Enhanced design of cascade control systems for unstable processes with time delay

In this paper, optimal H₂ internal model controller (IMC) is designed for control of unstable cascade processes with time delays. The proposed control structure consists of two controllers in which inner loop controller (secondary controller) is designed using IMC principles. The primary controller (master controller) is designed as a proportional-integral-derivative (PID) in series with a lead-lag filter based on IMC scheme using optimal H₂ minimisation. Selection of tuning parameter is important in any IMC based design and in the present work, maximum sensitivity is used for systematic selection of the primary loop tuning parameter. Simulation studies have been carried out on various unstable cascade processes. The present method provides significant improvement when compared to the recently reported methods in the literature particularly for disturbance rejection. The present method also provides robust closed loop performances for large uncertainties in the process parameters. Quantitative comparison has been carried out by considering integral of absolute error (IAE) and total variation (TV) as performance indices.     

Improved constrained cascade control for parallel processes

This paper addresses, first, the problem of constraint handling for a system with one input and multiple outputs, where one output must reach a given set point and the other outputs must lie between lower and an upper limits. Three algebraic solutions based on cascade control are outlined. One method employs the traditional cascade controllers, applied to serial transfer functions. The second uses cascade controllers applied to parallel transfer function processes. The latter method shows sensitivity to disturbance and tuning of inner loops. A third innovative method, called a pseudo-cascade controller, is introduced for parallel transfer functions. The new method allows independent tuning of the controllers, and requires no special anti-reset windup feature. An extension is also given for decoupled two-input processes. A simulated example and a distributed control design for an industrial application are given to illustrate the proposed methods.     

积分时滞过程的数字P I D 控制

对积分时滞过程提出一种数字PID控制结构，通过一个内部反馈回路对积分时滞过程进行预稳定控制，并给出数字PI控制器的设计算法，仿真结果显示该控制结构具有良好的设定值跟踪特性，并且对时滞偏差具有很强的鲁棒性能，最后简要讨论了抗负载干扰的控制结构。     

IMC-based iterative learning control for batch processes with uncertain time delay

Based on the internal model control (IMC) structure, an iterative learning control (ILC) scheme is proposed for batch processes with model uncertainties including time delay mismatch. An important merit is that the IMC design for the initial run of the proposed control scheme is independent of the subsequent ILC for realization of perfect tracking. Sufficient conditions to guarantee the convergence of ILC are derived. To facilitate the controller design, a unified controller form is proposed for implementation of both IMC and ILC in the proposed control scheme. Robust tuning constraints of the unified controller are derived in terms of the process uncertainties described in a multiplicative form. To deal with process uncertainties, the unified controller can be monotonically tuned to meet the compromise between tracking performance and control system robust stability. Illustrative examples from the recent literature are performed to demonstrate the effectiveness and merits of the proposed control scheme.     

Iterative learning control with Smith time delay compensator for batch processes

How to improve the control of batch processes is not an easy task because of modeling errors and time delays. In this work, novel iterative learning control (ILC) strategies, which can fully use previous batch control information and are attached to the existing control systems to improve tracking performance through repetition, are proposed for SISO processes which have uncertainties in modeling and time delays. The dynamics of the process are represented by transfer function plus pure time delay. The stability properties of the proposed strategies for batch processes in the presence of uncertainties in modeling and/or time delays are analyzed in the frequency domain. Sufficient conditions guaranteeing convergence of tracking error are stated and proven. Simulation and experimental examples demonstrating these methods are presented.     

A double two-degree-of-freedom control scheme for improved control of unstable delay processes

A double two-degree-of-freedom control scheme is proposed for enhanced control of unstable delay processes. The scheme is motivated by the modified Smith predictor control in [IEE Proc. Control Theory Appl. 16(5) (1999) 359] and devised to improve in the following ways: (i) one more freedom of control is introduced in our scheme to enable manipulation of disturbance transient response, and is tuned based on minimization of the integral squared error criterion; (ii) four controllers in the scheme are well placed to separately tune the denominators and numerators of closed-loop transfer functions from the set-point and disturbance. This allows easy design of each controller and good control performance for both set-point and disturbance responses. Especially, improvement of disturbance response is extremely great, compared with [IEE Proc. Control Theory Appl. 16(5) (1999) 359; Automatica 36 (2000) 1651]. Internal stability of the proposed structure is analyzed, which has not been reported in the literature on modified Smith predictor control before. Examples are provided for illustration.     

An optimal control method for linear systems with time delay

An optimal control method for linear systems with time delay is developed in this paper. In the proposed control method, the differential equation with time delay of the system dynamics is first rewritten into a form without any time delay through a particular transformation. Then, the optimal controller is designed by using the classical optimal control theory. A numerical algorithm for control implementation is presented, since the obtained expression of the optimal controller contains an integral term that is not convenient for online calculation. The time delay is considered at the very beginning of the control design, and no approximation and estimation are made in the control system. Thus the system performance and stability are prone to be guaranteed. Instability in responses might occur only if a system with time delay is controlled by the optimal controller that was designed with no consideration of time delay. The effectiveness of the proposed optimal controller is demonstrated by simulation studies.     

一类非自衡加纯滞后系统的双预测P I 控制

提出了一类基于非自衡加大纯滞后过程的双预测PI控制器的结构形式，这种控制器结构筒单，可调参数少，参数的调节方便、直观，仿真结果表明：在干扰和模型失配的情况下，此类控制器仍具有良好的控制性能和鲁棒稳定性，是一种值得在实际工程中推广应用的新型控制器。     

Analytical design of two-degree-of-freedom control scheme for open-loop unstable processes with time delay

This paper proposes an analytical two-degree-of-freedom control scheme for open-loop unstable processes with time delay, which leads to the remarkable improvement of regulatory capacity for both of reference input tracking and load disturbance rejection. Firstly a conventional proportional or plus derivative controller is deliberately employed for stabilizing the setpoint response. Then the setpoint tracking controller is analytically derived in terms of the integral-squared-error (ISE) performance specification. By proposing the desired closed-loop complementary sensitivity function for rejecting load disturbances, the corresponding controller, i.e. disturbance estimator, is inversely figured out. Hence the nominal setpoint response is decoupled from the load disturbance response by virtue of the open-loop control manner for the setpoint tracking. In consequence, both of them can be optimized simultaneously and separately. At the same time, robust stability analysis for the proposed control structure is provided in the presence of the process multiplicative uncertainty. Accordingly the on-line tuning rule for the single adjustable parameter of each controller is suggested to cope with the process unmodeled dynamics in practice. Finally, several illustrative examples are included to demonstrate the superiority of the proposed method.     

Robust model predictive control of integrating time delay processes

This work focuses on the solution to the problem of model predictive control of time delay processes with both integrating and stable modes and model uncertainty. The controller is developed for the practical case of zone control and input target tracking. The method is based on a state-space model that is equivalent to the analytical form of the step response model corresponding to the system transfer function. Here, this model is extended to the time delay system. The proposed controller is evaluated through simulation of the of two control reactor systems and the results confirms the robustness of the proposed approach.     

化工不稳定时滞过程鲁棒控制的解析设计

针对化工不稳定时滞过程,提出一种两自由度控制结构.首先基于鲁棒H2最优性能指标,设计给定值跟踪控制器;然后根据系统稳态运行时的抗负载干扰要求,在过程输入与输出端之间设计控制闭环,利用其反馈通道上的扰动观测器抑制负载干扰,通过提出期望的闭环余灵敏度函数的方法,反向确定扰动观测器,同时给出了该控制闭环保证鲁棒稳定性的充要条件.仿真实例验证了该控制结构的优越性.     

具有时变通信延迟的多智能体系统改进蜂拥控制

针对不确定非线性二阶多智能体系统中存在的时变通信时延和未知干扰问题,提出了一种鲁棒自适应蜂拥控制规律。为了使二阶多智能体系统能够具有更好的抗干扰能力,设计了基于智能体位置状态信息和速度状态信息的鲁棒自适应算子,实现了系统在时变通信时延扰动下的分布控制。通过使用Lyapunov-Krasovskii方法构造能量函数,证明了多智能体系统的网络连通性,智能体的速度收敛于虚拟领导者的速度,并给出了具有时变通信时延的多智能体系统收敛条件。仿真实验结果表明,在不同干扰强度和不同通信时延下系统均能实现快速收敛,形成稳定的拓扑结构,证明所提方法正确有效。     

Generalized multi-scale control scheme for cascade processes with time-delays

The cascade control is a well-known technique in process industry to improve regulatory control performance. The use of the conventional PI/PID controllers has often been found to be ineffective for cascade processes with long time-delays. Recent literature report has shown that the multi-scale control (MSC) scheme is capable of providing improved performance over the conventional PID controllers for processes characterized by long time-delays as well as slow RHP zeros. This paper presents an extension of this basic MSC scheme to cascade processes with long time-delays. This new cascade MSC scheme is applicable to self-regulating, integrating and unstable processes. Extensive numerical studies demonstrate the effectiveness of the cascade MSC scheme compared with some well-established cascade control strategies.     

几种不稳定滞后对象的预测PID 控制

针对几种不稳定滞后过程，给出一种预测PID控制器的结构形式．该控制器具有内环和外环两种控制器：内环控制器主要用于稳定系统；外环控制器具有预测PID控制的结构形式，主要用于消除输入干扰的影响和改善控制系统的动态性能．这种控制器结构简单，可调参数少，且参数的调节方便、直观．仿真结果表明，在干扰和模型失配的情况下，此类预测PID控制器仍具有良好的控制性能和鲁棒稳定性能．     

Adaptive generic model control for a class of nonlinear time-varying processes with input time delay

In this article, an adaptive control approach––Adaptive Generic Model Control (AGMC) for a class of nonlinear time-varying processes with input time delay is proposed. First, a nonlinear state predictor (NSP) is introduced, which extends the conventional generic model control (GMC) to a class of nonlinear processes with input time delay. Then a class of nonlinear time-varying processes with input time delay is further considered. A modified strong tracking filter (MSTF) is adopted to estimate the time-varying parameters of the nonlinear processes, and the state estimates are then utilized to update the plant models used in the NSP and MSTF, this results in an adaptive generic model control scheme for a class of nonlinear time-varying processes with input time delay. A modified mathematical model of a three-tank-system is used for computer simulations, the results show that the proposed AGMC algorithm is satisfactory, and it has definite robustness against model/plant mismatch in the measurement noise.     

Optimal control of non-minimum phase integrating processes with time delay using disturbance observer-based control scheme

A systematical design method of optimal control for non-minimum phase integrating processes with time delay using disturbance observer-based (DOB) control scheme is presented. All stabilising controllers and the filter of DOBs for integrating plants are developed. Then the optimal set-point tracking controller and the optimal filter of DOB are systematically derived by minimising the H₂ norm performance specifications. The proposed design method has three main advantages. First, the design procedure is systematical and simple. Specified weight functions are chosen for step inputs and inputs similar to steps. The designed set-point tracking controller and the filter of DOB are given in analytical forms. Second, the designed set-point tracking controller and the filter of the DOB are optimal. They are derived from minimising the performance indexes of set-point tracking and input load disturbance rejection (ILDR). Finally, the set-point tracking performance specification and ILDR specification can be quantitatively achieved by conveniently tuning the adjustable parameters. Numerical simulations are given to illustrate the effectiveness of the proposed method.     

Proportional-derivative controllers for stabilisation of first-order processes with time delay

This paper considers the problems of determining the complete stabilising set of proportional-derivative controllers for a first-order process with time delay. First, by employing a version of the Hermite–Biehler theorem applicable to quasi-polynomials, a complete set of all stabilising proportional-derivative parameters for first-order processes with constant time delay are obtained. Next, we provide an approach to design a robust PD controller to stabilise a first-order process with uncertain time delay, which lies inside a known interval.     

Energy-shaping for Hamiltonian control systems with time delay

This paper investigates the asymptotical stabilization of Hamiltonian control systems with time delay. First, Hamiltonian control systems with time delay are proposed. Second, a two-to-one (TTO) principle is introduced that two different Hamiltonian functions are simultaneously energy-shaping by one desired energy function. Third, a novel matching equation is built via the TTO principle for the Hamiltonian control systems with time delay, which generates an effective control law for the Hamiltonian control systems with time delay. Finally, a numerical example shows the effectiveness of proposed method.     

Synthesis of PID controllers for integral processes with time delay

This article deals with the problem of determination of the stabilizing parameter sets of Proportional‐Integral‐Derivative (PID) controllers for first‐order and second‐order integral processes with time‐delay. First, the admissible stabilizing range of proportional‐gain is determined analytically in terms of a version of the Hermite–Biehler Theorem applicable to quasi‐polynomials. Then, based on a graphical stability condition developed in parameter space, the complete stabilizing regions in an integral‐derivative plane are drawn and identified graphically, not calculated mathematically, by sweeping over the admissible range of proportional‐gain. An actual algorithm for finding the stabilizing parameter sets of PID controllers is also proposed. Simulations show that the stabilizing regions in integral‐derivative space are either triangles or quadrilaterals. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society