COMMENTS ON «TUNING RULES FOR THE PID CONTROLLER USING A DMC STRATEGY»

It is pointed out that the tuning rules for under damped system and non‐minimum phase system that given by Haeri is incorrect.     

PID TUNING FOR DOMINANT POLES AND PHASE MARGIN

A simple PID tuning method for dominant pole placement and phase margin specification is proposed in this paper. Time domain specifications as settling time and percentage overshoot are represented by a pair of dominant poles, which is combined with phase margin specification to achieve closed‐loop stability and robustness. A graphical method is developed to determine PID settings to meet these specifications simultaneously. An example is given for illustration.     

REVISITING THE ZIEGLER‐NICHOLS TUNING RULES FOR PI CONTROL — PART II THE FREQUENCY RESPONSE METHOD

This paper presents an analysis of the Ziegler‐Nichols frequency response method for tuning PI controllers, showing that this method has severe limitations. The limitations can be overcome by a simple modification for processes where the time delay is not too short. By a major modification it is possible to obtain new tuning rules that also cover processes that are lag dominated.     

GLOBAL CONVERGENCE OF MINIMUM VARIANCE SELF‐TUNING SCHEME BASED UPON DAMPED LEAST SQUARES

This paper presents an analysis of the stability and convergence of a damped least squares identification algorithm and establishes the global convergence of a minimum variance self‐tuning scheme based upon damped least squares. The results mathematically demonstrate that the damped least squares can generally be applied to achieve system identification and adaptive control.     

A comparative study on a novel model‐based PID tuning and control mechanism for nonlinear systems

This work presents a novel predictive model‐based proportional integral derivative (PID) tuning and control approach for unknown nonlinear systems. For this purpose, an NARX model of the plant to be controlled is obtained and then it used for both PID tuning and correction of the control action. In this study, for comparison, neural networks (NNs) and support vector machines (SVMs) have been used for modeling. The proposed structure has been tested on two highly nonlinear systems via simulations by comparing control and convergence performances of SVM‐ and NN‐Based PID controllers. The simulation results have shown that when used in the proposed scheme, both NN and SVM approaches provide rapid parameter convergence and considerably high control performance by yielding very small transient‐ and steady‐state tracking errors. Moreover, they can maintain their control performances under noisy conditions, while convergence properties are deteriorated to some extent due to the measurement noises. Copyright © 2009 John Wiley & Sons, Ltd.     

A STABLE ON‐LINE SELF‐TUNING OPTIMAL PID CONTROLLER FOR A CLASS OF UNKNOWN SYSTEMS

In this paper, a novel self‐tuning method of optimal PID control laws is proposed for both continuous‐time systems and discrete‐time systems. The controlled plant is assumed to be unknown except the system order (or system delay) and the direction of transmitting control input. Through the minimization of PID gains subject to the Lyapunov stability based reaching condition, the tuning of the three PID control gains is transformed to solve the inequality constraint optimization problem. An unknown SISO nonlinear system subject to a unit step input, and the tracking control problem of the piezoelectric actuator (PZA) with unknown dynamics are simulated. The simulation results show that the excellent tracking performance can be achieved.     

抽取对象输出响应特征设计控制器的新方法

提出了抽取对象动态响应特征的设计方法，并把理论与专家经验结合进行控制系统设计，给出了设计流程和实例．     

一种新的离散系统最优闭环极点配置方法

分析了LQ逆问题解的存在条件,以便合理选择期望的闭环极点,使之成为一组最优极点．提 出了一种以离散系统LQ逆问题分析为基础的新的最优控制系统设计方法,得到了开环、闭环 特征多项式系数与加权矩阵之间的解析关系,只要给定一组期望闭环极点,即可确定与 之对应的加权矩阵Q和R,从而得到一个具有指定极点的最优控制系统．     

DELAY‐DEPENDENT ROBUST CONTROL OF DESCRIPTOR SYSTEMS WITH TIME DELAY

This paper deals with the problem of stability and robust control for both certain and uncertain continuous‐time singular systems with state delay. Systems with norm‐bounded parameter uncertainties are considered. Robust delay‐dependent stability criteria and linear memoryless state feedback controllers based on linear matrix inequality are obtained. By choosing some Lyapunov‐Krasovskii functionals, neither model transformation nor bounding for cross terms is required in the derivation of our delay‐dependent results. Finally, numerical example is provided to illustrate the effectiveness of the proposed method.     

STATE‐SPACE DIGITAL PID CONTROLLER DESIGN FOR MULTIVARIABLE ANALOG SYSTEMS WITH MULTIPLE TIME DELAYS

This paper presents a discrete‐time state‐space methodology for optimal design of digital PID controllers for multivariable analog systems with multiple time delays. The multiple time‐delayed multivariable analog systems are formulated in a state‐space generic form so that the exact discrete‐time state‐space model can be constructed. Then, the optimal digital PID controller is designed via a state‐feedback and state‐feedforward LQR approach. The developed PID controller can be applied to a general time‐delayed multivariable analog system represented by a semi‐proper or strictly proper transfer function matrix. Illustrative examples are given to compare the performance of the proposed approach with alternative techniques.     

ROBUST ADAPTIVE CONTROL WITH MULTIPLE ESTIMATION MODELS FOR STABILIZATION OF A CLASS OF NON‐INVERSELY STABLE TIME‐VARYING PLANTS

This paper presents an indirect adaptive control scheme for nominally stabilizable non‐necessarily inversely stable continuous‐time systems with unmodelled dynamics. The control objective is the adaptive stabilization of the closed‐loop system with the achievement of a bounded tracking‐error between the system output and a reference signal given by a stable filter. The adaptive control scheme includes several estimation algorithms and a supervisor which selects the appropriate estimator at every certain time and keeping it operating for at least a minimum period of residence time. This selection is based on a performance criterion related to a measure of the estimation errors obtained with each estimator. In this way, the performance of the output signal is improved with regard to the performance achieved with a unique estimation algorithm. All the estimators are either of the least‐squares type or gradient type. However, any well‐posed estimation algorithm is potentially valid for application. These estimators include relative dead‐zones for robustness purposes and parameter ‘a posteriori’ modifications to ensure the controllability of the estimated models of the plant, which is crucial for proving the stabilizability of the plant via adaptive pole‐placement designs.     

一种参数自适应模糊PID控制器

基于Ｔａｇａｇｉ和Ｓｕｇｅｎｏ的确定性模糊模型，提出了一种参数自适应模糊ＰＩＤ控制器。该控制器的参数调整也采用确定性模糊调整规则，从而使控制器的设计简易、容易，同时与一般的参数自适应相具有很强的适应性和鲁棒性。仿真结果表明，该控制器明显地改善了控制系统的动态性能。     

A DESIGN OF MULTILOOP PID CONTROLLERS WITH A NEURAL‐NET BASED DECOUPLER

In process industries, PID control schemes have been widely used due to their simple structures and easiness of comprehending the physical meanings of control parameters. However, the good control performance cannot be obtained by simply using PID controlschemes, since most processes are considered as nonlinear multivariable systems with mutual interactions. In this paper, a design method of multiloop PID controllers neural‐net based decoupler is proposed for nonlinear multivariable systems with mutual interactions. The proposed method consists of a decoupler given by the sum of a static decoupler and a neural‐net based decoupler, and multi‐loop PID controllers. Finally, the effectiveness of the proposed control scheme is evaluated on the simulation examples.     

A new anti‐windup strategy for PID controllers with derivative filters

This paper presents a new strategy for suppressing the windup effect caused by actuator saturation in proportional–integral–derivative (PID) controlled systems. In the proposed approach, the windup effect is modeled as an external disturbance imported to the PID controller and an observer‐based auxiliary controller is designed to minimize the difference between the controller output signal and the system input signal in accordance with an H‐infinite optimization criterion. It is shown that the proposed anti‐windup (AW) scheme renders the performance of the controlled system more robust toward the effects of windup than conventional PID AW schemes and provides a better noise rejection capability. In addition, the proposed PID AW scheme is system independent and is an explicit function of the parameters of the original PID controller. As a result, the controller is easily implemented using either digital or analog circuits and facilitates a rapid, on‐line tuning of the controller parameters as required in order to prevent the windup effect. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于给定的相角裕度和幅值裕度的PID参数自整定新方法

给出一种新的基于给定相角裕度和幅值裕度的ＰＩＤ参数自整定方法ＳＰＡＭ法．该方法可独立整定ＰＩＤ调节器所有参数．仿真结果表明ＳＰＡＭ法明显优于其它整定方法     

A NEW ALGORITHM FOR DISCRETE‐TIME SLIDING MODE CONTROL USING INFREQUENT OUTPUT OBSERVATIONS

This paper presents a new approach for sliding‐mode control of discrete‐time systems using the reaching law approach together with periodic output feedback technique. This method does not need the system states for feedback as it makes use of only the output samples for designing the controller. Thus, this methodology is more practical and easy to implement. A numerical example is presented to illustrate the design technique.     

NETWORK‐INDUCED DELAY‐DEPENDENT H∞ CONTROLLER DESIGN FOR A CLASS OF NETWORKED CONTROL SYSTEMS

This paper is concerned with the problem of robust H_∞ controller design for a class of uncertain networked control systems (NCSs). The network‐induced delay is of an interval‐like time‐varying type integer, which means that both lower and upper bounds for such a kind of delay are available. The parameter uncertainties are assumed to be normbounded and possibly time‐varying. Based on Lyapunov‐Krasovskii functional approach, a robust H_∞ controller for uncertain NCSs is designed by using a sum inequality which is first introduced and plays an important role in deriving the controller. A delay‐dependent condition for the existence of a state feedback controller, which ensures internal asymptotic stability and a prescribed H_∞ performance level of the closed‐loop system for all admissible uncertainties, is proposed in terms of a nonlinear matrix inequality which can be solved by a linearization algorithm, and no parameters need to be adjusted. A numerical example about a balancing problem of an inverted pendulum on a cart is given to show the effectiveness of the proposed design method.     

OPTIMAL TRACKING CONTROL FOR DISCRETE TIME‐DELAY SYSTEMS WITH PERSISTENT DISTURBANCES

Optimal tracking control (OTC) for discrete time‐delay systems affected by persistent disturbances with quadratic performance indexes is considered. Optimal tracking controller is designed based on a sensitivity approximation approach. By introducing a sensitivity parameter, we transform the original OTC problem into a series of difference equations without time‐advance on time‐delay terms. The obtained OTC law consists of analytic feedback and feedforward terms, and a compensation term, which is the sum of the infinite series of adjoint vectors. The compensation term can be obtained with an iterated formula for the adjoint vectors. A simulation example shows that the approximation approach is effective in tracking the reference input and robust with respect to exogenous persistent disturbances.     

LINEAR OPTIMAL FEEDBACK AND LOAD‐DECOUPLED CONTROL OF A BUCK DC‐DC CONVERTER

This paper describes a new controller design procedure and tuning method for a PWM buck dc‐dc converter. First, linear optimal feedback is designed using the LQR approach. Then the designed control law is implemented using a PID controller incorporated with a load‐decoupled PD compensator. The PID controller is tuned to achieve the optimal design based on the output error voltage directly, instead of using an estimator. When the proposed PD compensator is used, the converter is robust with respect to the input voltage and output current changes and the parameter perturbations. We also provide the conditions for the robust stability assurance of the closed‐loop system.     

大规模系统两层递阶控制的直接分解算法

提出一个新的递阶控制的分解协调方法，它是由最优化问题的直接梯度解及性能函数的一个柔性分解组成。通过性能函数分解的自由度得到所需要的混合结构控制律，其下层控制器是闭环控制部分，上层是保证全局系统最优化的开环控制部分，局部性能函数的柔性选取，使两层优化任务的重新划分既能离线计算，也能在线修正。