Nonlinear model-based control algorithm for a distillation column using software sensor

This paper presents the design of model-based globally linearizing control (GLC) structure for a distillation process within the differential geometric framework. The model of a nonideal binary distillation column, whose characteristics were highly nonlinear and strongly interactive, is used as a real process. The classical GLC law is comprised of a transformer (input-output linearizing state feedback), a nonlinear state observer, and an external PI controller. The tray temperature based short-cut observer (TTBSCO) has been used as a state estimator within the control structure, in which all tray temperatures were considered to be measured. Accordingly, the liquid phase composition of each tray was calculated online using the derived temperature-composition correlation. In the simulation experiment, the proposed GLC coupled with TTBSCO (GLC-TTBSCO) outperformed a conventional PI controller based on servo performances with and without measurement noise as well as on regulatory behaviors. In the subsequent part, the GLC law has been synthesized in conjunction with tray temperature based reduced-order observer (GLC-TTBROO) where the distillate and bottom compositions of the distillation process have been inferred from top and bottom product temperatures respectively, which were measured online. Finally, the comparative performance of the GLC-TTBSCO and the GLC-TTBROO has been addressed under parametric uncertainty and the GLC-TTBSCO algorithm provided slightly better performance than the GLC-TTBROO. The resulting control laws are rather general and can be easily adopted for other binary distillation columns.     

Nonlinear control of a multicomponent distillation process coupled with a binary distillation model as an EKF predictor

The work is devoted to design the globally linearizing control (GLC) strategy for a multicomponent distillation process. The control system is comprised with a nonlinear transformer, a nonlinear closed-loop state estimator [extended Kalman filter (EKF)], and a linear external controller [conventional proportional integral (PI) controller]. The model of a binary distillation column has been used as a state predictor to avoid huge design complexity of the EKF estimator. The binary components are the light key and the heavy key of the multicomponent system. The proposed GLC-EKF (GLC in conjunction with EKF) control algorithm has been compared with the GLC-ROOLE [GLC coupled with reduced-order open-loop estimator (ROOLE)] and the dual-loop PI controller based on set point tracking and disturbance rejection performance. Despite huge process/predictor mismatch, the superiority of the GLC-EKF has been inspected over the GLC-ROOLE control structure.     

Sliding mode controller with sliding perturbation observer based on gain optimization using genetic algorithm

The Stewart platform manipulator is a closed-kinematics chain robot manipulator that is capable of providing high structural rigidity and positional accuracy. However, this is a complex and nonlinear system, so the control performance of the system is not so good. In this paper, a new robust motion control algorithm is proposed. The algorithm uses partial state feedback for a class of nonlinear systems with modeling uncertainties and external disturbances. The major contribution is the design of a robust observer for the state and the perturbation of the Stewart platform, which is combined with a variable structure controller (VSC). The combination of controller and observer provides the robust routine called sliding mode control with sliding perturbation observer (SMCSPO). The optimal gains of SMCSPO, which is determined by nominal eigenvalues, are easily obtained by genetic algorithm. The proposed fitness function that evaluates the gain optimization is to put sliding function. The control performance of the proposed algorithm is evaluated by the simulation and experiment to apply to the Stewart platform. The results showed high accuracy and good performance.     

A hybrid feedback linearizing-Kalman filtering control algorithm for a distillation column

This paper studies the design of a discrete-time multivariable feedback linearizing control (FLC) structure. The control scheme included (i) a transformer [also called the input/output (I/O) linearizing state feedback law] that transformed the nonlinear u-y to a linearized v-y system, (ii) a closed-loop observer [extended Kalman filter (EKF)], which estimated the unmeasured states, and (iii) a conventional proportional integral (PI) controller that was employed around the v-y system as an external controller. To avoid the estimator design complexity, the design of EKF for a binary distillation column has been performed based on a reduced-order compartmental distillation model. Consequently, there is a significant process/predictor mismatch, and despite this discrepancy, the EKF estimated the required states of the simulated distillation column precisely. The FLC in conjunction with EKF (FLC-EKF) and that coupled with a measured composition-based reduced-order open-loop observer (FLC-MCROOLO) have been synthesized. The FLC structures showed better performance than the traditional proportional integral derivative controller. In practice, the presence of uncertainties and unknown disturbances are common, and in such situations, the proposed FLC-EKF control scheme ensured the superiority over the FLC-MCROOLO law.     

Tracking control of robot manipulators via output feedback linearization

This paper presents a robot manipulator tracking controller based on output feedback linearization. A sliding mode perturbation observer (SPO) is designed to estimate unmeasurable states and system perturbations that involve system nonlinearities, disturbances and unmodelled dynamics. The use of SPO allows to input/output linearize and decouple the strongly coupled nonlinear robot manipulator system merely by the feedback of joint angles. The controller design does not need an accurate model of the robot manipulator. Simulation studies are undertaken based on a two-link robot manipulator to evaluate the proposed approach. The simulation results show that the proposed controller has more superior tracking control performance, with payload changing in a wide range, in comparison with a sliding mode controller (SMC) designed based on state feedback linearization with full states available. Selected from Journal of Shenzhen University (Science & Engineering), 2005, 22(3)     

Quasi-minimal active disturbance rejection control of MIMO perturbed linear systems based on differential neural networks and the attractive ellipsoid method

This study addresses the problem of designing an output-based controller to stabilize multi-input multi-output (MIMO) systems in the presence of parametric disturbances as well as uncertainties in the state model and output noise measurements. The controller design includes a linear state transformation which separates uncertainties matched to the control input and the unmatched ones. A differential neural network (DNN) observer produces a nonlinear approximation of the matched perturbation and the unknown states simultaneously in the transformed coordinates. This study proposes the use of the Attractive Ellipsoid Method (AEM) to optimize the gains of the controller and the gain observer in the DNN structure. As a consequence, the obtained control input minimizes the convergence zone for the estimation error. Moreover, the control design uses the estimated disturbance provided by the DNN to obtain a better performance in the stabilization task in comparison with a quasi-minimal output feedback controller based on a Luenberger observer and a sliding mode controller. Numerical results pointed out the advantages obtained by the nonlinear control based on the DNN observer. The first example deals with the stabilization of an academic linear MIMO perturbed system and the second example stabilizes the trajectories of a DC-motor into a predefined operation point.     

Fractional active disturbance rejection control

A fractional active disturbance rejection control (FADRC) scheme is proposed to improve the performance of commensurate linear fractional order systems (FOS) and the robust analysis shows that the controller is also applicable to incommensurate linear FOS control. In FADRC, the traditional extended states observer (ESO) is generalized to a fractional order extended states observer (FESO) by using the fractional calculus, and the tracking differentiator plus nonlinear state error feedback are replaced by a fractional proportional-derivative controller. To simplify controller tuning, the linear bandwidth-parameterization method has been adopted. The impacts of the observer bandwidth ω_o and controller bandwidth ω_c on system performance are then analyzed. Finally, the FADRC stability and frequency-domain characteristics for linear single-input single-output FOS are analyzed. Simulation results by FADRC and ADRC on typical FOS are compared to demonstrate the superiority and effectiveness of the proposed scheme.     

A nonlinear updated gain observer for MIMO systems: Design,analysis and application to marine surface vessels

In this paper, the state estimation problem of a class of multi-input-multi-output nonlinear systems with measurement noise is studied. We develop an extended updated-gain high gain observer to make a tradeoff between reconstruction speed and measurement noise attenuation. The designed observer, whose gains are driven by nonlinear functions of the available output estimation errors, has the ability to reconstruct system states quickly and reduce the effect of measurement noise. We establish that, if there exists a state feedback law exponentially stabilizing the system with respect to an invariant set, the estimations and estimation errors are bounded. Besides, the trajectories of state- and output-feedback (based on the proposed observer) are sufficiently close, namely performance recovery. The observer performance is illustrated by various examples in marine control, including a case of transformation into the predefined structure.     

汽车主动悬架非线性振动的VOFB控制

提出了一种应用于汽车主动悬架非线性振动主动控制的新型鲁棒自适应控制算法——VOFB算法(Variable-structure-control output feedback backstepping),并证明了稳定性, 还进行了仿真验证。引入了一个非线性滤波器,简化了设计,设计了一输出反馈观测器,最后将变结构控制的设计方法引入Backstepping控制器设计,得到了对系统扰动的鲁棒性。     

基于自抗扰控制的转台伺服系统摩擦非线性补偿仿真研究

为克服非线性摩擦在转台伺服系统低速运行时对控制性能的影响,设计一种线性自抗扰控制器.该控制器采用线性扩张状态观测器及线性反馈,将摩擦作为系统总扰动进行实时估计,并加以补偿.基于Lugre摩擦模型建立转台伺服系统的数学模型,对这种线性自抗扰控制器进行仿真实验.结果表明,和传统PID控制器相比,所设计的控制器对非线性摩擦有良好的抑制作用,同时具有响应速度快、稳态误差小,抗扰能力强的特点.     

基于遗传算法的可控励磁直线磁悬浮同步电动机自抗扰控制

对可控励磁直线磁悬浮电动机控制系统提出基于遗传算法的自抗扰控制策略。根据可控励磁直线磁悬浮电动机的运行机理,建立其数学模型。设计反馈跟踪微分器、扩张状态观测器、非线性反馈控制律,对传统函数fal进行改进,应用到控制器中。实现对给定信号的跟踪,并将系统耦合量和外界扰动作为系统的“总扰动”,并对总扰动进行观测与补偿。针对控制器中存在多个参数难以整定的问题,采用遗传算法对控制器参数进行寻优。对控制系统进行仿真研究,结果表明,基于遗传算法的自抗扰控制系统具有对参考信号良好的跟踪性能,以及对干扰信号的抑制能力。     

双框架控制力矩陀螺框架系统的扰动观测及抑制

内外框架间的耦合力矩、非线性摩擦和未建模动态是影响双框架控制力矩陀螺框架系统高精度角速率伺服控制的主要因素。为提高框架系统的干扰抑制能力,保证框架系统输出角速率精度,本文提出了一种基于非线性级联扩张状态观测器和滑模控制的复合扰动抑制方法。框架系统中的所有干扰都被认为是集总干扰并由设计的NCESO估计,通过滑模控制可从系统输出通道中消除集总干扰的影响。最后,将本文提出的控制方法与线性级联扩张状态观测器和状态反馈结合的复合控制方法进行了对比仿真实验。仿真和实验结果表明,本文提出的方法具有更好的干扰抑制和动态响应性能,内框架角速度波动从0.5(°)/s减小到0.2(°)/s,外框架角速度波动从0.45(°)/s减小到0.15(°)/s;跟踪正弦参考信号时,速度跟踪误差从1.8(°)/s减小到1.2(°)/s,相位滞后从8°减小到1.3°。     

Semiactive nonlinear control of a building with a magnetorheological damper system

This paper proposes a linear matrix inequality (LMI)-based systematic design methodology for nonlinear control of building structures equipped with a magnetorheological (MR) damper. This approach considers stability performance as well as transient characteristics in a unified framework. First, multiple Lyapunov-based controllers are designed via LMIs such that global asymptotical stability of the building structure is guaranteed and the performance on transient responses is also satisfied. Such Lyapunov-based state feedback controllers are converted into output feedback regulators using a set of Kalman estimators. Then, these Lyapunov-based controllers and Kalman observers are integrated into a global nonlinear control system via fuzzy logic. To demonstrate the effectiveness of the proposed approach, a three-story building structure employing an MR damper is studied. The performance of the nonlinear control system is compared with that of a traditional linear optimal controller, i.e., H₂/linear quadratic Gaussian (LQG), while the uncontrolled system response is used as the baseline. It is demonstrated from comparison of the uncontrolled and semiactive controlled responses that the proposed nonlinear control system design framework is effective in reducing the vibration of a seismically excited building structure equipped with an MR damper. Furthermore, the newly developed controller is more effective in mitigating responses of the structure than the H₂/LQG controller.     

Coupled-disturbance-observer-based position tracking control for a cascade electro-hydraulic system

The disturbance suppression is one of the most common control problems in electro-hydraulic systems. especially largely an unknown disturbance often obviously degrades the dynamic performance by biasing the desired actuator outputs (e.g., load forces or torques). In order to reject the dynamic disturbances in some multi-degree-of-freedom manipulators driven by electro-hydraulic actuators, this paper proposes a state feedback control of the cascade electro-hydraulic system based on a coupled disturbance observer with backstepping. The coupled disturbance observer is designed to estimate both the independent element and the coupled element of the external loads on each electro-hydraulic actuator. The cascade controller has the ability to compensate for the disturbance estimating, as well as guarantees the system state error convergence to a prescribed steady state level. The effectiveness of the proposed controller for the suppression of largely unknown disturbances has been demonstrated by comparative study, which implies the proposed approach can achieve better dynamic performance on the motion control of Two-Degree-of-Freedom robotic arm.     

基于自抗扰控制器的磁浮平台水平推力控制

介绍一种新型的磁浮平台,针对该磁浮平台水平运动这一多变量、非线性、强耦合的系统,提出一种改进的自抗扰控制器,克服常规自抗扰控制器非线性状态误差反馈控制律中非线性函数的不平滑性,并探索出一套行之有效的控制器参数整定规则,同时利用扩张状态观测器观测出内部扰动和外部扰动,并对它们进行补偿。仿真对比分析和试验结果表明,这种改进的自抗扰控制器具有很好的动态、静态特性及鲁棒性。     

直接驱动型机械手的变结构控制

针对直接驱动型机械手的随动控制问题,提出了一种基于滑动模态扰动观测器的变结构控制器.通过观测由系统的非线性、模型的不确定性和外来干扰所造成的广义扰动,将非线性、强耦合的机械手动力学系统线性化,并解耦为多个单输入、单输出线性系统.控制器的设计不再依赖于机械手的精确模型.在二连杆机械手上做的仿真研究表明,在负载大范围变化的条件下,采用滑动模态扰动观测器的控制系统,比全状态反馈的控制系统具有更好的鲁棒性.     

Output feedback neurolinearization

Output-feedback neurolinearization as a new method in model independent input/output linearization has been developed. In this method input-output linearization is done only based on the input-output data of the system. The performance of this new method is compared to the global linearizing control (GLC) and to a conventional PI controller. The systems selected for comparison purposes are temperature control of a CSTR reactor and pH control in a neutralization process. Output feedback neurolinearization, outperforms the other controllers both in setpoint tracking and disturbance rejection. The other important advantage of Output Feedback Neurolinearization is the fact that it does not depend upon the process model at all.     

线性自抗扰气缸位置伺服控制研究

针对气动伺服系统复杂的非线性问题,提出了一种线性自抗扰控制策略对气动伺服系统进行位置控制。利用线性自抗扰控制器不依赖于被控对象精确数学模型的特点,解决被控气动系统内外各种不确定性,设计了线性扩张状态观测器来估计和补偿系统的全部干扰,同时给出了线性状态误差反馈控制器来保证系统的闭环响应性能。证明了线性扩张状态观测器的收敛性和闭环系统的镇定性。应用线性自抗扰控制策略与PID控制策略在气缸伺服系统中进行实验、比较,实验结果表明所设计的线性自抗扰控制器具有良好的控制效果。     

气动人工肌肉驱动单关节机械臂的自抗扰控制

针对气动人工肌肉驱动单关节机械臂存在严重的非线性问题,提出一种自抗扰控制策略,来改善单关节机械臂的控制效果。对于给出的不精确系统模型,首先利用跟踪微分器安排输入信号的过渡过程,从而有效地解决了系统的快速性和超调之间的矛盾;其次利用扩张状态观测器观估计出系统状态以及系统的非线性和外部扰动,并对其进行补偿;最后设计了带扩张状态补偿的非线性误差反馈控制器来保证系统的闭环响应性能。实验结果表明,该控制方法在气动单关节机械臂关节关节角度控制方面具有良好的控制效果。     

Output feedback model predictive control of hydraulic systems with disturbances compensation

Enhancing the robustness of output feedback control has always been an important issue in hydraulic servo systems. In this paper, an output feedback model predictive controller (MPC) with the integration of an extended state observer (ESO) is proposed for hydraulic systems. The ESO was designed to estimate not only the unmeasured system states but also the disturbances, which will be synthesized into the design of the output prediction equation. Based on the mechanism of receding horizon and repeating optimization of MPC, the output prediction equation will be updated in real time and the future behavior of the system will be accurately predicted since the disturbances are compensated effectively. Hence, the ability of the traditional MPC to suppress disturbances will be improved evidently. The experiment results show that the proposed controller has high-performance nature and strong robustness against various model uncertainties, which verifies the effectiveness of the proposed control strategy.