Simultaneous automatic tuning of cascade control systems from closed-loop step response data

This study presents a novel automatic tuning method for cascade control systems in which both primary and secondary controllers are tuned simultaneously using a single closed-loop step test. The proposed technique identifies the required process information with the help of B-spline series representation for the step responses. The two proportional–integral–derivative (PID) controllers are then tuned using an internal model control (IMC) approach. Considering the rationale of cascade control, the secondary controller is designed for faster disturbance attenuation. Without requiring an additional experiment, the primary controller is designed based on an identified process model that accurately accounts for inner loop dynamics. Finally, this study includes robustness considerations in the controller tuning process, and develops explicit guidelines for the selection of the IMC tuning parameters, completing the automatic tuning procedure for cascade control systems. The proposed method is robust to measurement noise because of the filtering property of the B-splines, and can provide superior control performance for both set-point tracking and disturbance rejection. Simulation examples demonstrate the effectiveness of the proposed automatic tuning method.     

Robust IMC–PID tuning for cascade control systems with gain and phase margin specifications

In this article, an internal model control plus proportional-integral-derivative (IMC–PID) tuning procedure for cascade control systems is proposed based on the gain and phase margin specifications of the inner and outer loop. The internal model control parameters are adjusted according to the desired frequency response of each loop with a minimum interaction between the inner and outer PID controllers, obtaining a fine tuning and the desired gain and phase margins specifications due to an appropriate selection of the PID controller gains and constants. Given the design specifications for the inner and outer loop, this tuning procedure adjusts the IMC parameter of each controller independently, with no interference between the inner and outer loop obtaining a robust method for cascade controllers with better performance than sequential tuning or other frequency domain-based methods. This technique is accurate and simple, providing a convenient technique for the PID tuning of cascade control systems in different applications such as mechanical, electrical or chemical systems. The proposed tuning method explained in this article provides a flexible tuning procedure in comparison with other tuning procedures because each loop is tuned simultaneously without modifying the robustness characteristics of the inner and outer loop. Several experiments are shown to compare and validate the effectiveness of the proposed tuning procedure over other sequential or cascade tuning methods; some experiments under different conditions are done to test the performance of the proposed tuning technique. For these reasons, a robustness analysis based on sensitivity is shown in this article to analyze the disturbance rejection properties and the relations of the IMC parameters.     

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.     

Data-driven dual-rate cascade control and application to pitch angle control of UAV

A data-driven design method for a cascade control system is proposed. The cascade control system consists of inner and outer loops, where the control interval of the outer loop is an integer multiple of the inner loop; hence, the system is a dual-rate system. In the proposed method, controllers in the inner and outer loops are designed based on one-shot data. In such a dual-rate cascade system, since the controllers are designed using different data-rate signals, the lifting technique is applied to align the dual-rate data. To show its effectiveness, the proposed method is compared with a conventional single-rate cascade control method, and numerical simulations and experiments are presented to examine servo and regulation performance.     

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．     

Analytical method of PID controller design for parallel cascade control

An analytical method of PID controller design is proposed for parallel cascade control. Firstly, a general structure for parallel cascade control is proposed that takes both setpoint and load disturbance responses into account. Analytical tuning rules for the PID controllers are then derived for the general process model by employing the IMC design procedure. The proposed method offers a simple and effective way to obtain the PID controller rules for parallel cascade control system which takes into account the interaction between primary and secondary control loops. The simulation results illustrate the application of the proposed method and demonstrate its superiority compared to several alternatives.     

Robust tuning of Two-Degree-of-Freedom (2-DoF) PI/PID based cascade control systems

A design approach for Two-Degree-of-Freedom (2-DoF) PID controllers within a cascade control configuration that guarantees robust and smooth control is presented in this paper. The use of a cascade control configuration comes into place when the use of an additional (intermediate) sensor provides the possibility for a compensation of a load-disturbance before it affects the output variable. The rationale of operation associated to both the inner and outer controllers determines the need of good performance for disturbance attenuation (regulation) as well as set-point following (tracking). Therefore, the use of 2-DoF controllers is introduced. However, the use of 2-DoF controllers, introduces additional parameters that need to be tuned appropriately. Specially for the case of PI/PID controllers there are not known clear auto-tuning guidelines for such situation. The approach undertaken in this paper provides the complete set of tuning parameters for the inner (2-DoF PI) controller and the outer (2-DoF PID) controller. The trade-off among control system performance (measured in terms of closed-loop response speed) and robustness allows to derive a recommendation for the design-parameter lower limit. The design equations are formulated in such a way that a non-oscillatory response is specified for both the inner and outer loop. A side advantage of providing the complete set of parameters is that it avoids the need for the usual identification experiment for the tuning of the outer controller.     

Cascade generalized predictive controller: two in one

The paper presents a cascade generalized predictive controller. The cascade control task is performed by one predictive controller and the cascade feature is incorporated in a special predictor. Simulation results are presented comparing the performances of the proposed control algorithm to traditional cascade loops including two PI or two GPC controllers. The paper investigates the effects of noise filter on the robustness of the control loops in the cascade control structure. It shows, that with the proposed predictor it is possible to adjust independently the robustness of the inner and outer loops, meanwhile in the traditional cascade loop there are cross effects in this sense. Finally a real time application of the proposed algorithm is presented: the cascade GPC was tested in the oxygen control loop of an experimental fluidized bed boiler.     

Cascade active disturbance rejection control of single-rod electrohydrostatic actuator

Electrohydrostatic actuators (EHAs) are used to replace traditional centralized hydraulic systems to reduce weight and improve efficiency and maintainability. This paper proposes a cascade active disturbance rejection control (C-ADRC) method for single-rod EHAs with parametric uncertainties and severe external disturbances. The studied EHA can be transformed into a cascade connection of a first-order pressure system and a second-order position system. Two linear active disturbance rejection controllers are designed for the inner pressure system and the outer position system to estimate and compensate for various uncertainties in the two loops, respectively. The uniqueness of the C-ADRC is that the two linear active disturbance rejection controllers are designed by making full use of the measurable states and known model information of the EHA system. It is theoretically proved that the closed-loop system is semi-globally uniformly ultimately bounded. Moreover, the proposed controller can theoretically ensure position tracking with desired accuracy as the bandwidth of extended state observers (ESOs) becomes sufficiently high. Simulation and experimental results verify the effectiveness of the proposed method.     

Manipulator motion control in operational space using joint velocity inner loops

This paper addresses the operational space motion control—trajectory tracking—of robot manipulators endowed with joint velocity feedback inner loops. A general structure for model-based joint velocity controllers is proposed for the inner loop. The required joint velocity reference is provided by an outer loop inspired from the robot kinematic control approach. It is shown that above two-loops control schemes lead to a nice cascade structure for the corresponding closed-loop systems. A stability result adapted for analysis of this particular kind of systems is developed in the paper; sufficient conditions for global exponential stability of this class of cascade systems are obtained. The effectiveness of the proposed control approach is evaluated on a direct-drive mechanical arm, and compared with a typical control strategy based on inverse kinematics resolution for computation of the desired motion in joint space, and the use of the computed-torque technique. The experimental evidences show better performance of the proposed two-loops controller.     

Tuning algorithms for fractional order internal model controllers for time delay processes

This paper presents two tuning algorithms for fractional-order internal model control (IMC) controllers for time delay processes. The two tuning algorithms are based on two specific closed-loop control configurations: the IMC control structure and the Smith predictor structure. In the latter, the equivalency between IMC and Smith predictor control structures is used to tune a fractional-order IMC controller as the primary controller of the Smith predictor structure. Fractional-order IMC controllers are designed in both cases in order to enhance the closed-loop performance and robustness of classical integer order IMC controllers. The tuning procedures are exemplified for both single-input-single-output as well as multivariable processes, described by first-order and second-order transfer functions with time delays. Different numerical examples are provided, including a general multivariable time delay process. Integer order IMC controllers are designed in each case, as well as fractional-order IMC controllers. The simulation results show that the proposed fractional-order IMC controller ensures an increased robustness to modelling uncertainties. Experimental results are also provided, for the design of a multivariable fractional-order IMC controller in a Smith predictor structure for a quadruple-tank system.     

Frequency analysis and compensation of valve stiction in cascade control loops

Valve stiction is often a common problem in control loops and stiction induced oscillation is the main cause of poor performance in control systems. Cascade control is extensively applied in process industry as an effective strategy to restrain disturbances and compensate process nonlinearities. In recent years many studies have been performed on the detection and quantification of valve stiction in single feedback control loops. However, there is a lack in developing a mechanism which can analyze stiction induced oscillation in cascade control loops. This work focuses on the frequency analysis of stiction induced oscillations in cascade control loops and proposes a mechanism of oscillation compensation through outer and inner controller tuning. The effect of oscillation compensation by changing control strategies is also discussed. The theoretical analysis is evaluated through simulation examples and a pilot-scale flow-level cascade control experiment.     

A simple output-feedback strategy for the control of perfused mammalian cell cultures

This paper presents a framework for the multivariable robust control of perfusion animal cell cultures. It consists of a cascade control structure and an estimation algorithm, which provides the unmeasurable variables needed in the design of the control law, and ensures the regulation of the cell and glucose concentrations at imposed levels by manipulating the bleed and the dilution rates. The cascade control structure uses a feedback linearizing controller in the inner loop and linear (PI) controllers in the outer loops, and requires the measurement of the cell concentration and the glucose concentration in the bioreactor. Two approaches are provided: the first one assumes the availability of an approximate model of the process kinetics and uses an extended Kalman filter (EKF) to estimate the system states; the second approach does not require the prior knowledge of the process kinetics. These are estimated from the available measurements using sliding mode observers (SMO). A receding horizon optimization algorithm is employed to (periodically) tune the gains of the outer loop controllers. The proposed framework is easy to implement and tune, and may be applied to a general class of perfusion cell culture systems. Its effectiveness and robustness are illustrated by means of simulation results.     

多无人直升机的相对动力学建模方法及其编队控制

本文将多无人直升机编队控制分解为若干对具有主从结构的无人直升机相对状态控制问题,并提出利用相对动力学建模方法设计编队控制器.无人直升机相对动力学由6自由度空间刚体相对动力学和单体直升机飞行动力学两部分组成.基于这种相对动力学模型利用反馈线性化和扩展高增益观测方法设计具有内外环阶梯结构的控制器.最后,通过仿真验证了这种方法能够跟踪给定期望值并具有一定扰动抑制能力.     

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.     

A multivariable IMC-PID method for non-square large time delay systems using NPSO algorithm

Multiple time delays and strong interactions among different loops are the main problems in the design of multivariable controller for non-square systems. In this paper, the concept of effective open-loop transfer function (EOTF) is extended to non-square systems. By applying the internal model control (IMC) method, the controllers with equivalent models are designed. For practical applications, the NPSO algorithm is used to obtain the parameters of the incremental PID with first-order lag filter. This new method does not only avoid the complex computation caused by the procedure of decoupling first and then designing controllers but also employs the advantages of IMC-PID's suitable for large time delay systems and strong robustness. Simulation is carried out to demonstrate the effectiveness of the proposed method; also significant performance improvement has been achieved with the proposed method compared with other methods.     

自抗扰实现飞翼布局无人机全包线飞行控制

本文以大展弦比飞翼布局无人机为研究对象,基于线性自抗扰控制(linear active disturbance rejection control,LADRC)理论设计了包含内环姿态控制和外环轨迹控制的全包线飞行控制器.在姿态控制中,提出一种抗时滞LADRC控制方法,可以有效解决控制延迟和执行机构动态特性引起的LADRC响应振荡;在轨迹控制中,考虑飞翼布局无人机的气动特性,分别设计了高度、航向、侧向偏离等常用飞行模态的跟踪控制器.仿真结果表明,在气动参数存在不确定性及强风干扰的全包线环境中连续飞行时,所设计的控制器具有较好的控制性能和较强的鲁棒特性.与常规全包线控制方案相比,本文设计的全包线飞行控制器待整定参数较少,参数整定过程相对简单,为进一步的工程应用提供了参考.     

Application of two‐loop robust control to air‐conditioning systems

This paper presents the design and application of a two‐loop robust controller for temperature control in air‐conditioning systems. A Takagi‐Sugeno fuzzy model with uncertain local models is developed to describe the associated nonlinearities and uncertainties in the operation of the air handling units. Parallel distributed compensation is used to design the global control law. The local control law consists of two loops: an inner‐loop integral controller and an outer‐loop min‐max predictive controller with short prediction horizon. A discounting scheme is developed to weight the contribution of the two loops. Experimental results are presented which show that the proposed strategy can achieve acceptable control performance with a minimum of onsite tuning. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Fractional Order PI‐PD Control of Liquid Level in Coupled Two Tank System and its Experimental Validation

This paper presents a level control problem of a coupled two tank single input single output (SISO) system. A cascade control strategy is adopted having a fractional order proportional integral (FOPI) controller and fractional order proportional derivative (FOPD) controller in the outer and the inner loops, respectively. Cascaded integer order proportional integral (IOPI) and integer order proportional derivative (IOPD) controllers are also designed to compare the performances. A frequency domain approach is followed to design all the controllers. It is mathematically shown that the FOPI and FOPD controllers can achieve less steady state error and consume less energy than that of the IOPI and IOPD controllers while meeting the same phase margin and gain crossover frequency. All propositions are validated on an experimental setup.     

积分加纯滞后系统的双预测PI控制及其应用

Smith预估控制器控制积分加大纯滞后过程时,鲁棒稳定性差,输出存在静态余差,无实际应用价值.提出了一类基于该过程的双预测PI控制器:具有内环和外环两种预测PI控制器.内环将系统稳定,外环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,参数的调节方便、直观.仿真和实际应用表明:在干扰和模型失配的情况下,此类控制器仍然具有良好的控制性能和鲁棒稳定性能,是一种值得在实际工程中推广应用的新型控制器.