A novel adaptive sliding mode control with application to MEMS gyroscope

This paper presents a new adaptive sliding mode controller for MEMS gyroscope; an adaptive tracking controller with a proportional and integral sliding surface is proposed. The adaptive sliding mode control algorithm can estimate the angular velocity and the damping and stiffness coefficients in real time. A proportional and integral sliding surface, instead of a conventional sliding surface is adopted. An adaptive sliding mode controller that incorporates both matched and unmatched uncertainties and disturbances is derived and the stability of the closed-loop system is established. The numerical simulation is presented to verify the effectiveness of the proposed control scheme. It is shown that the proposed adaptive sliding mode control scheme offers several advantages such as the consistent estimation of gyroscope parameters including angular velocity and large robustness to parameter variations and external disturbances.     

Sliding mode control of a simulated MEMS gyroscope

The microelectromechanical systems (MEMS) are penetrating more and more into measurement and control problems because of their small size, low cost, and low power consumption. The vibrating gyroscope is one of those MEMS devices that will have a significant impact on the stability control systems in transportation industry. This paper studies the design and control of a vibrating gyroscope. The device has been constructed in a Pro-E environment and its model has been simulated in the finite-element domain in order to approximate its dynamic characteristics with a lumped model. A model reference adaptive feedback controller and the sliding mode controller have been considered to guarantee the stability of the device. It is shown that the sliding mode controller of the vibrating proof mass results in a better estimate of the unknown angular velocity than that of the model reference adaptive feedback controller.     

高Q值微机电陀螺的快速起振控制

针对高Q值微机电陀螺的快速起振问题,研究其驱动轴控制方法。分析了高Q值谐振器的振动相位随频率的变化率,阐明了锁相环方案启动时间长且对初始频率偏差敏感的原因。用平均法推导了自激振荡方案下起振初始阶段振幅随时间的变化规律。提出了"自激-锁相"驱动轴控制方案,先采用自激振荡方式使陀螺快速起振,再转为锁相环方式使振动频率精确稳定。经实验测试,采用锁相环方案,当初始频率偏差在±10 Hz以内,陀螺的启动时间为2s;采用自激-锁相方案,只要初始频率偏差在±1 000Hz以内,陀螺均可在0.3s内达到频率误差小于0.01%,在0.4s内达到振幅误差小于0.1%。"自激-锁相"方案大幅度缩短了陀螺的启动时间,而且对陀螺初始频率的设置偏差不敏感,对环境温度变化的适应性好,适用于微机电陀螺的批量生产。     

A novel Kalman filter for combining outputs of MEMS gyroscope array

In this paper, a Kalman filter for combining outputs of a gyroscope array is presented to improve the accuracy of microelectromechanical system (MEMS) gyroscope. A theoretical mathematical model for the accuracy improvement is described. Especially, a discrete-time filter is designed by solving the covariance differential equation with an analytic solution. Performances of presented filter are analyzed by the simulations. Finally, a developed system consisting of six-gyroscope array is implemented to test the performance of the Kalman filter. The experimental results showed a noise density of 0.03°/s/√Hz for the combined rate signal compared to the 0.11°/s/√Hz for the individual gyroscope in the array. The analysis of results measured from Allan variance demonstrated a bias instability of 17.2°/h and angular random walk of 1.6°/√h, whereas the corresponding values for the individual gyroscope is 62°/h and 6.2°/√h, respectively. It proved that the presented approach is effective to improve the MEMS gyroscope accuracy.     

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°。     

Parameter estimation and interval type-2 fuzzy sliding mode control of a z-axis MEMS gyroscope

This paper reports a hybrid intelligent controller for application in single axis MEMS vibratory gyroscopes. First, unknown parameters of a micro gyroscope including unknown time varying angular velocity are estimated online via normalized continuous time least mean squares algorithm. Then, an additional interval type-2 fuzzy sliding mode control is incorporated in order to match the resonant frequencies and to compensate for undesired mechanical couplings. The main advantage of this control strategy is its robustness to parameters uncertainty, external disturbance and measurement noise. Consistent estimation of parameters is guaranteed and stability of the closed-loop system is proved via the Lyapunov stability theorem. Finally, numerical simulation is done in order to validate the effectiveness of the proposed method, both for a constant and time-varying angular rate.     

基于刚度轴偏角预估机制的 MEMS 多环谐振陀螺全闭环控制方法

针对微机电系统多环谐振陀螺正交闭环回路存在控制误差问题,提出一种基于刚度轴偏角预估机制的多环陀螺全闭环控制方法。该方法通过对微机电系统多环谐振陀螺刚度轴偏角预估,实现正交闭环回路参数自动优化调整。同时,提出了基于刚度轴偏角预估机制的全数字化闭环控制方法,实现微机电系统多环谐振陀螺的驱动、检测、正交、模态匹配环路的全闭环控制。该方法可提升正交闭环回路信噪比,增强陀螺正交漂移的抑制能力,降低陀螺零偏输出,改善陀螺的零偏不稳定性。实验结果表明,采用本文提出的基于刚度轴偏角预估机制的全闭环控制方法后,微机电系统多环谐振陀螺的零偏输出由0.201°/s降低为0.021 3°/s,零偏不稳定性由39.42°/h降低为1.237°/h,分别降低了9.44倍和31.86倍,验证了该方法对提升微机电系统多环谐振陀螺仪性能的有效性。     

Continuous higher-order sliding mode control with time-varying gain for a class of uncertain nonlinear systems

This paper presents a continuous higher-order sliding mode (HOSM) control scheme with time-varying gain for a class of uncertain nonlinear systems. The proposed controller is derived from the concept of geometric homogeneity and super-twisting algorithm, and includes two parts, the first part of which achieves smooth finite time stabilization of pure integrator chains. The second part conquers the twice differentiable uncertainty and realizes system robustness by employing super-twisting algorithm. Particularly, time-varying switching control gain is constructed to reduce the switching control action magnitude to the minimum possible value while keeping the property of finite time convergence. Examples concerning the perturbed triple integrator chains and excitation control for single-machine infinite bus power system are simulated respectively to demonstrate the effectiveness and applicability of the proposed approach.     

基于最小分辨率的MEMS陀螺漂移抑制方法研究

针对油气井MEMS陀螺定向测斜仪存在的漂移大,精度较低的问题,本文从实际工程应用角度出发,在研究MEMS陀螺仪输出信号漂移特性的基础上,提出了基于最小分辨率的MEMS陀螺漂移抑制方法,利用输出采样的差分值,从MEMS陀螺输出中将传感信号和漂移信号分离,同时通过静态测点对漂移进行估计.实验表明,该方法大幅提高了仪器测量精度,使定向精度提高50％以上,同时该方法为其它类似传感器漂移抑制提供了一种有益的参考.     

Optimal second order sliding mode control for nonlinear uncertain systems

In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.     

Kinematics and dynamics of a double-gimbaled control moment gyroscope

Control moment gyroscopes (CMGs) are torque-generating mechanisms that can be used for attitude and vibration control of spacecraft. CMGs consist of a rotating flywheel as well as a wheel-tilting actuator. Most CMG designs allow the flywheel spin axis to tilt about only one axis––a single-gimbaled CMG. This paper develops and analyzes the kinematics and dynamics of a novel double-gimbaled CMG design. The compact CMG design involves two four-bar linkages allowing the axis of rotation of the spinning flywheel to have two degrees of freedom.     

Suppression of the noise-induced effects in an electrostatic micro-plate using an adaptive back-stepping sliding mode control

In this work, an adaptive backstepping sliding mode control approach is applied through the piezoelectric layer in order to control and to stabilize an electrostatic micro-plate. The mathematical model of the system by taking into account the small fluctuations in the gap considered as bounded noise is carried out. The accuracy of the proposed modal equation is proven using the method of lines. By using both approaches, the effects of noise are presented. It is found that they lead to pull-in instability as well as to random chaos. A suitable backstepping approach to improve the tracking performance is integrated to the adaptive sliding mode control in order to eliminate chattering phenomena and reinforce the robustness of the system in presence of uncertainties and external random disturbances. It is proved that all the variables of the closed-loop system are bounded and the system can follow the given reference signals as close as possible. Numerical simulations are provided to show the effectiveness of proposed controller.     

微隧穿式陀螺仪检测模态的线性二次高斯控制

为了将微隧穿式陀螺仪(MTG)的隧尖与检测电极之间的隧道间隙及其变动量分别维持在1nm和0.1nm并降低系统噪声和扩大带宽,本文为其检测模态设计了线性二次高斯(LQG)闭环反馈系统。在利用微小量法对呈指数规律的隧道效应进行线性化的基础上,建立了MTG检测模态的线性化模型,并将哥氏加速度和电子隧道1/f噪声分别当作主要的过程噪声和输出噪声,设计了由最优状态估计器和线性二次(LQ)状态调节器组成的LQG控制器。搭建了仿真系统和实际的LQG控制电路并进行动态测试。仿真结果显示,LQG控制在将系统的信噪比提高24dB的同时,能够将两个隧道电极之间的间隙的变动量控制在10-4 nm。实验曲线表明,隧道电流噪声的峰峰值为0.4nA,LQG反馈控制系统在动态加速度信号的激励下可维持恒定隧道间隙为1nm。     

Optimal second order sliding mode control for linear uncertain systems

In this paper an optimal second order sliding mode controller (OSOSMC) is proposed to track a linear uncertain system. The optimal controller based on the linear quadratic regulator method is designed for the nominal system. An integral sliding mode controller is combined with the optimal controller to ensure robustness of the linear system which is affected by parametric uncertainties and external disturbances. To achieve finite time convergence of the sliding mode, a nonsingular terminal sliding surface is added with the integral sliding surface giving rise to a second order sliding mode controller. The main advantage of the proposed OSOSMC is that the control input is substantially reduced and it becomes chattering free. Simulation results confirm superiority of the proposed OSOSMC over some existing.     

A new discrete-time robust adaptive time-delay control for a class of uncertain nonlinear strict-feedback systems using sliding mode

This paper presents a new discrete-time adaptive second-order sliding mode control with time delay estimation (TDE) for a class of uncertain nonlinear time-varying strict-feedback systems. The existing researches on time delay control (TDC) are conventionally established based on a stability criterion that is subject to the infinitesimal time delay assumption. Recently, this criterion was rejected and a new criterion was proposed for the development of a controller for systems with fully known dynamics. In this study, this approach is extended to uncertain systems. Specifically, a new criterion is developed for the stability of the TDE-error within an adaptive robust controller design without the infinitesimal time delay assumption. With the proposed adaptive robust control, there is no need for determination of uncertainties upper-bounds. Simulation results illustrate the efficacy of the proposed controller.     

四旋翼飞行器的自适应鲁棒滑模控制器设计

针对四旋翼欠驱动系统的姿态控制问题,提出一种自适应鲁棒滑模控制方法。对四旋翼系统实现了双环控制,内环为姿态控制,外环为位置控制。根据牛顿-欧拉方程建立了四旋翼系统的动力学模型,针对系统中的外部扰动和参数摄动等不确定性因素,设计了基于Lyapunov稳定控制算法,内环使用自适应鲁棒滑模控制;外环使用鲁棒控制。仿真和实验表明所提控制策略对外界扰动和模型的不确定性具有较强的鲁棒性。     

Anti-disturbance speed control of low-speed high-torque PMSM based on second-order non-singular terminal sliding mode load observer

This paper presents an anti-disturbance speed control of low-speed high-torque permanent magnet synchronous motor (PMSM) based on the second-order non-singular terminal sliding mode load observer. According to the coordinate transformation theory, the mathematical model of PMSM is established. Subsequently, the second-order non-singular terminal sliding mode observer (SNTSMO) is designed to observe the changes of load disturbance in the PMSM system. The SNTSMO combines the advantages of both high-order sliding mode and non-singular terminal sliding mode to achieve the fast convergence and no chattering. Next, the sliding mode controller (SMC) is designed to achieve speed loop control of PMSM. Then, the anti-disturbance compound speed controller is established on the basis of SMC and SNTSMO, wherein the feed-forward compensation is used to reduce the disturbance from the load. Finally, the numerical simulations and experiments are presented according to the schematic diagram of the designed compound speed controller of PMSM. The results demonstrate that the designed SNTSMO can precisely estimate the load disturbance and suppress the effects of buffeting in the traditional sliding mode observer (SMO). Additionally, the designed compound speed controller of PMSM can achieve smooth speed control in the presence of load disturbance, achieve the purpose of anti-disturbance speed control and further improve the robustness of the control system.     

On decentralized adaptive full-order sliding mode control of multiple UAVs

In this study, a novel decentralized adaptive full-order sliding mode control framework is proposed for the robust synchronized formation motion of multiple unmanned aerial vehicles (UAVs) subject to system uncertainty. First, a full-order sliding mode surface in a decentralized manner is designed to incorporate both the individual position tracking error and the synchronized formation error while the UAV group is engaged in building a certain desired geometric pattern in three dimensional space. Second, a decentralized virtual plant controller is constructed which allows the embedded low-pass filter to attain the chattering free property of the sliding mode controller. In addition, robust adaptive technique is integrated in the decentralized chattering free sliding control design in order to handle unknown bounded uncertainties, without requirements for assuming a priori knowledge of bounds on the system uncertainties as stated in conventional chattering free control methods. Subsequently, system robustness as well as stability of the decentralized full-order sliding mode control of multiple UAVs is synthesized. Numerical simulation results illustrate the effectiveness of the proposed control framework to achieve robust 3D formation flight of the multi-UAV system.     

Design of a fractional order PID controller using GBMO algorithm for load–frequency control with governor saturation consideration

Load–frequency control is one of the most important issues in power system operation. In this paper, a Fractional Order PID (FOPID) controller based on Gases Brownian Motion Optimization (GBMO) is used in order to mitigate frequency and exchanged power deviation in two-area power system with considering governor saturation limit. In a FOPID controller derivative and integrator parts have non-integer orders which should be determined by designer. FOPID controller has more flexibility than PID controller. The GBMO algorithm is a recently introduced search method that has suitable accuracy and convergence rate. Thus, this paper uses the advantages of FOPID controller as well as GBMO algorithm to solve load–frequency control. However, computational load will higher than conventional controllers due to more complexity of design procedure. Also, a GBMO based fuzzy controller is designed and analyzed in detail. The performance of the proposed controller in time domain and its robustness are verified according to comparison with other controllers like GBMO based fuzzy controller and PI controller that used for load–frequency control system in confronting with model parameters variations.