规范形Qi系统的Hopf分岔分析及控制

文章研究了一个Qi系统的Hopf分岔控制问题.根据计算的极限环曲率系数,判定原系统的Hopf分岔类型,并采用washout滤波器控制该系统的分岔行为.首先讨论了控制器的线性增益对Hopf分岔点位置的影响,然后引入规范形计算方法,求出受控系统的Hopf分岔规范形.分析了规范形中系数对控制参数的选择原则所产生之影响,以及对Hopf分岔类型及极限环幅值的影响.理论和仿真结果表明,控制器的线性增益能使原系统的Hopf分岔点延迟或消失,而非线性增益能则改变极限环的稳定性和极限环幅值的大小.最后把washout滤波器和线性控制器的控制效果作了对比,发现washout滤波器比之线性控制器具有一定的优势.     

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     

机床无刷直流电机系统的分岔分析与控制

文章主要研究了机床无刷直流电机系统的Hopf分岔控制问题.首先,对系统进行分岔分析,通过计算极限环曲率系数判定系统的Hopf分岔类型;然后设计Washout滤波器对系统进行分岔控制,根据Hopf分岔理论给出使原系统Hopf分岔位置发生改变的参数条件,利用Normal Form方法计算出受控系统的Hopf分岔正规型,根据正规型的实部大小判定Hopf分岔类型,给出使原系统Hopf分岔类型发生改变的参数条件;并借助MATLAB软件对理论结果进行数值仿真,理论结果和数值仿真表明:控制器中的线性增益能使系统在所期望的参数值处发生Hopf分岔,甚至消除Hopf分岔,控制器中的非线性增益能改变原系统的Hopf分岔类型及极限环幅值的大小.研究结果对无刷直流电动机系统的工程实际具有一定的指导意义.     

适用于非线性对象的模糊-神经元控制方法

针对具有严重非线性的受控对象，提出了一种模糊-神经元控制方法。该方法将模糊PID控制器与神经元控制器相结合，用于改善控制器控制非线性对象的性能，以误差、误差变化率及设定值的变化来自调整神经元控制器增益，提高了控制系统的响应速度和鲁棒性。将所提出控制方法用于pH中和过程控制，仿真实验结果表明，该方法具有满意的控制品质及很强的适应性。     

Robust stability of systems with integral control

A number of necessary and sufficient conditions are derived, which must be satisfied by the plant d.c. gain matrix of a linear time invariant system in order for an integral controller to exist for which the closed loop system is stable. Based on these results, the robustness of integral control systems is analyzed, i.e., the family of plants is defined which are stable when controlled with the same integral controller. Conditions for actuator/sensor failure tolerance of systems with integral control are also given. Finally, parallels are drawn between the results of this paper and the bifurcation theory of nonlinear systems.     

Identification of time-varying pH processes using sinusoidal signals

This paper presents an approach to the identification of time-varying, nonlinear pH processes based on the Wiener model structure. The algorithm produces an on-line estimate of the titration curve, where the shape of this static nonlinearity changes as a result of changes in the weak-species concentration and/or composition of the process feed stream. The identification method is based on the recursive least-squares algorithm, a frequency sampling filter model of the linear dynamics and a polynomial representation of the inverse static nonlinearity. A sinusoidal signal for the control reagent flow rate is used to generate the input-output data along with a method for automatically adjusting the input mean level to ensure that the titration curve is identified in the pH operating region of interest. Experimental results obtained from a pH process are presented to illustrate the performance of the proposed approach. An application of these results to a pH control problem is outlined.     

Linearizing feedforward–feedback control of pH processes based on the Wiener model

This paper examines the control of pH processes based on the Wiener model construct (a dynamic linear element representing the mixing dynamics of the process in series with a static nonlinearity representing the titration curve). Conditions under which the pH process behaves like an exact Wiener system are examined. Linearization by output transformation using both the true inverse of the titration curve and an estimate of the inverse is employed to make the pH process appear linear enabling the application of a linear feedback (PI) controller. Although many others have utilized an identified nonlinearity for linearizing feedback control of pH processes, much less work has been done on using the nonlinearity for linearizing feedforward control. Here, a simple linearizing feedforward controller is proposed based on a current estimate of the inverse titration curve. Simulated closed-loop results demonstrate the superiority of the linearizing feedforward–feedback strategy versus linearizing feedback only, when the inverse titration curve is accurately estimated.     

一类不确定广义系统的非脆弱保性能控制

研究了一类时变时滞不确定广义系统的非脆弱保性能控制问题。在系统矩阵、滞后状态矩阵、输入矩阵和滞后输入矩阵都具有不确定性时,带有反馈增益扰动的控制器能够保证闭环系统是正则、无脉冲、指数稳定的;且性能函数存在上界。对于出现的两个不确定项乘积的问题,采用两个线性矩阵不等式,两次运用Schur补引理的方法得以解决。控制器的增益可通过求解一系列严格线性矩阵不等式得到。数值仿真实例证明了所提方法的有效性。     

Relay feedback tuning of robust PID controllers with iso-damping property.

A new tuning method for proportional-integral-derivative (PID) controller design is proposed for a class of unknown, stable, and minimum phase plants. We are able to design a PID controller to ensure that the phase Bode plot is flat, i.e., the phase derivative w.r.t. the frequency is zero, at a given frequency called the "tangent frequency" so that the closed-loop system is robust to gain variations and the step responses exhibit an iso-damping property. At the "tangent frequency," the Nyquist curve tangentially touches the sensitivity circle. Several relay feedback tests are used to identify the plant gain and phase at the tangent frequency in an iterative way. The identified plant gain and phase at the desired tangent frequency are used to estimate the derivatives of amplitude and phase of the plant with respect to frequency at the same frequency point by Bode's integral relationship. Then, these derivatives are used to design a PID controller for slope adjustment of the Nyquist plot to achieve the robustness of the system to gain variations. No plant model is assumed during the PID controller design. Only several relay tests are needed. Simulation examples illustrate the effectiveness and the simplicity of the proposed method for robust PID controller design with an iso-damping property.     

The setpoint overshoot method: A simple and fast closed-loop approach for PID tuning

A simple method has been developed for PID controller tuning of an unidentified process using closed-loop experiments. The proposed method requires one closed-loop step setpoint response experiment using a proportional only controller, and it mainly uses information about the first peak (overshoot) which is very easy to identify. The setpoint experiment is similar to the classical Ziegler–Nichols (1942) experiment, but the controller gain is typically about one half, so the system is not at the stability limit with sustained oscillations. Based on simulations for a range of first-order with delay processes, simple correlations have been derived to give PI controller settings similar to those of the SIMC tuning rules (Skogestad (2003) [6]). The recommended controller gain change is a function of the height of the first peak (overshoot), whereas the controller integral time is mainly a function of the time to reach the peak. The method includes a detuning factor that allows the user to adjust the final closed-loop response time and robustness. The proposed tuning method, originally derived for first-order with delay processes, has been tested on a wide range of other processes typical for process control applications and the results are comparable with the SIMC tunings using the open-loop model.     

一种空间曲线轨迹跟踪的无人机自适应导航控制算法

随着固定翼无人机飞行任务复杂化,为了实现高精度的空间曲线导航控制,基于L1-Navigation非线性导航控制算法,设计自适应模糊控制器优化固定翼无人机跟踪空间曲线导航控制方法。以球面上的空间八字曲线为例,对八字曲线建模,通过坐标转换求得目标航点位置来计算无人机飞行加速度。为了优化加速度控制无人机跟踪空间曲线性能,在L1-Navigation导航控制器中,针对增益系数设计一个双输入单输出模糊控制系统,以轨迹误差和轨迹误差变化率为输入量,以计算横向加速度的增益系数常数为输出量。最后,在Ardupilot飞控中进行飞行模拟实验,飞行实验表明,所提出方法能够精确跟踪空间曲线路径,并且有很好的自适应性。     

Robust self-tuning PID controller for nonlinear systems

In this paper, we propose a robust self-tuning PID controller suitable for nonlinear systems. The control system employs a preload relay (P_Relay) in series with a PID controller. The P_Relay ensures a high gain to yield a robust performance. However, it also incurs a chattering phenomenon. In this paper, instead of viewing the chattering as an undesirable yet inevitable feature, we use it as a naturally occurring signal for tuning and re-tuning the PID controller as the operating regime digresses. No other explicit input signal is required. Once the PID controller is tuned for a particular operating point, the relay may be disabled and chattering ceases correspondingly. However, it is invoked when there is a change in setpoint to another operating regime. In this way, the approach is also applicable to time-varying systems as the PID tuning can be continuous, based on the latest set of chattering characteristics. Analysis is provided on the stability properties of the control scheme. Simulation results for the level control of fluid in a spherical tank using the scheme are also presented.     

基于分岔理论的永磁同步电机有限时间混沌控制

永磁同步电机运行系统具有不稳定的分岔特性,随着系统参数的变化,系统会在平衡点处发生分岔行为.首先,基于分岔理论构建了永磁同步电机的混沌模型.其次,通过研究系统的分岔参数,分析了系统在平衡点处的分岔特性,发现系统在零平衡点处会产生静态分岔并出现新的平衡点,随着参数的继续变化,系统在新的平衡点处发生连续的Hopf分岔,而连...     

Robust discrete adaptive input-output-based sliding mode controller

A robust input-output-based discrete adaptive sliding mode controller is proposed. It combines an integral action, a nonlinear output feedback, an adjustable sliding mode and an adaptive plant parameter estimator. The controller design is carried out via the Lyapunov direct method. A pole assignment procedure is developed for determination of the integral control gain and the coefficients of the sliding mode hyperplane. An on-line update for coefficients of the hyperplane is used to improve control loop behaviour further. Compared with the optimally tuned proportional-integral-derivative (PID) controller, the new controller has increased robustness with regard to the variation in the main process parameters and it has much better set point tracking characteristics. The new controller also exhibits very good disturbance rejection property comparable work or better than to that obtained by the optimally tuned PID controller. Simulation experiments are made to illustrate the quality and robustness of control achieved.     

Stabilization of oscillations through backstepping in high-dimensional systems

This note introduces a method for obtaining stable and robust self-sustained oscillations in a class of single input nonlinear systems of dimension n/spl ges/2. The oscillations are associated to a limit cycle that is produced in a second-order subsystem by means of an appropriate feedback law. Then, the controller is extended to the full system by a backstepping procedure. It is shown that the closed-loop system turns out to be generalized Hamiltonian and that the limit cycle can be thought as born in a Hopf bifurcation after moving a parameter.     

一类具有饱和发生率的时滞恶意病毒传播模型的分岔控制策略

考虑非线性的饱和发生率,建立一种刻画信息物理融合系统(cyber-physical systems, CPS)中恶意病毒传播的SIRS(susceptible-infected-recovered-susceptible)模型.为了避免因Hopf分岔的产生致使恶意病毒传播扩散,采用参数调节法和状态反馈法相结合的混合分岔控制策略,研究信息物理融合系统的Hopf分岔控制问题,建立受控系统的稳定性条件和分岔判据,探明控制增益参数对Hopf分岔点和分岔极限环幅值的影响规律,并给出分岔阈值与增益参数间的关系图.数值仿真结果表明,所提出的混合分岔控制策略不仅能够改变Hopf分岔点的位置,而且可以有效调节极限环幅值的大小,使得信息物理融合系统产生预期的动力学行为,有效降低恶意病毒传播的危害.     

Design of the PID Controller for Hydro-turbines Based on Optimization Algorithms

In this study, multiple objective particle swarm optimization (MOPSO), genetic algorithm, bees, and reinforcement learning (RL) are used to calculate the rise time (tr), integral square-error, integral of time-multiplied-squared-error, integral absolute error, and integral of time multiplied by absolute error of the system transfer function and then we use a fuzzy algorithm on MOPSO, GA, bees, and RL based on the frequency sensitivity margin of a water turbine governor to optimize the proportional gain (kp) and integral gain (ki) and calculate the relative collapsing frequency response values. The MOPSO algorithm returned the optimal result. The radial basis function (RBF) neural network curve is obtained from the MOPSO algorithm with three variables (i.e., kp, ki, kd = 0.6 and grid frequency deviations values), and finally we identify and predict three variable values near the RBF neural network curve through deep learning. The result of the grid frequency deviation is close to 0, and the gain response time is better for damping the frequency oscillations in different operating conditions.

     

循环流化床锅炉燃烧优化控制

本文在全面分析了循环流化床燃烧常规控制方案的基础上,结合我国循环流化床锅炉结构的实际,对它的燃烧控制系统提出了一种新的控制方法.首先,设置主气流量——给煤量关系曲线及总风量——给煤量关系曲线在线学习单元,在线改变曲线拐点坐标,以适应由于燃料热值变化给控制带来的影响.其次,提出以主气流量——-给煤量关系曲线为主,以主汽压力,主汽流量模糊控制器为辅的燃料给定值设定方案,在大大提高了控制系统投运率的同时,提高了锅炉的效率.以上控制方案经实践证明控制效果良好.     

Excel软件在酸碱滴定分析教学中的应用

通过对一元强碱滴定同浓度一元强酸及弱酸滴定曲线的绘制步骤,介绍其在绘制酸碱滴定曲线中的应用;通过求解高次方程从而实现对二元弱酸石酸pH的计算,介绍其在计算某些复杂酸碱体系pH值时的应用。利用Microsoft Excel软件绘制滴定曲线,免去了大量数据的输入及复杂计算,简便、快速;利用其计算复杂酸碱体系的pH,其便利是传统逐步逼近法无可比拟的。     

基于多模型的非线性系统自适应最小方差控制

对于一类典型的离散时间非线性系统, 提出了一种基于多模型的自适应最小方差控制方法. 通过在平衡点附近建立线性模型, 用径向基函数神经元网络来补偿建模误差和未建模动态, 形成了非线性系统的多模型表示. 采用了具有积分性质的切换指标函数作为切换法则和最小方差的控制方法构成了多模型自适应控制器. 仿真实验的结果表明了这种方法的有效性.