Optimal dead-time compensator design for stable and integrating processes with time delay

Recently, a modified Smith predictor with a prefilter has been proposed for first-order stable and integrating processes with time delay. The paper is a further investigation on the empirical method. In this paper, an optimal design procedure is developed for the scheme. With respect to the proposed controller and corresponding processes with time delay, the closed-loop time domain responses are estimated quantitatively. The robustness of the closed-loop system is analyzed. Finally, a simple tuning rule is proposed, which allows to tune the controller for desired time domain properties such as overshoot and rise time, or frequency domain criteria such as stability margin and bandwidth.     

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.     

Integral criteria for optimal tuning of PI/PID controllers for integrating processes

Tuning formulas for PI/PID controllers for integrating processes are presented in this paper. The controller parameters are obtained by minimizing various integral performance index. Bacterial Foraging strategy, a new entrant to the family of evolutionary algorithms is used for minimization to avoid the local minima in the optimization procedure. A setpoint filter is used to reduce the large overshoot, and a significant improvement in control performance is obtained when compared to recently reported methods. Simulation results for an assumed perturbation in the plant delay are also given to illustrate the robustness of the proposed controller design method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

非自衡时滞对象的改进内模控制

针对化工生产中常见的具有积分和时滞特性的过程对象，采用一种改进的两自由度内模控制方案．其中一个新增的控制器用于设定值跟踪响应的期望极点配置，利用直接合成法设计设定值跟踪控制器；另一个新增的控制器用于稳定对象和抑制扰动，并采用期望闭环余灵敏度法确定控制器．设定值跟踪控制器和扰动抑制控制器可通过性能参数独立调节，并保证系统具有较好的鲁棒稳定性．最后，通过仿真实例验证了控制方案的有效性．     

时滞过程改进型Smith预估器的整定

证明Majhi和Atherton(1999)文所提出的改进型Smith预估器等价于一改进的内模控制结构 (IMC), 并对该结构提出一种三阶段设计方法. 为获得扰动抑制和稳定鲁棒性的均衡, 采用了鲁棒控制方法来整定反馈环控制器. 针对某些典型的积分和不稳定时滞过程的设计表明所提方法能获得较好的扰动抑制和稳定鲁棒性的均衡.     

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.     

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.     

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 sliding mode control scheme for non-minimum phase non-linear uncertain input-delay chemical processes

This paper considers the robust control of non-linear uncertain chemical processes in the presence of input-delay and inverse response. A novel and systematic sliding mode control (SMC) scheme, which integrates a time-advanced non-linear predictor and a statically equivalent output map (SEOM), is proposed to compensate for the process’s input-delay and to circumvent the negative effect of inverse response. A Lyapunov-based approach is utilized to ensure the robust control performance of the proposed SMC system. To demonstrate the effectiveness and applicability of the SMC control strategy, we applied it to the regulation control of a Van de Vusse reactor in the presence of input-delay, non-minimum phase behavior, and diversified uncertainties such as unmodeled side reaction, measuring error, parameter uncertainties, and/or extra unmeasured disturbances. The potential use of a sliding observer along with the proposed scheme is also investigated in this work. Extensive simulation results reveal that the proposed SMC design methodology is applicable and promising for the robust control of non-linear, uncertain, non-minimum phase, time-delay chemical processes.     

A generalized relay identification method for time delay and non-minimum phase processes

A generalized relay identification method is proposed in this paper for time delay and non-minimum phase processes. A distinct merit of the proposed method is that the process gain can be uniformly derived from a single run of the relay test, independent of the relay type being unbiased or biased. An analytical relay response expression is derived for assessing the process response under an unbiased or biased relay test. A frequency response algorithm is also derived for estimating the multiple frequency response points of the process. By categorizing cases of the model parameters to be identified, the corresponding identification algorithms are developed using fitting conditions established for the process response at the oscillation frequency. Based on the improved estimation of multiple frequency response points, a recursive least-squares identification algorithm is then proposed for obtaining further enhanced fitting accuracy over a user specified frequency range, e.g., the low frequency range often concerned in practical controller tuning. Illustrative examples from the recent literature are given to demonstrate the effectiveness and merits of the proposed algorithms.     

Optimal disturbance rejection controller design for integrating processes with dead time based on algebraic theory

In this paper, an H₂ optimal input-load disturbance rejection (ILDR) controller for integrating processes with dead time is proposed based on the internal model control principle. The main contribution of this work is that the optimal solution under ILDR criterion for integrating processes with dead time and input constant disturbances has been derived based on algebraic theory. To further improve the performance for both set-point tracking and input disturbance rejection, a two-degree-of-freedom (TDOF) control design method has also been developed. Compared with previous advanced control methods, the proposed design method has three main advantages. First, the optimal ILDR controller is derived systematically on the basis of algebraic theory. The designed controller is given in an analytical form. Second, a simple tune principle is developed. The set-point tracking performance specification and robustness stability specification can be quantitatively achieved by monotonously tuning the performance degree in the designed controller. Finally, both optimal set-point tracking performance and input disturbance rejection can be achieved by the proposed TDOF control structure. Numerical simulations are given to illustrate the effectiveness of the proposed method.     

Optimal tracking control of a flexible hub–beam system with time delay

In this paper, a new technique of time-delay compensation is proposed for active control of a flexible hub–beam system. The first-order approximation coupling (FOAC) model proposed recently for dynamics of hub–beam systems is used to verify the applicability of this technique. The FOAC model is first linearized to obtain a linearized equation. The linearized equation with time delay is then transformed into a standard form with no time delay by a particular integral transformation. The time-delay controller is designed based on this standard equation using the classical optimal tracking control theory. Since the controller is a function of modal coordinates, a modal filter is presented to estimate the modal coordinates from physical sensor measurements. The effectiveness of the proposed technique for time delay is demonstrated by numerical simulations. Simulation results indicate that a very small time delay may result in instability of the control system if it is not compensated in control design. The proposed time-delay controller is effective in controlling the system even when the maximum time delay for stability without time-delay compensation is greatly exceeded. Moreover, for the system without time delay, the proposed time-delay controller may possibly obtain much better control effectiveness than the controller without time delay.     

具有时滞的积分和不稳定对象的鲁棒控制

针对含时滞的积分和不稳定对象提出了一种新颖的两自由度控制结构,首先用一个比例控制器镇定给定值响应,然后基于鲁棒H₂最优性能指标设计给定值跟踪控制器.根据实际运行抗干扰要求,在对象输入和输出端之间设计负载扰动抑制闭环,利用扰动观测器抑制负载干扰信号,通过提出期望的闭环余灵敏度函数来确定扰动观测器,同时给出了扰动抑制闭环保证鲁棒稳定性的充要条件.最后通过仿真实例验证了该方法相对于近期其它方法的优越性.     

A new dead-time compensator to control stable and integrating processes with long dead-time

This paper presents a new dead-time compensator for stable and integrating processes when a reduced model of the process is considered. The output is estimated from a discrete time representation of the continuous time model and the tuning of the controllers can be made by any classical control design approach for systems without delay. The internal stability and the robust stability of the proposed scheme is proved and a deep analysis of the disturbance rejection performance is included. As a result, a tuning procedure is derived. An illustrative example shows that the robustness and performance of the proposed scheme are similar or better to those of the more recently proposed dead-time compensators for stable and integrating processes, its capability to reject ramp disturbances being also addressed. The proposed scheme has been tested in a real-time application to control the roll angle in a laboratory prototype of a quad-rotor helicopter.     

Fractional order internal model control of non-minimum phase and time-delayed plants

Several applications on fractional order (FO) control have gained considerable significance in the recent years, which led to the evolution of novel tuning strategies of the generalized order FO controllers. Some of the methods in available literatures are based on constrained minimization optimization techniques or analytical method defined only for specific plants. They are valid only for some special model cases. On the contrary, in this technical note, a generalized non-integer order internal model control (IMC) framework is realized for any order non-minimum phase (NMP) plants with right half plane (RHP) zero as well as time delayed plants having any finite relative order. Its parameters are graphically interpreted satisfying the frequency domain design stipulations for single input and single output (SISO) higher order linear time invariant (LTI) plants. The performance of the same on a bioreactor fermentation process for its temperature control is found to have outperformed in contrast to its integer order (IO)-IMC. It is therefore inferred here that this new approach pledges to impart unique solution of the controller parameters, formulating a highly efficient tool outperforming the existing paradigms. Simulation and real time experimentation are presented to validate the method put forward providing satisfactory performance in reference tracking, disturbance rejection, and robustness to various plant parameter perturbations.     

A nonregressor nonlinear disturbance observer-based adaptive control scheme for an underwater manipulator

A new nonlinear disturbance observer-based tracking control scheme for an underwater manipulator is presented in this paper. This observer overcomes the disadvantages of existing disturbance observers, which are designed or analyzed by the linear system techniques. It can be applied in underwater manipulator systems for various purposes such as payload compensation, interaction effects compensation, underwater current or external disturbance compensation, and independent system control. The performance of the proposed tracking control scheme is demonstrated numerically by the payload compensation and interaction effects compensation for a two degrees of freedom vertical underwater manipulator.     

Impulse control of piecewise-deterministic processes

In a recent paper we presented a numerical technique for solving the optimal stopping problem for a piecewise-deterministic process (P.D.P.) by discretization of the state space. In this paper we apply these results to the impulse control problem. In the first part of the paper we study the impulse control of P.D.P.s. under general conditions. We show that iteration of the single-jump-or-intervention operator generates a sequence of functions converging to the value function of the problem. In the second part of the paper we present a numerical technique for computing optimal impulse controls for P.D.P.s. This technique reduces the problem to a sequence of one-dimensional minimizations. We conclude by presenting some numerical examples.     

Robust fault-tolerant control of a class of non-minimum phase nonlinear processes

This article concerns with the regulation and fault-tolerant control of non-minimum phase nonlinear processes with mismatched uncertainties. A variable structure controller, switching between a first-order sliding mode control and a second-order sliding mode control, is proposed to regulate the output and to stabilize the unstable zero dynamics with mismatched uncertainties. Once detected, the fault is estimated on-line by an approximator of radial basis function network; the control law is reconfigured to compensate the fault with closed-loop system asymptotically stable. The application of the proposed algorithm to a non-minimum phase continuously stirred tank reactor (CSTR) is illustrated in the presence of matched and mismatched uncertainties and component fault.     

Multivariable disturbance observer-based H2 analytical decoupling control design for multivariable systems

In this paper, an H₂ analytical decoupling control scheme with multivariable disturbance observer for both stable and unstable multi-input/multi-output (MIMO) systems with multiple time delays is proposed. Compared with conventional control strategies, the main merit is that the proposed control scheme can improve the system performances effectively when the MIMO processes with severe model mismatches and strong external disturbances. Besides, the design method has three additional advantages. First, the derived controller and observer are given in analytical forms, the design procedure is simple. Second, the orders of the designed controller and observer are low, they can be implemented easily in practice. Finally, the performance and robustness can be adjusted easily by tuning the parameters in the designed controller and observer. It is useful for practical application. Simulations are provided to illustrate the effectiveness of the proposed control scheme.     

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．