Simultaneous closed-loop tuning of cascade controllers based directly on set-point step-response data

This study presents a novel closed-loop tuning method for cascade control systems, in which both primary and secondary controllers are tuned simultaneously by directly using set-point step-response data without resorting to process models. The tuning method can be applied on-line to improve the performance of existing underperforming cascade controllers by retuning controller parameters, using routine operating data. The goal of the proposed design is to obtain the parameters of two proportional-integral-derivative (PID)-type controllers, so that the resulting inner and outer loops behave as similarly as possible to the appropriately specified reference models. The tuning rule and optimization problem related to the proposed design are derived. Based on the rationale behind cascade control, the secondary controller is designed based on disturbance rejection to quickly attenuate disturbances. The primary controller is designed to accurately account for the inner-loop dynamics, without requiring an additional test. In addition, robustness considerations are included in the proposed tuning method, which enable the designer to explicitly address the trade-off between performance and robustness for inner and outer loops independently. Simulation examples show that the proposed method exhibits superior control performance compared with the previous (model-based) tuning methods, confirming the effectiveness of this novel tuning method for cascade control systems.     

交会对接模拟系统姿态位置耦合有限时间控制

针对航天器交会对接模拟系统的姿态同步和位置跟踪控制问题,在存在外界扰动和系统不确定性的情况下,基于改进的快速非奇异终端滑模面和改进的自适应律,采用双闭环控制结构分别设计内环和外环有限时间姿态位置耦合控制器.所提出的自适应律不仅能有效地抑制扰动和不确定性且能保证控制器是连续的.李雅普诺夫理论推导和仿真结果表明,所提出的控制方法能保证系统内环和外环跟踪误差的有限时间稳定性和准确收敛性.     

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.     

Nonlinear cascade control of an electro-hydraulic actuator with large payload variation

Electro-hydraulic actuators have been widely used in industrial production, but the unknown variable payload seriously affects its position control accuracy. Therefore, a radial basis function neural network disturbance observer is designed to estimate the lumped disturbance force through strong online learning ability in the absence of force sensor. Besides, a nonlinear cascade controller with double loop structure is proposed in this paper. A global fast terminal sliding mode control method is firstly applied in the outer loop position system, which can eliminate chattering and improve convergence speed comparing to traditional sliding mode control. The inner loop force system adopts a backstepping control method to calculate the actual input of the whole system. Theoretical analysis indicates that the proposed controller is stable even if existing time-variant disturbance. Moreover, three comparative controllers are designed and tested in both simulations and experiments. Comparative results show that the developed method has absolute average errors of 1.14 and 0.49 mm in different position tracking, which means more satisfactory tracking performance compared to the contrast controllers.     

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.     

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.     

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.     

Cascade direct adaptive fuzzy control design for a nonlinear two-axis inverted-pendulum servomechanism.

This paper presents and analyzes a cascade direct adaptive fuzzy control (DAFC) scheme for a two-axis inverted-pendulum servomechanism. Because the dynamic characteristic of the two-axis inverted-pendulum servomechanism is a nonlinear unstable nonminimum-phase underactuated system, it is difficult to design a suitable control scheme that simultaneously realizes real-time stabilization and accurate tracking control, and it is not easy to directly apply conventional computed torque strategies to this underactuated system. Therefore, the cascade DAFC scheme including inner and outer control loops is investigated for the stabilizing and tracking control of a nonlinear two-axis inverted-pendulum servomechanism. The goal of the inner control loop is to design a DAFC law so that the stick angle vector can fit the stick angle command vector derived from the stick angle reference model. In the outer loop, the reference signal vector is designed via an adaptive path planner so that the cart position vector tracks the cart position command vector. Moreover, all adaptive algorithms in the cascade DAFC system are derived using the Lyapunov stability analysis, so that system stability can be guaranteed in the entire closed-loop system. Relying on this cascade structure, the stick angle and cart position tracking-error vectors will simultaneously converge to zero. Numerical simulations and experimental results are given to verify that the proposed cascade DAFC system can achieve favorable stabilizing and tracking performance and is robust with regard to system uncertainties.     

四旋翼飞行器建模及其运动控制

针对四旋翼飞行器是一个欠驱动、强耦合、非线性系统,提出了运用反步法解决系统非线性问题,达到对飞行器快速、准确、稳定控制目的.研究了以反步法作为非线性设计工具对飞行器控制系统的设计问题,将飞行控制系统分为内外环2个子系统.建立四旋翼飞行器动力学及运动学方程,并对数学模型进行适当简化.利用反步法求解飞行器内环姿态控制律,实现对目标姿态角的稳定控制;利用比例—积分—微分(PID)作为飞行器外环位置控制律,实现对目标位置的稳定控制.搭建飞行器系统模型,进行Matlab/Simulink仿真实验,结果表明:在小角度飞行和悬停状态下,飞行器的位置与姿态精度得到了有效控制,验证了数学模型与控制律设计的准确性.     

基于Hamilton理论的冷带轧机速度张力系统非奇异 快速终端滑模控制

针对交流异步电机驱动的冷带轧机速度张力系统的跟踪控制问题,给出一种基于Hamilton理论的非奇异快速终端滑模控制器设计方法.首先,设计了一种新型扰动观测器对系统中由参数摄动和负载扰动引起的不确定项进行观测;其次,通过预反馈控制建立了冷带轧机系统速度张力磁链外环的耗散Hamilton模型,进而基于互联–阻尼配置及能量整形方法完成耗散Hamilton控制器的设计;再次,基于串级控制思想完成了冷带轧机系统电流内环非奇异快速终端滑模控制器的设计.通过理论分析证明了所提控制方法能够保证闭环系统全局稳定.最后,基于某交流异步电机驱动的冷带轧机系统的现场实际数据进行仿真对比研究,仿真结果验证了本文所提方法的有效性.     

Closed-loop analysis and control of a non-inverting buck–boost converter

In this article, a cascade controller is designed and analysed for a non-inverting buck–boost converter. The fast inner current loop uses sliding mode control. The slow outer voltage loop uses the proportional–integral (PI) control. Stability analysis and selection of PI gains are based on the nonlinear closed-loop error dynamics incorporating both the inner and outer loop controllers. The closed-loop system is proven to have a nonminimum phase structure. The voltage transient due to step changes of input voltage or resistance is predictable. The operating range of the reference voltage is discussed. The controller is validated by a simulation circuit. The simulation results show that the reference output voltage is well-tracked under system uncertainties or disturbances, confirming the validity of the proposed controller.     

基于Hamilton理论的可逆冷带轧机速度张力系统无张力计控制

基于反馈耗散Hamilton理论研究了可逆冷带轧机速度张力系统的无张力计控制问题. 首先,对系统速度张力外环(主轧机速度环和左、右卷取机张力控制环)进行预反馈控制, 并采用反馈耗散Hamilton理论完成了速度张力外环控制器的设计. 其次, 为了实现系统的无张力计控制及对摄动参数的自适应估计, 基于"扩张系统+反馈"方法完成了系统速度张力外环自适应状态观测器的设计. 再次, 为了实现可逆冷带轧机主轧机速度和左、右卷取机张力间的协调控制及对外扰不确定项的干扰抑制, 基于backstepping方法完成了系统电流内环鲁棒控制器的设计. 理论分析表明, 所提出的控制方法能够保证闭环系统的鲁棒稳定性. 最后, 基于某1422mm可逆冷带轧机速度张力系统的实际数据进行仿真, 并同串级PI控制方法相比较, 结果验证了本文所提方法的有效性.     

高阶不确定系统的线性串级自抗扰控制

自抗扰控制是我国著名学者韩京清原创的先进控制技术,本文针对自抗扰控制(ADRC)在高阶系统应用中控制器设计和参数整定问题,提出了串级自抗扰控制(CADRC). CADRC把高阶被控对象分解为含确定性部分和含总扰动的低阶部分的串联组合,采用由内环和外环组成的串级控制系统来完成控制.该CADRC方案的内环采用内模控制,外环采用经典ADRC.外环ADRC的被控对象是一个等效的低阶系统,可以采用带宽法进行整定,而内环的内模控制采用高阶低通滤波器进行回路成形设计和参数整定.仿真研究表明,所提出的方法是有效的,具有良好的工程应用前景.     

基于扩展$L_1$自适应的战斗机大迎角非线性控制

针对常规动态逆控制对系统不确定性较为敏感的缺点,提出一种扩展$L_1$自适应控制方法,用于战斗机大迎角非线性控制.采用时标分离原理将控制系统分为内外两个回路,分别设计动态逆控制器作为基本控制器,用于角速率和角度的跟踪控制.设计$L_1$自适应控制器作为扩展控制器,用于抵消系统中的不确定性.分别在标称和加入参数摄动的情况下进行仿真验证与对比,仿真结果表明所提出的控制方法能够有效抵消系统中的不确定性,提高控制效果.     

Design of Cascade Adaptive Fuzzy Sliding-Mode Control for Nonlinear Two-Axis Inverted-Pendulum Servomechanism

Because the dynamic characteristic of a two-axis inverted-pendulum servomechanism is a nonlinear underactuated system, it is difficult to design a suitable control scheme that realizes real-time stabilization and accurate tracking control simultaneously. In general, the techniques developed for fully actuated systems cannot be used directly in underactuated systems. In this study, a cascade adaptive fuzzy sliding-mode control (AFSMC) scheme including inner and outer control loops is investigated for the stabilizing and tracking control of a nonlinear two-axis inverted-pendulum servomechanism. The aim of the inner control loop is to design an AFSMC law with fuzzy estimators so that the stick-angle vector can fit the stick-angle command vector derived from the stick-angle reference model. In the outer loop, the reference signal vector is designed via a fuzzy path-planning scheme so that the cart position vector tracks the cart-position command vector and the stick-angle tracking-error vector converges to zero simultaneously. All adaptive algorithms in the cascade AFSMC system are derived in the sense of Lyapunov stability analysis, so that system stability can be guaranteed in the entire closed-loop system. The effectiveness of the proposed control strategy is verified by numerical simulations and experimental results, and the superiority of the cascade AFSMC system is indicated in comparison with a cascade sliding-mode control system.      

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.     

Adaptive intelligent cascade control of a ball-riding robot for optimal balancing and station-keeping

This paper presents an adaptive intelligent cascade control strategy to maintain the dynamic stability of a ball-riding robot (BRR). The four-wheeled mechanism beneath the robot body balances it on a spherical wheel. The BRR is modeled as a combination of two decoupled inverted pendulums. Therefore, two independent controllers are used to control its pitch and roll rotations. An incremental proportional–integral–derivative (PID) is implemented in the inner loop of the cascade to maintain the vertical balance. A generic PD controller is used in the outer loop to keep the station by controlling its spatial position. The controller parameters are automatically tuned via a fuzzy adaptation mechanism. The centers of fuzzy output membership functions are dynamically updated via an extended Kalman filter (EKF). The proposed controller quickly responds to changes in system’s state and effectively rejects the exogenous disturbances. The results of real-time experiments are presented to validate the effectiveness of the proposed hybrid controller over the conventional classical controllers.     

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.     

再磨过程的泵池液位和给矿压力双速率区间控制

赤铁矿再磨过程是以矿浆泵频率为输入、以给矿压力为内环输出、以泵池液位为外环输出的强非线性串级工业过程.当赤铁矿粒度分布大范围变化,导致一段磨矿与磁选矿浆流量和再磨排矿流量频繁波动,使泵池液位频繁波动,造成内外环频繁波动.本文将上述动态特性变化用未建模动态来描述,通过设计消除前一时刻未建模动态补偿信号叠加于基于线性模型设计的反馈控制器,采用一步最优前馈控制律和提升技术,提出了泵池液位和给矿压力双速率区间控制算法.给出了所提控制算法的稳定性和收敛性分析,通过半实物仿真实验表明所提出的控制算法可以将处于频繁随机波动的泵池液位和给矿压力变化率控制在目标值范围内.