Reduced-order Disturbance Observer Research Articles

Non-smooth integral sliding surface based control for systems with mismatched disturbances

This paper addresses the problem of traditional sliding mode control design subject to the mismatched disturbance. Existing methods fail to provide an efficient and simple solution. To counteract the unmatched disturbance in the system, a new sliding mode control strategy based on a non-smooth integral sliding manifold is proposed. The proposed sliding manifold has two important features. First, it acts like a reduced order disturbance observer since it estimates the mismatched disturbances by itself without any requirement of an additional observer design. Secondly, the system always starts from the sliding surface, hence, there is no reaching phase dynamics. Thus, the system trajectory is insensitive towards the disturbance from the initial point. The proposed method is tested on a coupled tank system to demonstrate its effectiveness. Both the simulation and experimental results are provided.

비선형 자기부상시스템의 저차 외란관측기 제어기 설계에 대한 연구

In this paper, we study on a reduced-order disturbance observer (DOB) controller for nonlinear Electro-magnetic suspension (EMS) systems with mass uncertainty. Since it is rather complicated to design a nonlinear DOB controller for nonlinear systems, this paper aims to design a linear DOB controller for nonlinear systems. Since noise suppression of reduced-order DOB controller is superior to that of standard DOB controller, this paper focuses on the reduced-order DOB controller. Using the case study of nonlinear EMS systems, it is found that the followings should be carefully chosen for the design of reduced-order DOB controller: high-frequency gain of the nominal model, pole and zero location of the nominal model, selection of Q-filter, and the choice of primary controller.

Reduced-order disturbance observer-based adaptive reaching law control for discretized MIMO systems with unmatched uncertainties

In this paper, an adaptive discrete-time sliding mode control based on reduced-order disturbance observer is proposed for discretized multi-input multi-output systems subjected to unmatching condition. By using the designed discrete reduced-order disturbance observer, a new sliding surface is constructed to counteract the unmatched uncertainties. Then, to guarantee a smaller width of the quasi-sliding mode domain, an adaptive reaching law is developed, whose switching gain is adaptively tuned to prevent overestimation of disturbance on the premise of ensuring the reaching condition of sliding surface; meanwhile, the ranges of the quasi-sliding mode band and attractiveness region are deduced. The proposed control algorithm has low computational complexity and needs no information about the upper bound of unmatched uncertainty. The simulations on the control of a bank-to-turn missile demonstrates that the proposed method can effectively reject unmatched disturbance and provide higher accuracy in comparison with traditional methods.

An Improved Deadbeat Predictive Stator Flux Control With Reduced-Order Disturbance Observer for In-Wheel PMSMs

In this article, an improved deadbeat predictive stator flux control (DPSFC) based on disturbance observer is proposed to address the problems of the steady-state tracking error and robustness decrease due to the detrimental parameter mismatch and disturbance. First, the sensitivity of conventional deadbeat predictive current control to the parameter variation, including flux linkage, stator inductance, and resistance, is analyzed. Then, a reduced-order observer based on additional disturbance state variables in discrete time is designed to predict the future stator flux and observe the system disturbance caused by parameter mismatch. The proposed DPSFC method is able to enhance the robustness of the drive performance effectively via applying the estimated disturbance as the feed-forward compensations of one-step delay and stator voltage. Additionally, the theoretical proof is given. Finally, the superiority of the proposed control method is validated by simulations and experiments on a prototype of an in-wheel permanent magnet synchronous motor drive.

Probabilistic robust anti-disturbance control of uncertain systems

<p style='text-indent:20px;'>We propose a novel method for constructing probabilistic robust disturbance rejection control for uncertain systems in which a scenario optimization method is used to deal with the nonlinear and unbounded uncertainties. For anti-disturbance, a reduced order disturbance observer is considered and a state-feedback controller is designed. Sufficient conditions are presented to ensure that the resulting closed-loop system is stable and a prescribed <inline-formula><tex-math id="M1">\begin{document}$ H_{\infty} $\end{document}</tex-math></inline-formula> performance index is satisfied. A numerical example is presented to illustrate the effectiveness of the techniques proposed and analyzed.

Adaptive Tracking Control for Spacecraft Formation Flying System via Modified Fast Integral Terminal Sliding Mode Surface

In this paper, the fast integral terminal sliding mode control for spacecraft formation flying system is concerned subjected to external disturbances and parametric uncertainties. First, a novel modified fast integral terminal sliding mode control law is designed, which contains the advantages of fast terminal sliding mode. Then, for estimating the external disturbances in the system, the control law based on the reduced-order disturbance observer is proposed which not only reduce the order of the observer but also guarantee the tracking errors converge in finite time. Further, to identify the unknown parameters accurately, by introducing an adaptive parametric updating law, the adaptive fast integral terminal sliding mode control law is proposed, which has better robustness against external disturbances and parameter uncertainties simultaneously. Finally, the effectiveness of the proposed control laws is demonstrated by the simulation results.

Trajectory Tracking Control of Surface Vehicles: A Prescribed Performance Fixed-Time Control Approach

This article focuses on the fixed-time trajectory tracking problem for surface vehicles (SVs) with prescribed performance. First, to realize prescribed performance, the error transformation and fixed-time prescribed performance function are proposed. In this way, the constrained tracking error problem can be solved by the stabilization of the transformed system. Second, by introducing a reduced-order disturbance observer, a fixed-time sliding mode controller is developed to realize trajectory tracking control while satisfying both predefined performance and perturbance rejection. It notices that the associated settling time can be preselected by parameters and independent of system initial conditions. Finally, some simulation examples are provided to illustrate the effectiveness of our theoretical results.

Further results on “Reduced order disturbance observer for discrete-time linear systems”

Reduced order Disturbance OBservers (DOB) have been proposed in Kim et al. (2010) and Kim and Rew (2013) for continuous-time and discrete-time linear systems, respectively. The existence condition of the promising algorithm has been established but is not straightforward to check. This work further improves the reduced order DOB design by formulating it as a functional observer design problem. By carefully designing the state functional matrix, a generic DOB is resulted with an easily-checked necessary and sufficient existence condition and an easily-adjusted convergence rate. It is also shown that both the reduced order DOB in Kim and Rew (2013) and the full order DOB in Chang (2006) are special cases of this new DOB.

Output Feedback Practical Coordinated Tracking of Uncertain Heterogeneous Multi-Agent Systems Under Switching Network Topology

This note proposes a dynamic controller for practical coordinated tracking of uncertain heterogeneous multi-agent systems. The agents are high-order linear systems subject to external disturbances and plant uncertainties, the input to the leader is not known to other agents, and the network topology is time-varying. We adopt a recently developed reduced-order disturbance observer to present a distributed tracking controller which uses only relative measurements. It is shown that the proposed controller can be tuned to ensure the ultimate boundedness of tracking error which can be chosen arbitrarily small despite the network switching, plant uncertainties, and disturbances. Simulation results are provided to show the effectiveness of the proposed controller.

Robust Design of the Uncertainty and Disturbance Estimator

In this paper, the robust design of the Uncertainty and Disturbance Estimator is tackled for a class of nonlinear systems. This strategy combines state-feedback control with a reduced-order disturbance observer. The design procedure is derived in the state-space framework, in contrast to frequency-based design methodologies, which are already studied in the literature. Based on Lyapunov theory, sufficient conditions to ensure closed-loop stability are given in terms of Linear Matrix Inequalities. Furthermore, a computable criterion is derived in order to obtain both the feedback gain matrix and the observer tuning ensuring robust asymptotic stability.

Adaptive backstepping control for an engine cooling system with guaranteed parameter convergence under mismatched parameter uncertainties

This paper proposes a novel adaptive backstepping control for a special class of nonlinear systems with both matched and mismatched unknown parameters. The parameter update laws resemble a nonlinear reduced-order disturbance observer. Thus, the convergence of the estimated parameter values to the true ones is guaranteed. In each recursive design step, only single parameter update law is required in comparison to the existing standard adaptive backstepping techniques based on overparametrization and tuning functions. To make a fair comparison with the overparametrization and tuning function methods, a second-order nonlinear engine cooling system is taken as a benchmark problem. This system is subject to both matched and mismatched state-dependent lumped disturbances. Moreover, the proposed model-based controllers are compared with a classical PI control by using performance metrics, i.e., root-mean-square error and control effort. The comparative analysis based on these performance metrics, simulations as well as experiments highlights the effectiveness of the proposed novel adaptive backstepping control in terms of asymptotic tracking, global stability and guaranteed parameter convergence.

무게변동을 고려한 자기부상시스템의 저차 외란관측기 제어기 설계

무게변동을 고려한 자기부상시스템의 저차 외란관측기 제어기 설계

Reduced-order disturbance observer design for discrete-time linear stochastic systems

Conventional disturbance observers for discrete-time linear stochastic systems assume that the system states are fully estimable and the disturbance estimate is dependent on the estimated system states, hereafter termed full-order disturbance observers (FODOs). This paper investigates the design of reduced-order disturbance observers (RODOs) when the system state variables are not fully estimable. An existence condition of RODOs is established, which is shown to be more easily satisfied than that of conventional FODOs and consequently it has substantially extended the scope of applications of disturbance observer theory. Then a set of recursive formulae for the RODO is developed for online applications. Finally, it is further shown that the conventional FODOs are a special case of the proposed RODO in the sense that the former reduces to the RODO when the states become fully estimable in the presence of disturbances. Examples are given to demonstrate the effectiveness and advantages of the proposed approach.

Adaptive Sliding-Mode Control of an Innovative Engine Cooling System

Abstract: This paper proposes a novel adaptive sliding-mode control for an innovative engine cooling system under the influence of both matched and mismatched lumped disturbances. The parameter update laws resemble a nonlinear reduced-order disturbance observer and guarantee the convergence of the estimated parameter values to the real ones. Experiments on a dedicated test rig highlight the effectiveness of the proposed novel adaptive sliding-mode control in terms of asymptotic tracking, global stability and guaranteed parameter convergence. The closed-loop stability of the overall system is established by using Lyapunov’s direct method. To provide a fair comparison, the performance of the proposed controller is compared with a PI-controller.

축소 차수 외란 관측기를 이용한 이종 다개체 시스템의 협조 추종 제어

This paper proposes a reduced-order disturbance observer based coordinated tracking controller for uncertain heterogeneous multi-agent systems. To this end, first the control problem is converted as a robust control problem. Then, a dynamic coordinated controller is designed based on the recently proposed reduced-order disturbance observer. Simulation results are given to show the effectiveness of the proposed control scheme.

Comparison of Nonlinear Flatness-Based Control of two Coupled Hydraulic Servo Cylinders

This paper presents two nonlinear model-based control designs for a hydraulic system that consists of two mechanically coupled hydraulic cylinders actuated each by a separate servo-valve. Based on a physically-oriented nonlinear mathematical model of the test rig, a further model simplification results in a completely controllable MIMO system. Two different control structures are discussed and compared to each other in this paper: First, a cascaded flatness-based control is designed, where fast inner control loops determine the difference pressure in each hydraulic cylinder, while the position as well as the generated force is controlled in the outer loop. In the second approach, a centralised flatness-based control, with the same outputs as in the outer loop of the cascaded approach, is developed for the MIMO system. Model parameter uncertainties are estimated by a reduced-order disturbance observer and compensated by the control algorithm. The efficiency of the proposed control structures is demonstrated by experimental results from a dedicated test rig.

An Adaptive Nonlinear Control for Gyro Stabilized Platform Based on Neural Networks and Disturbance Observer

In order to improve the tracking performance of gyro stabilized platform with disturbances and uncertainties, an adaptive nonlinear control based on neural networks and reduced-order disturbance observer for disturbance compensation is developed. First the reduced-order disturbance observer estimates the disturbance directly. The error of the estimated disturbance caused by parameter variation and measurement noise is then approximated by neural networks. The phase compensation is also introduced to the proposed control law for the desired sinusoidal tracking. The stability of the proposed scheme is analyzed by the Lyapunov criterion. Experimental results show the validity of the proposed control approach.

A novel disturbance-observer based friction compensation scheme for ball and plate system

Friction is often ignored when designing a controller for the ball and plate system, which can lead to steady-error and stick-slip phenomena, especially for the small amplitude command. It is difficult to achieve high-precision control performance for the ball and plate system because of its friction. A novel reference compensation strategy is presented to attenuate the aftereffects caused by the friction. To realize this strategy, a linear control law is proposed based on a reduced-order observer. Neither the accurate friction model nor the estimation of specific characteristic parameters is needed in this design. Moreover, the describing function method illustrates that the limit cycle can be avoided. Finally, the comparative mathematical simulations and the practical experiments are used to validate the effectiveness of the proposed method.

Reduced order disturbance observer for discrete-time linear systems

In the paper, an output-based disturbance observer of reduced order is presented for a class of discrete-time linear systems. First, a general form of a disturbance observer is proposed when full states are available. Then, by combining a state function estimator of minimal order, an output-based disturbance observer is derived. The existence condition will be formulated in the form of a static output feedback. Through examples, the effectiveness and advantages of the proposed approach will be demonstrated. A servo control problem in practice is addressed to show the validity of the approach. Furthermore, it will be shown that the proposed approach does provide a smaller order of disturbance observer than that of conventional approaches, while maintaining satisfactory performances.

Robust Inverse Dynamics Control for a Hydrostatic Transmission with Actuator Uncertainties

This paper presents a robust inverse dynamics control strategy in combination with a reduced-order disturbance observer for a hydrostatic transmission. The corresponding nonlinear system model, however, is characterized by only imperfectly known system parameters – actuator time constants – and unknown disturbances – a leakage volume flow and a disturbance torque acting on the hydraulic motor. The proposed approach involves three different control actions: 1) an inverse dynamics control that allows for tracking desired trajectories for the difference pressure and the motor angular velocity, 2) a robust control that stabilizes the error dynamics despite uncertain actuator time constants, and 3) a reduced-order disturbance observer that estimates the leakage volume flow as well as the unknown load torque and allows for a disturbance compensation. Simulation results show that with the proposed approach an accurate trajectory tracking is achieved despite the uncertain time constants and the given disturbances in the system dynamics.