recovers the performance (rate of convergence) achieved under state feedback receding horizon control for a sufficiently large observer gain and sampling frequency.     

Nonlinear oscillations in magnetic bearing systems

Nonlinear oscillations in magnetic bearings caused by gyroscopic effects at high speeds are analyzed. First a nonlinear model for the magnetic bearing is set in state-variable form using airgap flux, gap displacement, and velocity as state variables. The system, which is unstable in nature, is stabilized locally around the equilibrium point of zero speed using an optimal robust servo controller. It is shown that as the speed changes the system undergoes Hopf bifurcation to periodic solutions around some critical speed. The periodic solutions are shown to be unstable, so the methods of nonlinear bifurcation control are used to stabilize them. An easily implemented nonlinear feedback control of quadratic order is derived to control the Hopf bifurcation occurring in the system. The transient response of the system with and without nonlinear feedback is obtained to show the effectiveness of nonlinear feedback     

Composite nonlinear feedback control for linear systems with input saturation: theory and an application

We study in this paper the theory and applications of a nonlinear control technique, i.e., the so-called composite nonlinear feedback control, for a class of linear systems with actuator nonlinearities. It consists of a linear feedback law and a nonlinear feedback law without any switching element. The linear feedback part is designed to yield a closed-loop system with a small damping ratio for a quick response, while at the same time not exceeding the actuator limits for the desired command input levels. The nonlinear feedback law is used to increase the damping ratio of the closed-loop system as the system output approaches the target reference to reduce the overshoot caused by the linear part. It is shown that the proposed technique is capable of beating the well-known time-optimal control in the asymptotic tracking situations. The application of such a new technique to an actual hard disk drive servo system shows that it outperforms the conventional method by more than 30%. The technique can be applied to design servo systems that deal with "point-and-shoot" fast targeting.     

基于多目标粒子群–稀疏提升算法的电网频率反馈优化控制

频率反馈控制策略是维持电网频率稳定性的主要手段.本文建立了频率反馈控制系数和电网拓扑与电网频率稳定性的小信号分析模型,推导得出了能改善电网频率稳定性的频率反馈控制系数的参数范围.提出了基于多目标粒子群的稀疏提升算法(multi-objective particle swarm optimization sparse promoting algorithm, MOPSO–SPA),进行频率反馈控制系数矩阵的优化,提高了电网频率响应性能并降低了成本代价.用本文提出的算法设计了IEEE–39标准测试系统和陕北局部电网的频率反馈控制系数,并进行仿真对比,验证了算法的高效性和优越性.     

模糊免疫非线性PID控制的优化设计

在深入分析生物免疫系统中T细胞对B细胞辅助调节作用的基础上，提出了免疫反馈原理。针对非最小相位极点系统控制的难点，借鉴免疫反馈原理，结合积分控制的规律，提出了一种模糊免疫非线性HD控制方法。由于该方法中的参数确定比较复杂，利用免疫进化算法进行参数优化设计，实现了控制参数的合理设计。仿真结果表明，该方法在非最小相位极点系统控制中可行且有效，优于PID控制方法，具有更好的响应特性和抗干扰性能。     

A stability criterion for nonlinear feedback systems

A frequency domain criterion is formulated to prove global asymptotic stability of feedback control system with more than one nonlinear element. The input-output characteristics of the nonlinearities are confined to sectors of the input-output planes. Sufficient conditions for global asymptotic stability are derived in terms of a number of inequalities equal to the number of nonlinear elements.