一类时滞对象的PID控制器参数稳定域计算

针对任意阶时滞对象,通过求解控制参数的稳定边界线和判断边界线的哪侧具有更少的不稳定极点,给出一种确定PID控制器参数稳定域的准确计算方法．只要在所得到的稳定域中调节PID控制器参数,就能够保证闭环系统的稳定性,这不仅为时滞对象的PID控制器设计建立了基础,也为其在线调节提供了一条简单有效的途径．仿真实例验证了该方法的有效性,并表明该方法不仅适用于不稳定时滞对象而且也适用于非最小相位时滞对象．     

分数阶时滞系统的频域子空间辨识

研究了利用频率响应数据辨识分数阶时滞系统子空间模型的问题,给出了一种差分进化算法与频域子空间方法相结合的辨识算法.利用差分进化算法搜索最优分数微分阶次和时滞参数,而对于固定的分数微分阶次和时滞,则采用分数阶频域子空间辨识方法得到状态空间模型.通过仿真算例验证了该算法的有效性.     

参数不确定时滞系统的鲁棒P ID 控制

提出一种简单而有效的参数不确定时滞系统鲁棒PID控制器设计方法．通过在kp-ki平面上绘制稳定边界线,确定稳定的PID控制器参数区域;推导了一阶不稳定时滞系统PI控制器和PID控制器的存在性条件;基于推广到时滞系统的棱边定理,确定所有鲁棒PID控制器参数集．仿真实例表明了该方法的优越性．     

不确定切换奇异时滞系统鲁棒指数容许性分析

讨论一类连续时间不确定切换奇异区间时变时滞系统的鲁棒指数容许性问题. 通过定义衰减率依赖李亚普诺夫函数并利用平均驻留时间法, 给出一个时滞区间依赖充分条件保证标称系统正则、无脉冲且均方指数稳定. 同时该准则也被推广至不确定系统. 本文获得的结论为连续时间切换奇异时滞系统的基本问题提供了一个解, 即识别切换信号使得切换奇异时滞系统正则、无脉冲且均方指数稳定. 数值例子说明本文结果的有效性.     

基于幅值裕度和相位裕度的PID参数最优整定方法

给出一种基于幅值裕度和相位裕度的PID参数最优整定方法.首先,基于改进的D–分割法确定满足幅值裕度和相位裕度要求的控制参数稳定域,然后根据最大灵敏度函数、超调和调节时间定义控制器设计的目标函数,在所得到的控制参数稳定域中计算出一组最优的控制参数值.仿真结果表明,该整定方法能够保证闭环系统具有强鲁棒性、良好的跟踪性能和抗干扰性能.它不仅适用于稳定时滞对象,而且还适用不稳定时滞对象.     

一类不确定切换奇异时滞系统的时滞依赖鲁棒镇定

针对一类不确定切换奇异时滞系统,对其鲁棒镇定问题进行了研究.首先利用多李亚普诺夫泛函方法和线性矩阵不等式工具,通过引入适当的自由权矩阵,在适当的切换律下,给出了基于严格线性矩阵不等式表示的标称自治切换奇异系统正则、无脉冲且渐近稳定的时滞依赖条件;然后基于此条件,通过设计相应的状态反馈子控制器,得到了保证闭环系统对所有允许的不确定性是正则、无脉冲且渐近稳定的时滞依赖条件,同时给出了子控制器的显示表达式.数值算例表明该方法的有效性.     

基于Matlab-Simulink-SISO及SRO的电磁轴承PID控制参数整定

介绍了电磁轴承PID控制系统, 采用Matlab SISO SRO开发电磁轴承控制仿真系统,研究PID控制参数对电磁轴承控制的影响,给出在不同的PID控制参数下的仿真结果,为电磁轴承控制系统的设计提供了一种简洁高效的方法。     

油料输送温度的智能预测控制

针对油料加热输送过程中具有大时滞非线性特点的流动加热控制问题,提出了一种智能预测控制方法。该方法采用自适应粒子群优化算法（APSO）辨识和优化预测模型及控制器的PID控制参数,克服油料流动加热控制模型的失配及系统的不确定性。通过对已知模型的仿真,以及与自整定PID控制的比较表明,该方法具有较好的控制效果。     

时滞系统PID 控制器增益的稳定范围研究

基于逆Nyquist 曲线，提出一种时滞系统在PID 控制下确定增益稳定范围的方法．根据时滞系统的逆 Nyquist 曲线特征和广义Hermite-Biehler 定理，确定用于判断系统稳定性所需的频率范围，以及该范围内逆Nyquist 曲线上两类关键点的横坐标．关键点将PID 增益分成若干区间，通过纵向直线与逆Nyquist 曲线的交点数，以及文 中给出的一个推理和两个定理，可判断PID 增益稳定的范围．该方法能有效解决时滞系统在PID 控制下增益稳定范 围的确定问题．     

一类不确定非线性系统的自适应鲁棒控制

针对一类由非线性微分方程描述的不确定单输入单输出(SISO)系统,提出了一种自适应鲁棒控制算法.设计了一动态滤波器并将其与原系统组成扩展系统,由滤波器求得控制律稳定扩展系统.算法绕开辨识模型参数而是直接估计函数值,加快了控制律的求解.设计了状态误差观测器,用观测器的值构造控制律逼近状态反馈时的控制效果.基于Lyapunov 稳定理论分析了扩展系统的渐近稳定性并给出了闭环稳定的充分条件.最后仿真结果验证了算法的有效性和鲁棒性.     

Properties of Stabilizing PID Gain Set in Parameter Space

The properties of the PID gain set for which all the closed-loop poles lie in the left half of the complex plane are examined on the parameter plane. A new method of determining the increase in the number of unstable poles when the gain crosses the boundary of stability regions is proposed. This method is useful for determining the number of unstable poles in each region. These results are extended to Gamma-stability based on conformal mapping.     

基于偏置继电反馈的一种新的频域辨识方法

提出一种新的基于偏置继电反馈的频域辨识算法,能够对包括迟延在内的SISO系统的传递函数参数进行在线辨识。首先利用偏置继电反馈辨识过程的频率响应,一次继电测试可以辨识过程Nyquist曲线上的多点。接着利用最小二乘法估计过程传递函数参数的初值,最后应用非线性共轭梯度法准确的辨识传递函数参数。该方法辨识精度高,同时可以有效避免大多继电反馈辨识方法测试时间过长及只能辨识固定的低阶模型的缺点。仿真结果验证了算法的有效性与准确性。     

PD–PID controller for delayed systems with two unstable poles: a frequency domain approach

This paper deals with the stability problem of linear delayed systems containing two unstable real poles by means of PD controllers. The analysis presented is based on frequency domain techniques. Necessary and sufficient conditions for the existence of stabilising controllers are given in terms of the parameters of the system and the time delay size. The main result is extended to delayed systems with two unstable poles and n stable real poles. PID controllers are also considered in order to control the studied systems, obtaining similar stability conditions. Numerical examples are presented in order to illustrate the control performance.     

Design and implementation of a fuzzy supervisor for on-line compensation of nonlinearities: An instability avoidance module

Unstable behavior of a control loop is the most feared situation in control engineering. Since PID controllers are linear in nature, but still used in 90% of control loops in the process industry, their use in nonlinear processes increases the risk of closed-loop unstable response. This paper presents the design of an instability avoidance module for SISO PID control loops to automatically adjust the controller's tuning parameters when undesired oscillatory behavior is monitored. This module is a Fuzzy-based Supervisor composed of a dynamic parameter identification module that operates on-line, and a Fuzzy Inference System (FIS) with fuzzy rules to modify PID tuning. Tests in nonlinear process models are performed, demonstrating that this Fuzzy Supervisor—Type 1 (non-intrusive) provides the PID controller the ability to adapt its tuning to eliminate observed oscillatory behavior.     

Parametric system identification on logarithmic frequency responsedata

Gradient search methods that fit the parameters of a user-defined transfer function to experimental logarithmic frequency response data are presented. The methods match a model based on physically significant parameters, including natural frequencies of poles and zeros and damping ratios of complex poles and zeros. The algorithms construct and utilize their own analytical gradient descent functions, based on the desired model. One method attempts to fit both log magnitude and phase, while another identifies a minimum phase transfer function model from only log magnitude frequency response data. The log magnitude algorithm is shown to be superior to traditional methods using nonlogarithmic frequency response data, including those used in commercially available frequency response analyzers. The algorithms are shown to perform well, especially for systems with lightly-damped dynamics     

PID controller synthesis for a class of unstable MIMO plants with I/O delays

Conditions are presented for closed-loop stabilizability of linear time-invariant (LTI) multi-input, multi-output (MIMO) plants with I/O delays (time delays in the input and/or output channels) using PID (Proportional+Integral+Derivative) controllers. We show that systems with at most two unstable poles can be stabilized by PID controllers provided a small gain condition is satisfied. For systems with only one unstable pole, this condition is equivalent to having sufficiently small delay-unstable pole product. Our method of synthesis of such controllers identify some free parameters that can be used to satisfy further design criteria than stability.     

Optimal automatic tuning of active damping PID regulators

An automatic tuning method for the PID controller in single-input-single-output control loops involving processes with conjugate complex poles is presented. The development of the method lies in the principle of the well known Magnitude Optimum criterion and considers two fundamental constraints met frequently in many industry applications; (1) the existence of a poor process model and (2) access to the output of the process and not to its states. The presentation of the method is carried out in two steps. Over the first step, the straightforward PID tuning via the Magnitude Optimum criterion in the ideal case of a known single input-single output linear process model reveals a feature of the method called ‘the preservation of the shape of the step and frequency response’ of the final closed-loop control system. This shape is characterized by specific performance in terms of overshoot (4.4%), settling and rise time of the closed-loop control system. Over the second step, the PID controller parameters are tuned automatically so that the aforementioned performance is achieved. In this case, the existence of a poor process model is adopted assuming access to its output and not to its states. For applying the method an open-loop experiment of the process is carried out which serves for (1) initializing the algorithm and (2) determining the two zeros of the proposed PID controller. The method starts with I-Lag control action to the process by tuning the integral gain. After this tuning is over, the parasitic time constant of the closed-loop system is estimated. I-Lag control is then turned into PID control and the integrator's time constant of the PID controller is tuned accordingly, so that the shape of the control loop's output exhibits the aforementioned performance. Since the tuning of the PID controller is based on the Magnitude Optimum criterion, optimal disturbance rejection is expected to be achieved at the output of the controlled process. The potential of the proposed method is justified via simulation examples for two benchmark process models met frequently in various industry applications.     

The relationship between real poles and real zeros in SISO sampleddata systems

A relationship between real poles and real zeros of SISO (single-input, single-output) sampled data systems is presented, which is independent of the sampling period. The relation is stated in terms of a parity property involving the number of real zeros between any two real poles. This property allows the investigation of conditions for the preservation of stable or unstable zeros under sampling. A sufficient condition for stability of a sampled system with a continuous-time plant having all real zeros, and a sufficient condition for instability of a two-sampled system with an unstable plant is developed     

New reduction technique by step error minimization for multivariable systems

A method of reduction of system order is introduced, in which a lower-order transfer function/transfer matrix is obtained by minimizing an error function constructed from the time responses of the system and the reduced model. The denominator of the reduced model can be selected either by retaining dominant poles or by the Routh method. The numerator of the reduced model is obtained by minimizing the step response error along with a steady-state constraint. The error function is converted into the frequency domain and the minima operation is carried out in this domain. Since the numerator polynomial selection is independent of the denominator, the method is very general and can be applied for MIMO systems as well as for SISO systems. A numerical example of a multivariable system illustrates the procedure.