Control of linear systems using generalized sampled-data hold functions

This paper investigates the use of generalized sampled-data hold functions (GSHF) in the control of linear time-invariant systems. The idea of GSHF is to periodically sample the output of the system, and generate the control by means of a hold function applied to the resulting sequence. The hold function is chosen based on the dynamics of the system to be controlled. This method appears to have several advantages over dynamic controllers: it has the efficacy of state feedback without the requirement of state estimation; it provides the control system designer with substantially more freedom; and it requires few on-line computations. This paper focuses on four questions: pole assignment, specific behavior, noise sensitivity, and robustness. Among the problems solved are: simultaneous arbitrary pole assignment for a finite number of systems by a single GSHF controller, exact model matching, decoupling, and optimal noise rejection. Examples are given.     

一种有限对象集的输出通道任意增益/相角裕度调节方法

针对一类有限多输入多输出线性时不变对象集,提出一种调节输出通道增益/相角裕度的方法.采用增益相角裕度测试器理论,将问题转化为有限不确定对象集的稳定性问题;基于连续线性二次调节器理论,设计针对单个对象的输出反馈控制器;利用周期控制方法,设计针对有限对象集的线性周期控制器.该控制器可使有限对象集的所有反馈控制回路在输出通道同时实现任意大的增益裕度和直到90°的相角裕度.仿真结果表明了该方法的有效性.     

Optimal periodic feedback design for continuous-time LTI systems with constrained control structure

This paper aims to design a high-performance controller with any predefined structure for continuous-time LTI systems. The control law employed is the generalized sampled-data hold function (GSHF), which can have any special form, e.g. polynomial, exponential, piecewise constant, etc. The GSHF is first written as a linear combination of a set of basis functions obtained in accordance with its desired form and structure. The objective is to find the coefficients of this linear combination, such that a prespecified linear-quadratic performance index is minimized. A necessary and sufficient condition for the existence of such GSHF is first obtained in the form of matrix inequality, which can be solved by using the existing methods to obtain a set of stabilizing initial values for the coefficients or to conclude the non-existence of such structurally constrained GSHF. An efficient algorithm is then presented to compute the optimal coefficients from their initial values, so that the performance index is minimized. The paper utilizes the latest developments in the area of sum-of-square polynomials. The effectiveness of the proposed method is demonstrated in two numerical examples.     

Tuning of PID controllers based on simplified single parameter optimisation

A simple method to design PID controllers in the frequency domain based on a simplified constrained optimisation is proposed. The method is based on the use of a single tuning parameter, defined as the quotient between the final crossover frequency and the zero of the controller. The tuning procedure is based on the maximisation of the controller gain subject to an equality constraint in the phase margin and an inequality constraint in the gain margin. The main advantage of the proposed method is that, even though the maximisation of the controller gain is straightforward, since there is only one parameter to be tuned, the solution is close to the optimal tuning obtained with direct numerical optimisation methods. Moreover the method is applicable to any linear model structure, including dead time and non-minimum phase systems.     

一种解析的模糊PI自整定方法

针对模糊PID控制器缺乏系统的整定方法的问题,提出了一种解析的基于增益裕度和相位裕度的模糊PI控制器的参数自整定方法。首先推导出模糊PI控制器的解析模型,该解析模型包括线性控制器和非线性补偿控制器2个部分。参数整定时,将非线性补偿控制器看作过程的扰动,由线性控制器和被控对象的一阶纯时滞模型,基于系统的增益裕度和相位裕度,导出模糊PI控制器的参数。仿真结果表明,对于时变高阶系统,和传统的PI控制器相比,模糊PI控制器具有鲁棒性强,超调小,调整时间短等优点。     

Frequency-domain design of pid controllers for stable and unstable systems with time delay

An approach for tuning PID-type controllers is developed for single input single-output, linear time-invariant systems, based on an extension to the method of D-partition. This method permits design for simultaneous minimum gain and phase margin requirements. It also allows design for specified maximum gain and phase cross-over frequencies of the controlled system. The technique can be applied to systems with stable or unstable plants as well as to irrational systems with significant time delay. Another advantage of the method is that it can be used for various controller configurations including derivative in the feedback path. Three examples illustrate the tuning method.     

混合控制系统的稳定裕度分析与计算

数字控制与连续对象组成的混合系统是常见的控制形式，而通过有效的计算方法得到混合系统的稳定裕度是衡量控制系统性能指标的重要工作。通过一个具体的数字实例，对于目前常用的几种混合系统的稳定裕度计算方法进行了比较，明确了正确的计算步骤和方法，即只有对于整个开环传递函数进行整体ZOH离散化才能够得到真实结果，并指出通过Matlab中的相应函数可以得到精确的数值解。最后给出了混合系统设计的指导性意见。     

一种直流电机系统的稳定裕度估计方法

随着工业设备自动化程度和复杂度的不断提高,系统稳定性和鲁棒性成为日益关键的指标。而稳定裕度便是衡量系统稳定程度的一个指标,并且在控制系统设计中起着重要的作用。因此,一种数据驱动的稳定裕度估计方法被提出,并且以直流电机系统为例进行了应用。利用电机输入输出测量数据和原本的控制器信息,通过子空间投影,估计出了系统的稳定裕度,并比较了在常见的电机故障中,对控制系统稳定裕度变化量的估计。仿真结果显示此方法在系统参数发生变化时较好地估计出了相应的稳定裕度。     

基于周期控制的有限集输入通道任意增益/相角裕度调节方法

针对有限多输入多输出(MIMO)线性时不变(LTI)对象集,提出了一种调节输入通道增益/相角裕度的方法,采用离散线性二次调节器(LQR)理论和周期控制方法设计一个针对有限对象集的线性周期控制器.该控制器可使有限对象集的所有反馈控制回路在输入通道同时实现任意大的增益裕度和直到90°的相角裕度.仿真结果表明了该方法的有效性.     

A PI/PID controller for time delay systems with desired closed loop time response and guaranteed gain and phase margins

In this article we present a graphical tuning method of PI/PID controller for first order and second order plus time delay systems using dominant pole placement approach with guaranteed gain margin (GM) and phase margin (PM). The stability equation method and gain phase margin tester have been used to portray constant GM and PM boundaries. The PID controller parameters have been obtained for different dominant poles and plotted graphically in the parameters plane of controller within the specified GM and PM regions. To demonstrate the effectiveness and confirm the validity of the proposed methodology, three examples with numerical simulations are presented.