Trajectory Linearization Control Based Output Tracking Method for Nonlinear Uncertain System Using Linear Extended State Observer

Active disturbance rejection based trajectory linearization control for hypersonic reentry vehicle with bounded uncertainties

The problem of feedback linearization (FL) of continuous and discrete nonlinear MIMO systems is considered. The idea of FL method consists in converting the original nonlinear system into a linear one by means of feedback. Then, the methods of control theory for linear systems are used for system design. A widespread approach to FL design is based on the method of normal form, that uses a nonsingular transformation of system state variables z = T(x). In order to obtain a normal form of the nonlinear system in the neighbor of a some point, it is necessary to determine a special function - the system virtual output, for which a relative degree (in the case of single input) or a vector relative degree (in the case of multiple input) is determined. Applicability of the normal form method for FL is provided by the conditions of controllability and involutivity for the considered nonlinear system, which are not always true. Moreover, when developing a linearizing control law, the main difficulty lies in the transition from transformed variables z to state variables x of the original system. In this paper, we propose another approach, based on representing the original nonlinear system into a state-dependent coefficient form and applying the canonical similarity transformation z = T(x)x, that allow getting the system to canonical form, that considerably simplifies the FL problem. Such similarity transformation allow accomplishing linearization of system without determining of the virtual system output. Another advantage of the proposed method is that the technique of the transition from the transformed variables z to the state variables x of the original system is simpler. The results are illustrated by examples for continuous and discrete nonlinear systems.

Aiming at the attitude instability problem caused by the quadrotor’s nonlinearity, strong coupling and susceptibility to external interference, a linear extended state observer (LESO) controller with improved PD was designed. First, the incomplete differential control is formed by adding a first-order inertia system to the differential Elements of the PD algorithm. Then, LESO is used to estimate and compensate the internal and external disturbances in the control system to the original system, which can not only reduce system errors, but also enhance the anti-interference ability of the control system. The MATLAB simulation shows that the improved PD of LESO controller can quickly reach a stable state, effectively improve the stable control ability of the quadrotor’s attitude, with smaller overshoot and better control effect.

In the paper, a linear extended state observer (LESO) is designed for ship heading control with wave disturbance via linear active disturbance rejection control (LADRC). In frequency domain, the tracking ability and disturbance rejection capability of LESO has been analyzed in details. Furthermore, the tradeoff between the closed-loop stability and the system requirements, i.e., rudder, input actuator, can be achieved via parameter tuning, together with active disturbance filtering. Ship heading control is used to as a case study to prove the efficacy of the proposed LESO with simulation experiments.

The DC distribution network has more advantages in power transmission, grid connection of distributed energy, and reliability of power supply when compared with AC distribution network, but there are still many problems in the development of DC distribution network. DC bus voltage control is one of the hot issues in the research of DC distribution network. To solve this problem, in this paper, a new type of sliding mode active disturbance rejection control (SMADRC) controller for AC/DC converters is designed and applied to the voltage outer loop. The linear extended state observer (LESO) can observe the state variables and the total disturbance of the system. The SMADRC is composed of a sliding mode controller, LESO, and disturbance compensator, which can compensate the total disturbance observed by LESO properly. Therefore, it improves the dynamic. At the same time, it can also reduce the system jitter that is caused by sliding mode controller. The state variables that are observed by the LESO are used in the design of sliding mode controller, which greatly simplifies the design of sliding mode controller. Finally, the simulation results of Matlab/Simulink show that the controller has good start-up performance and strong robustness.

Optimized linear active disturbance rejection control for pneumatic servo systems via least squares support vector machine

Stability control of high-speed magnetic levitation turbomolecular pumps with shock-excited disturbance

The suspension gap of the electromagnetic suspension maglev train is around 8 mm. In practice, it is found that the system gap fluctuations are amplified due to the inner coupling of the suspension module system in the maglev train. In addition, maglev trains are affected by load disturbances and parameter perturbations during operation. These uncertainties reduce the ride comfort. Therefore, it is necessary to propose a novel control strategy to suppress inner coupling while reducing the influence of uncertainties on the system. In this paper, a control strategy based on feedback linearization and extended state observer (ESO) is proposed to address this challenge. Firstly, the suspension module system model is established with parameter uncertainties and external disturbances. Additionally, the inner coupling of the suspension module is represented in this model. Subsequently, the feedback linearization method based on differential geometry theory is applied to reduce the effect of inner coupling. Meanwhile, the system uncertainties are transformed into equivalent disturbances by this method. Afterward, a linear ESO is designed to estimate the equivalent disturbances. Finally, a state feedback controller is used to achieve stable suspension and compensate for the disturbances. Simulation and experimental results show that the proposed decoupled control strategy significantly suppresses the influence of inner coupling and uncertainties on the system compared with the traditional PID control strategy.

An improved quasi sliding mode rapid maneuver control algorithm based on linear extended state observer (LESO) of high agile small satellite is proposed. First of all, small satellite dynamics model and kinematics model are established in SGCMGs as actuator. Then, quaternion error feedback control scheme based on quasi sliding mode control is given, effectively weakening the chattering problem of sliding mode control system, realizing the fast mobile of small satellite. Considering the steady-state error of quasi sliding mode control system with disturbance, in order to further improve the steady state performance of the control system, using ADRC theory, the quasi sliding mode attitude control algorithm based on the LESO is designed in this paper. The experimental results show that, the algorithm proposed in this paper can stable and reliable work, motor speed reaches an average of 4.5°/s, the attitude pointing accuracy is better than 0.0035° (3σ), and attitude stability is better than 0.007°/s (3σ).

Moving-gimbal effect suppression for AMB-rotor systems with improved dynamic response in control moment gyroscopes

In this paper, a double closed-loop backstepping controller is designed for 3D trajectory tracking of a turtle-inspired amphibious spherical robot suffering from problems that include model uncertainties, environmental disturbances, and unmeasured velocity. The proposed controller scheme tackles three primary challenges: the differentiation explosion of the traditional backstepping method, unmeasured velocity, and the consideration of lumped disturbances. Beginning with an outer-loop backstepping controller, a virtual feedback variable is constructed to simplify the design of the backstepping controller. Meanwhile, to avoid the problem of differentiation explosion, tracking differentiators (TDs) are utilized to estimate the differentiation of the desired velocity in an inner-loop backstepping controller. Moreover, there are some uncertainty disturbances in the task of tracking the trajectory of a turtle-inspired amphibious spherical robot (TASR), such as the parameters of the hydrodynamic model and environmental disturbances. A linear extended state observer (LESO) is designed to estimate and compensate for the lumped disturbances. Furthermore, as the velocity states of the TASR are unmeasured, the LESO is also utilized to estimate the velocity states in surge, yaw, and heave degrees. Therefore, the TASR only needs to supply its position and orientation information for the trajectory tracking task. Note that this paper details both the design process of the proposed controller and a rigorous theoretical analysis. In addition, numerical simulations are conducted, and the results demonstrate the feasibility and superiority of the proposed method.

Considering the existence of disturbance in the induction machine (IM) drive system, this paper develops a composite control scheme based on linear extended state observer (LESO) and continuous finite time control (FTC) to improve the disturbance rejection property of system. First, a LESO is introduced to estimate the disturbances of system. The estimated value is used in the feed-forward compensation design. Second, a continuous finite-time feedback control technique is applied in the feedback design. Then the stability of the controller is analyzed. Simulation and experimental comparisons with two other control methods, traditional Proportional Integral (PI) and Proportional feedback plus feedforward compensation based on LESO(P+LESO), are provided to verify the effectiveness of the proposed method.

The dual observation of periodic and aperiodic interferences cannot be balanced by traditional linear extended state observer (T-LESO). Therefore, the speed fluctuations caused by uncertain periodic and aperiodic interferences in the interior permanent magnet synchronous motor control system cannot be suppressed by the traditional linear active disturbance rejection controller. To resolve the aforementioned problem, an improved linear active disturbance rejection controller (I-LADRC) in which multifrequency quasi-resonant filtering decoupling linear extended state observer and generalized linear extended state observer (G-LESO) are cascaded is proposed. In this controller, the interference feedforward control method of T-LESO is first changed, the observer bandwidth <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ω_o</i> and controller bandwidth <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ω_c</i> in the transfer function based on the interference term are decoupled from each other, reducing the difficulty of parameter tuning. On this basis, a multifrequency quasi-resonant filter is embedded in the decoupled linear extended state observer (LESO), so that periodic interferences can be accurately observed. For G-LESO, a fourth-order LESO is adopted to enable more accurate observation of aperiodic high-order interferences. The outer loop controller based on I-LADRC is designed, and the correctness and effectiveness of this method are verified through experiments.

In this paper, a systematic procedure for controller design is proposed for a class of nonlinear underactuated systems (UAS), which are non-feedback linearizable but exhibit a controllable (flat) tangent linearization around an equilibrium point. Linear extended state observer (LESO)-based active disturbance rejection control (ADRC) is shown to allow for trajectory tracking tasks involving significantly far excursions from the equilibrium point. This is due to local approximate estimation and compensation of the nonlinearities neglected by the linearization process. The approach is typically robust with respect to other endogenous and exogenous uncertainties and disturbances. The flatness of the tangent model provides a unique structural property that results in an advantageous low-order cascade decomposition of the LESO design, vastly improving the attenuation of noisy and peaking components found in the traditional full order, high gain, observer design. The popular ball and beam system (BBS) is taken as an application example. Experimental results show the effectiveness of the proposed approach in stabilization, as well as in perturbed trajectory tracking tasks.

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.