Nonlinear adaptive robust backstepping force control of hydraulic load simulator: Theory and experiments

High performance robust force control of hydraulic load simulator with constant but unknown hydraulic parameters is considered. In contrast to the linear control based on hydraulic linearization equations, hydraulic inherent nonlinear properties and uncertainties make the conventional feedback proportional-integral-derivative (PID) control not yield to high performance requirements. Furthermore, the hydraulic system may be subjected to non-smooth and discontinuous nonlinearities due to the directional change of valve opening. In this paper, based on a nonlinear system model of hydraulic load simulator, a discontinuous projection-based nonlinear adaptive robust back-stepping controller is developed with servo valve dynamics. The proposed controller constructs a novel stable adaptive controller and adaptation laws with additional pressure dynamic related unknown parameters, which can compensate for the system nonlinearities and uncertain parameters, meanwhile a well-designed robust controller is also synthesized to dominate the model uncertainties coming from both parametric uncertainties and uncertain nonlinearities including unmodeled and ignored system dynamics. The controller theoretically guarantee a prescribed transient performance and final tracking accuracy in presence of both parametric uncertainties and uncertain nonlinearities; while achieving asymptotic output tracking in the absence of unstructured uncertainties. The implementation issues are also discussed for controller simplification. Some comparative results are obtained to verify the high-performance nature of the proposed controller.     

Motion control of industrial robots by considering serial two-link robot arm model with joint nonlinearities

This paper presents a model based motion control approach for industrial robots by considering a serial two-link robot arm model with joint nonlinearities. In order to achieve the desired performance using the model based control approaches, it is important to obtain relevant models of both kinematics and dynamics including nonlinear characteristics. Main nonlinear components that lead to trajectory tracking errors of typical multi-axis industrial robot are joint nonlinearities in each axis and dynamic coupling effects between different axes. In this paper, a parametric modeling approach is introduced to reproduce behaviors of a serial two-link robot arm with joint nonlinearities. Nonlinear stiffness, angular transmission errors, and friction in these two links are directly identified as joint nonlinearities. This approach is applied for the serial two-link arm of a typical multi-axis industrial robot, which has low frequency vibration modes and significantly affects to the trajectory performance. Effectiveness of the modeling is verified by comparative studies with numerical simulations and experiments. Finally, a 2-DOF control scheme with the identified two-link dynamic model and a feedback loop-shaping with a variable notch filter are applied to improve the performance of trajectory tracking and residual vibration suppression.     

Submicrometer control of a traction drive using state feedback and estimation

Traction drives are direct-drive systems that are more sensitive to noise and disturbances than lead screws. Their performance using PID control is not always satisfactory. Therefore, there is a need to improve the tracking performance of traction drives while overcoming their inherent sensitivity to disturbances. To understand their behavior better, their operating characteristics are investigated and a system model is developed. Using this model, a state feedback regulator is designed. To eliminate steady-state errors to step commands and improve tracking performance, an outer PID loop is added. The performance of this controller is then compared with that of a PID controller. It is shown that the state feedback/PID scheme rejects disturbances more than three times as fast as the PID controller and reduces tracking errors by over 50%.     

Modeling a multivariable reactor and on-line model predictive control

A nonlinear first principle model is developed for a laboratory-scaled multivariable chemical reactor rig in this paper and the on-line model predictive control (MPC) is implemented to the rig. The reactor has three variables-temperature, pH, and dissolved oxygen with nonlinear dynamics-and is therefore used as a pilot system for the biochemical industry. A nonlinear discrete-time model is derived for each of the three output variables and their model parameters are estimated from the real data using an adaptive optimization method. The developed model is used in a nonlinear MPC scheme. An accurate multistep-ahead prediction is obtained for MPC, where the extended Kalman filter is used to estimate system unknown states. The on-line control is implemented and a satisfactory tracking performance is achieved. The MPC is compared with three decentralized PID controllers and the advantage of the nonlinear MPC over the PID is clearly shown.     

Memoryless disturbance-observer-based adaptive tracking of uncertain pure-feedback nonlinear time-delay systems with unmatched disturbances

This paper presents a delay-independent nonlinear disturbance observer (NDO) design methodology for adaptive tracking of uncertain pure-feedback nonlinear systems in the presence of unknown time delays and unmatched external disturbances. Compared with all existing NDO-based control results for uncertain lower-triangular nonlinear systems where unknown time delays have been not considered, the main contribution of this paper is to develop a delay-independent design strategy to construct an NDO-based adaptive tracking scheme in the presence of unknown time-delayed nonlinearities and non-affine nonlinearities unmatched in the control input. The proposed delay-independent scheme is constructed by employing the appropriate Lyapunov-Krasovskii functionals and the same function approximators for the NDO and the controller. It is shown that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to an adjustable neighborhood of the origin.     

A frequency independent approximation and a sliding mode control scheme for a system of a micro-cantilever beam

In the present article, a sliding mode controller is proposed for a micro-cantilever beam (μCB) with fringing and squeezed film damping effects. The narrow micro-cantilever beam can move via the application of an external electrically induced force. The introduction of the squeezed film parameters results in a frequency-dependent nonlinear system. Particular attention, has been paid, in order to approximate the frequency dependent μCB model, with a valid, frequency independent one, that would be incorporated in the design of a robust sliding mode controller. The suggested control technique enables compact realization of a robust controller tolerant in device characteristics' variations, nonlinearities and types of inherent instabilities. Robustness of the proposed control scheme against disturbances is proved by Lyapunov's second method. In addition, bifurcation analysis is carried on the beam's nonlinear model, and numerous simulation test cases are presented in order to test the suggested modeling and control techniques.     

压电陶瓷微动台的复合控制

压电陶瓷微动台的迟滞非线性严重影响其动态定位精度,为了解决这一问题,采用一种改进的PI模型对微动台的迟滞非线性进行了建模.为了提高传统PID算法对压电陶瓷微动台的动态定位性能,将改进的PI模型与传统PID算法组合构成前馈复合控制算法,并进行了微动台的慢速与快速动态定位实验.结果表明,对同频曲线定位时,前馈PID复合算法的最大误差为传统PID算法的40％左右,平均误差为传统算法的20％～30％左右;对多频曲线定位时,前馈PID复合算法的最大误差和平均误差为传统PID算法的33％左右.数据表明前馈PID复合算法的动态定位性能明显优于传统PID算法.     

FEEDBACK LINEARIZATION CONTROL FOR ELECTRONICALLY CONTROLLABLE CLUTCH OF VEHICLE

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A novel auto-tuning PID control mechanism for nonlinear systems

In this paper, a novel Runge–Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence.     

Robust friction compensation for submicrometer positioning and tracking for a ball-screw-driven slide system

Ball-screw-driven slide systems are largely used in industry for motion control applications. Their performance using standard proportional-integral-derivative (PID) control algorithm is unsatisfactory in submicrometer motion control because of nonlinear friction effects. In this article, controllers based on a bristle-type nonlinear contact model are developed and implemented for submicrometer motion. For submicrometer positioning, a proportional-derivative (PD) control scheme with a nonlinear friction estimate algorithm is developed, and its performance is compared with that of a PID controller. For tracking, a disturbance observer was added to reject external disturbances and to improve robustness. The experimental results indicate that the proposed controller has consistent performance in positioning with under 1.5% of steady-state error in the submicrometer range. For tracking performance, the proposed controller shows good and robust tracking with respect to parameter variation.     

Robust tracking and distributed synchronization control of a multi-motor servomechanism with H-infinity performance

The multi-motor servomechanism (MMS) is a multi-variable, high coupling and nonlinear system, which makes the controller design challenging. In this paper, an adaptive robust H-infinity control scheme is proposed to achieve both the load tracking and multi-motor synchronization of MMS. This control scheme consists of two parts: a robust tracking controller and a distributed synchronization controller. The robust tracking controller is constructed by incorporating a neural network (NN) K-filter observer into the dynamic surface control, while the distributed synchronization controller is designed by combining the mean deviation coupling control strategy with the distributed technique. The proposed control scheme has several merits: 1) by using the mean deviation coupling synchronization control strategy, the tracking controller and the synchronization controller can be designed individually without any coupling problem; 2) the immeasurable states and unknown nonlinearities are handled by a NN K-filter observer, where the number of NN weights is largely reduced by using the minimal learning parameter technique; 3) the H-infinity performances of tracking error and synchronization error are guaranteed by introducing a robust term into the tracking controller and the synchronization controller, respectively. The stabilities of the tracking and synchronization control systems are analyzed by the Lyapunov theory. Simulation and experimental results based on a four-motor servomechanism are conducted to demonstrate the effectiveness of the proposed method.     

二自由度门式起重机器人控制系统硬件的选择

为了解决二自由度门式起重机器人的吊运轨迹精确跟踪控制和反晃动的有效消除,在前人研究结果和建立其非线性动力学模型的基础上,运用基于模糊PID的轨迹跟踪控制方式可达到要求.基于这样的实验要求选择系统软硬件,在选定Matlab/Simulink等软件的情况下,介绍了几种控制硬件,根据设计方案,选定了符合要求的控制硬件,即固高多轴运动控制卡GTS - X00 - PV/PG - PCI来实现轨迹跟踪控制.     

火电机组单神经元非线性控制方法研究

把非线性逆系统原理和单神经元自适应PID控制相结合,设计出一种新的非线性输出跟踪控制器。针对火电单元机组模型,首先用逆系统原理对该模型求取稳定逆的解,然后用单神经元自适应PID作为该系统的反馈控制器。在不同负荷下的仿真结果表明,该控制系统具有很好的抗干扰、快速响应以及稳定跟踪能力。     

Model reference adaptive control for a piezo-positioning system

Piezoelectric (PZT) actuators having the characteristic of infinitely small displacement resolution are popularly applied as actuators in precision positioning systems. Due to its nonlinear hysteresis effect, the tracking control accuracy of the precision positioning system is difficultly achieved. Hence, it is desirable to take hysteresis effect into consideration for improving the trajectory tracking performance. In this paper, a model reference adaptive control scheme based on hyperstability theory is developed for a moving stage system driven by a PZT actuator. It is worth emphasizing that the controller can be constructed without a nonlinear hysteresis dynamic equation to compensate the hysteresis effect. According to simulation results, the tracking error was only nanometer order. Through experimental examinations, the tracking performance was obtained as precision as ten nanometers order which is the resolution limitation of the measurement system. The effectiveness of the proposed adaptive control scheme was validated.     

Controller designs for constant cutting force turning machine control

A simulation study of a constant cutting force metal turning process is investigated. The process is a challenging control problem due to its nonlinear and time varying dynamics. Simulated implementations of PID, adaptive and non-adaptive sliding mode and model reference adaptive controllers were developed. Tests of the closed loop systems were performed for a range of cutting conditions including specific machined part contours that are presented here to verify the force tracking capability and flexibility of each control scheme. Results indicate that careful design and use of a fixed-gain sliding mode controller with output feedback can give roughly equivalent performance to that of more complex adaptive controllers.     

Development of an adaptive radial basis function neural network estimator-based continuous sliding mode control for uncertain nonlinear systems

In this paper an adaptive neural network (NN)-based nonlinear controller is proposed for trajectory tracking of uncertain nonlinear systems. The adopted control algorithm combines a continuous second-order sliding mode control (CSOSMC), the radial basis function neural network (RBFNN) and the adaptive control methodology. First, a second-order sliding mode control scheme (SOSMC), which is published recently in literature for linear uncertain systems, is extended for nonlinear uncertain systems. Second, an adaptive radial basis function neural network estimator-based continuous second order sliding mode control algorithm (CSOSMC-ANNE) is adopted. In CSOSMC-ANNE control methodology, a radial basis function neural network with adaptive parameters is exploited to approximate the unknown system parameters and improve performance against perturbations. Also, the discontinuous switching control of SOSMC is supplanted with a smooth continuous control action to completely eliminate the chattering phenomenon. The convergence and global stability of the closed-loop system are proved using Lyapunov stability method. Numerical computer simulations, with dynamical model of the nonlinear inverted pendulum system, are presented to demonstrate the effectiveness and advantages of the presented control scheme.     

被动式电液伺服加载系统复合控制方法研究

研究了基于新型补偿结构和非线性PID控制器的被动式电液伺服加载复合控制方法.提出了将加载马达输出轴角位移作为输入信号的多余力矩前馈补偿方案,在有效抑制多余力矩的同时降低了系统阶次.研究了一种带调节因子的非线性PID控制器,克服了常规PID控制器难以解决的快速性与稳定性之间的矛盾.仿真与试验结果证明,该复合控制策略具有较高的载荷谱跟踪精度.     

Performance analysis of two-degree of freedom fractional order PID controllers for robotic manipulator with payload

The robotic manipulators are multi-input multi-output (MIMO), coupled and highly nonlinear systems. The presence of external disturbances and time-varying parameters adversely affects the performance of these systems. Therefore, the controller designed for these systems should effectively deal with such complexities, and it is an intriguing task for control engineers. This paper presents two-degree of freedom fractional order proportional-integral-derivative (2-DOF FOPID) controller scheme for a two-link planar rigid robotic manipulator with payload for trajectory tracking task. The tuning of all controller parameters is done using cuckoo search algorithm (CSA). The performance of proposed 2-DOF FOPID controllers is compared with those of their integer order designs, i.e., 2-DOF PID controllers, and with the traditional PID controllers. In order to show effectiveness of proposed scheme, the robustness testing is carried out for model uncertainties, payload variations with time, external disturbance and random noise. Numerical simulation results indicate that the 2-DOF FOPID controllers are superior to their integer order counterparts and the traditional PID controllers.     

压电陶瓷执行器的神经网络实时自适应逆控制

目的：为了提高压电陶瓷执行器执行精度,提出消除压电陶瓷的非线性、非光滑的迟滞特性的方法。 方法：提出了基于内积的压电陶瓷动态神经网络非线性、非光滑的迟滞逆模型,采用反馈误差学习方法,避免了求取压电陶瓷的Jacobian信息,快速地在线得到压电陶瓷的逆模型,并结合PID反馈控制,在dSPACE系统平台上,实现压电陶瓷的神经网络自适应逆控制,为了提高实时性,程序采用效率高、速度快的C-MEX S Function编程。结果：实验结果表明：神经网络自适应逆控制的控制精度为：0.13μm,而PID控制精度为：0.32μm 。结论：所提出方法有效地消除了迟滞的影响,控制精度高。