Experimental evaluations of proportional–integral–derivative type fuzzy controllers with parameter adaptive methods for an active magnetic bearing system

Abstract: This paper deals with the experimental control of a rotating active magnetic bearing (AMB) system using proportional–integral–derivative type fuzzy controllers (PIDFCs) with parameter adaptive methods. Three kinds of parameter adaptive method, including fuzzy tuner, function tuner and relative rate observer, have been proposed in the literature for tuning the coefficients of PIDFCs. However, only a simulation comparison between these methods for control of a second‐order linear system with varying parameters and time delay has been done. In general, theoretical models need to be confirmed and modified through experimental results. This paper provides experimental verification by applying PIDFCs with self‐tuning algorithms for control of a highly nonlinear AMB system. It is shown that the steady‐state error of the AMB system using the function tuner method is lower and the first resonant frequency of the AMB system using the relative rate observer method is higher than the other two methods, and the proportional–integral–derivative controller is quite unstable. The experimental results also show that all of the tuning methods can support a high rotation frequency of the AMB system. In practice, there are only a few differences between the three kinds of parameter adaptive methods.     

FHOSM Tolerant Control for Networked Control Systems with Disturbances and Faults

This paper investigates the networked control system (NCS) with faults and disturbances which affect both actuator and sensor. A fast high-order sliding mode (FHOSM) controller is proposed to compensate for actuator faults and sensor disturbances, which is constructed based on the estimated information of the NCS. Accordingly, an adaptive observer with multi-stage is designed to estimate the states and sensor disturbances and protect the NCS from actuator faults. Furthermore, a new sliding function is assembled to realize the finite-time convergence of system states. The stability of the system with the suggested procedure is illustrated by the stability analysis underneath the designed control law. Finally, the simulation results are implemented and confirm the effectiveness of the proposed method in defending the system against both issues and inhibiting system failures.

     

Adaptive nonlinear observer for state and unknown parameter estimation in noisy systems

This paper proposes a novel adaptive observer for Lipschitz nonlinear systems and dissipative nonlinear systems in the presence of disturbances and sensor noise. The observer is based on an H_∞ observer that can estimate both the system states and unknown parameters by minimising a cost function consisting of the sum of the square integrals of the estimation errors in the states and unknown parameters. The paper presents necessary and sufficient conditions for the existence of the observer, and the equations for determining observer gains are formulated as linear matrix inequalities (LMIs) that can be solved offline using commercially available LMI solvers. The observer design has also been extended to the case of time-varying unknown parameters. The use of the observer is demonstrated through illustrative examples and the performance is compared with extended Kalman filtering. Compared to previous results on nonlinear observers, the proposed observer is more computationally efficient, and guarantees state and parameter estimation for two very broad classes of nonlinear systems (Lipschitz and dissipative nonlinear systems) in the presence of input disturbances and sensor noise. In addition, the proposed observer does not require online computation of the observer gain.     

Applying discrete-time proportional Integral observers for state and disturbance estimations

In this note, we apply the proportional integral observer to simultaneously estimate system states and unknown disturbances for discrete-time nonminimum phase systems. Conditions for providing the existence of such observer are given. When the disturbances do not vary too much between two consecutive sampling instances, the proposed method can render the estimation errors of system states and disturbances to be constrained in a small bounded region. Simulation results support the theoretical developments.     

Robust observer-based optimal linear quadratic tracker for five-degree-of-freedom sampled-data active magnetic bearing system

This paper presents three observer/Kalman filter identification (OKID) approaches and develops a robust observer-based optimal linear quadratic digital tracker (LQDT) for the five-degree-of-freedom (five-DOF) sampled-data active magnetic bearing (AMB) system with various disturbances. The more detailed objectives are: (i) to construct both an equivalent linear time-invariant discrete-time model and its state estimator via the proposed OKID approaches for the AMB system, which might be an unknown nonlinear time-varying unstable system with both a specified rotation speed and a sampling rate; (ii) to provide an adaptive disturbance estimation scheme, which establishes an equivalent input disturbance (EID) estimator for the AMB system with unexpected disturbances; and (iii) to develop a robust observer-based optimal LQDT for the sampled-data AMB system with both a pre-specified time-varying speed and unexpected disturbances. The developed LQDT is able to recover the displacement of the rotor to the pre-specified trajectory position whenever it deviates from such trajectory.     

An observer with controller to detect and reject disturbances

In this paper, a novel states observer is designed. This observer not only estimates the states, but also detects the disturbances by creating estimated signals. Then, both the observed states and detected disturbances are used in a control law to reject the disturbances, avoiding the requirement to know the states and disturbances. The observer is designed by the combination of the poles assignation and geometric techniques. Both the observer and controller work simultaneously. The proposed method is applied in an active suspension system and a liquid-level hydraulic system.     

基于高阶观测器和干扰补偿控制的模型预测控制方法

针对状态不可测、外部干扰未知, 并且状态和输入受限的离散时间线性系统, 将高阶观测器、干扰补偿控制与标准模型预测控制(Model predictive control, MPC)相结合, 提出了一种新的MPC方法. 首先利用高阶观测器同步观测未知状态和干扰, 使得观测误差一致有界收敛;然后基于该干扰估计值设计新的干扰补偿控制方法, 并将该方法与基于状态估计的标准MPC相结合, 实现上述系统的优化控制. 所提出的MPC方法克服了利用现有MPC方法求解具有外部干扰和状态约束的优化控制问题时存在无可行解的局限, 能够保证系统状态在每一时刻都满足约束条件, 并且使系统的输出响应接近采用标准MPC方法控制线性标称系统时得到的输出响应. 最后, 将所提控制方法应用到船舶航向控制系统中, 仿真结果表明了所提方法的有效性和优越性.     

Observer-Based Adaptive Fuzzy Tracking Control Using Integral Barrier Lyapunov Functionals for A Nonlinear System With Full State Constraints

A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints. The fuzzy logic system is used to design the approximator, which deals with uncertain and continuous functions in the process of backstepping design. The use of an integral barrier Lyapunov function not only ensures that all states are within the bounds of the constraint, but also mixes the states and errors to directly constrain the state, reducing the conservativeness of the constraint satisfaction condition. Considering that the states in most nonlinear systems are immeasurable, a fuzzy adaptive states observer is constructed to estimate the unknown states. Combined with adaptive backstepping technique, an adaptive fuzzy output feedback control method is proposed. The proposed control method ensures that all signals in the closed-loop system are bounded, and that the tracking error converges to a bounded tight set without violating the full state constraint. The simulation results prove the effectiveness of the proposed control scheme.      

Reduced-order Generalized Proportional Integral Observer Based Continuous Dynamic Sliding Mode Control for Magnetic Levitation System with Time-varying Disturbances

In order to reduce the influence of time-varying disturbances for magnetic levitation system, we propose a reduced-order generalized proportional integral observer (RGPIO) based continuous dynamic sliding mode control scheme for magnetic levitation system in this paper. Unlike the popular extended state observer (ESO), it could deal with constant or slowing varying disturbances from theoretical point of view, the reduced-order generalized proportional integral observer (RGPIO) is designed to estimate the time-varying disturbances and system states, then the dynamic sliding mode surface is developed and deduce a continuous sliding mode controller (CSMC) for magnetic levitation system. Compared with ESO based continuous sliding mode controller, the proposed method not only ensures the position tracking accuracy, but also obtain better time-varying disturbance reject ability. Simulation and experimental results are also given to verify the effectiveness.

     

Output feedback control with disturbance rejection of a class of nonlinear MIMO systems

Output feedback control with disturbance rejection is developed for a class of nonlinear multi-input-multi-output (MIMO) systems. The availability of state variables and the bound of disturbances are not required to be known in advance. In the design of an adaptive observer, a robust adaptive nonlinear state feedback controller using the estimated states is proposed. The control methodology is robust to bounded disturbances that are both constant and time-varying, with effective performance. The adaptive laws are derived based on the Lyapunov synthesis method; therefore closed-loop asymptotic stability is also guaranteed. Moreover, chattering can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed controller. The text was submitted by the authors in English.     

Adaptive Output Feedback Control of Flexible-Joint Robots Using Neural Networks: Dynamic Surface Design Approach

In this paper, we propose a new robust output feedback control approach for flexible-joint electrically driven (FJED) robots via the observer dynamic surface design technique. The proposed method only requires position measurements of the FJED robots. To estimate the link and actuator velocity information of the FJED robots with model uncertainties, we develop an adaptive observer using self-recurrent wavelet neural networks (SRWNNs). The SRWNNs are used to approximate model uncertainties in both robot (link) dynamics and actuator dynamics, and all their weights are trained online. Based on the designed observer, the link position tracking controller using the estimated states is induced from the dynamic surface design procedure. Therefore, the proposed controller can be designed more simply than the observer backstepping controller. From the Lyapunov stability analysis, it is shown that all signals in a closed-loop adaptive system are uniformly ultimately bounded. Finally, the simulation results on a three-link FJED robot are presented to validate the good position tracking performance and robustness of the proposed control system against payload uncertainties and external disturbances.     

Adaptive tracking and asymptotic rejection of unknown but bounded disturbances in nonlinear MIMO systems

The goal of this paper is global disturbance rejection in nonlinear systems. An output feedback controller with disturbance rejection is developed for a class of nonlinear multi input-multi output (MIMO) systems. The availability of state variables and the bound of disturbances are not required to be known in advance and reference tracking will is guaranteed. By the aid of designing an adaptive observer, a robust adaptive nonlinear state feedback controller using the estimated states is proposed. For tracking problem, an adaptive pre-compensator is used. The control methodology is robust against both constant and time varying bounded disturbances, maintaining effective performance. The adaptive laws are derived based on the Lyapunov synthesis method, therefore closed-loop asymptotic stability is also guaranteed. Moreover, for chattering reduction we use a low-pass filter. Consequently, small gain theorem is adopted to prove the stability of the closed-loop system. Simulation results are employed to illustrate the effectiveness of the proposed controller.     

Speed tracking control for the gimbal system with harmonic drive

This paper presents a composite controller based on a disturbance observer for the gimbal system of double-gimbal magnetically suspended control moment gyro (DGMSCMG) with harmonic drives. The controller removes the influence by coupling moments and nonlinear transmission torques. The disturbances are estimated by the designed disturbance observer. By introducing a state feedback controller, the disturbances can be eliminated from the output channel of the system. The gain selection principle of the disturbance observer is also analyzed. Both the simulation and experimental results indicate that the proposed control method can reject mismatched disturbances and improve system performance.     

带有非匹配扰动的连铸结晶器振动位移系统自适应反步滑模控制

针对伺服电机驱动的连铸结晶器振动位移系统中存在非匹配的参数不确定性、干扰等问题,提出一种基于非线性扩张状态观测器(ESO)的自适应反步滑模控制方法.首先,基于双曲正切函数和高增益构造ESO对系统中的非匹配扰动进行估计.然后,利用反步法将非匹配扰动视为匹配扰动进行处理, 并在每一步设计自适应积分滑模控制器,以消除非匹配扰动对系统的影响.另外,在反步设计的后两步引入了积分滑模滤波器用于估计前一步虚拟控制律的导数.理论分析表明,所设计的ESO能够保证估计误差收敛到原点附近的小邻域内;所设计的控制器能够保证闭环系统所有信号有界,并且,通过选取适当的参数能够保证系统状态可渐近收敛到原点.最后,通过仿真结果验证了所提出方法的有效性.     

Aero‐Engine DCS Fault‐Tolerant Control with Markov Time Delay Based On Augmented Adaptive Sliding Mode Observer

With a focus on aero‐engine distributed control systems (DCSs) with Markov time delay, unknown input disturbance, and sensor and actuator simultaneous faults, a combined fault tolerant algorithm based on the adaptive sliding mode observer is studied. First, an uncertain augmented model of distributed control system is established under the condition of simultaneous sensor and actuator faults, which also considers the influence of the output disturbances. Second, an augmented adaptive sliding mode observer is designed and the linear matrix inequality (LMI) form stability condition of the combined closed‐loop system is deduced. Third, a robust sliding mode fault tolerant controller is designed based on fault estimation of the sliding mode observer, where the theory of predictive control is adopted to suppress the influence of random time delay on system stability. Simulation results indicate that the proposed sliding mode fault tolerant controller can be very effective despite the existence of faults and output disturbances, and is suitable for the simultaneous sensor and actuator faults condition.     

Simultaneous fault estimation for uncertain Markovian jump systems subjected to actuator degradation

This paper investigates simultaneous estimations of states, system fault, and sensor fault for a class of Markovian jump systems, resorting to the design of a robust observer, in which both the external disturbance and actuator degradation are taken into consideration. The loss‐of‐effectiveness, stuck, and outage fault cases are involved, and the considered Markovian jump system is assumed to possess generally uncertain transition rates, which can generalize the traditional bounded uncertain transition rates and partially unknown transition rates. In particular, an augmented system whose states cover the original states, system fault, and sensor fault is constructed. Then, a novel adaptive observer is presented with time‐varying gain matrices and parameter accommodation being injected to deal with the disturbance and actuator degradation. Finally, a practical example is shown to demonstrate the high efficiency of the proposed method as well as its advantages over some existing results.