Output tracking control for a velocity-sensorless VTOL aircraft with measurement delays

In this paper, we develop a non-linear controller to achieve output tracking for a velocity-sensorless vertical take-off and landing (VTOL) aircraft in the presence of measurement delays. By applying the Pade approximation technique, the original controlled system is transformed into an augmented dimension system without any time delay. After constructing full-order observers, error coordinate transformation, and system decomposition, the tracking problem of the newly transformed system is changed into the stabilisation problem of two non-minimum phase subsystems and one minimum phase subsystem. The resulting controller not only forces the VTOL aircraft to asymptotically track the desired trajectories, but also drives the unstable internal dynamics, which stands for the non-minimum property of VTOL aircraft, to follow the causal ideal internal dynamics (IID) solved via the stable system centre (SSC) method. Numerical simulation results illustrate the effectiveness of the proposed controller.     

Robust output tracking control of a class of non-minimum phase systems and application to VTOL aircraft

In this article, we study the output tracking control of a class of MIMO nonlinear non-minimum phase systems in the presence of input disturbances. In order to attenuate the effects of disturbances, the method of uncertainty and disturbance estimator (UDE) is extended to the controller design for non-minimum phase systems. Due to the fact that the accumulated disturbances is composed of internal states and external disturbances, a different stability analysis is given, and the overall closed-loop system is proved to be semi-globally stable. The proposed state-feedback controller not only forces system outputs to asymptotically track desired trajectories, but also drives the unstable internal dynamics to follow bounded and causal ideal internal dynamics (IID) solved via stable system centre (SSC) method. Simulation results demonstrate that the proposed controller achieves excellent tracking and disturbance rejection performance via the example of VTOL aircraft which has been the benchmark of nonlinear non-minimum phase systems.     

Additive‐state‐decomposition‐based tracking control framework for a class of nonminimum phase systems with measurable nonlinearities and unknown disturbances

This paper aims to propose an additive‐state‐decomposition‐based tracking control framework, based on which the output feedback tracking problem is solved for a class of nonminimum phase systems with measurable nonlinearities and unknown disturbances. This framework is to ‘additively’ decompose the output feedback tracking problem into two more tractable problems, namely an output feedback tracking problem for a linear time invariant system and a state feedback stabilization problem for a nonlinear system. Then, one can design a controller for each problem respectively using existing methods, and these two designed controllers are combined together to achieve the original control goal. The main contribution of the paper lies on the introduction of an additive state decomposition scheme and its implementation to mitigate the design difficulty of the output feedback tracking control problem for nonminimum phase nonlinear systems. To demonstrate the effectiveness, an illustrative example is given. Copyright © 2013 John Wiley & Sons, Ltd.     

Global asymptotic tracking for nonminimum‐phase nonlinear systems in output feedback form

The problem of global asymptotic tracking by output feedback is studied for a class of nonminimum‐phase nonlinear systems in output feedback form. It is proved that the problem is solvable by an n‐dimensional output feedback controller under the two conditions: (a) the nonminimum‐phase nonlinear system can be rendered minimum‐phase by a virtual output; and (b) the internal dynamics of the nonlinear system driven by a desired signal and its derivatives has a bounded solution trajectory. With the help of a new coordinate transformation, a constructive method is presented for the design of a dynamic output tracking controller. An example is given to validate the proposed output feedback tracking control scheme.     

Dynamic output feedback control with output quantizer for nonlinear uncertain T‐S fuzzy systems with multiple time‐varying input delays and unmatched disturbances

The dynamic output feedback control problem with output quantizer is investigated for a class of nonlinear uncertain Takagi‐Sugeno (T‐S) fuzzy systems with multiple time‐varying input delays and unmatched disturbances. The T‐S fuzzy model is employed to approximate the nonlinear uncertain system, and the output space is partitioned into operating regions and interpolation regions based on the structural information in the fuzzy rules. The output quantizer is introduced for the controller design, and the dynamic output feedback controller with output quantizer is constructed based on the T‐S fuzzy model. Stability conditions in the form of linear matrix inequalities are derived by introducing the S‐procedure, such that the closed‐loop system is stable and the solutions converge to a ball. The control design conditions are relaxed and design flexibility is enhanced because of the developed controller. By introducing the output‐space partition method and S‐procedure, the unmatched regions between the system plant and the controller caused by the quantization errors can be solved in the control design. Finally, simulations are given to verify the effectiveness of the proposed method.     

风浪流干扰及参数不确定欠驱动船舶航迹跟踪的滑模鲁棒控制

针对欠驱动船舶的模型参数不确定和外界风浪流干扰问题,为实现水平面的航迹跟踪控制,提出了一种基于上下界的滑模控制方法.首先利用反步法将控制器的设计分解为运动学回路和动力学回路.其次,在运动学回路中为实现位置跟踪误差的收敛,根据期望航迹与当前位置信息,设计船舶的纵向与侧移参考速度,并视为镇定位置误差的虚拟控制律;在动力学回路中,将虚拟控制律作为新的跟踪目标,利用滑模方法设计实际控制律实现对参考速度的跟踪控制,最终实现了欠驱动船舶的跟踪控制.最后对有无干扰下的欠驱动船模分别进行了仿真实验,仿真结果证明了控制律的有效性.     

Robust output tracking control of a laboratory helicopter for automatic landing

In this paper, robust output tracking control problem of a laboratory helicopter for automatic landing in high seas is investigated. The motion of the helicopter is required to synchronise with that of an oscillating platform, e.g. the deck of a vessel subject to wave-induced motions. A robust linear time-invariant output feedback controller consisting of a nominal controller and a robust compensator is designed. The robust compensator is introduced to restrain the influences of parametric uncertainties, nonlinearities and external disturbances. It is shown that robust stability and robust tracking property can be achieved simultaneously. Experimental results on the laboratory helicopter for automatic landing demonstrate the effectiveness of the designed control approach.     

Finite-time consensus tracking for multi-agent systems with inherent uncertainties and disturbances

In this paper, finite-time consensus tracking is investigated via time-varying feedback for uncertain nonlinear multi-agent systems (NMASs). The presence of inherent uncertainties and disturbances in the NMASs highlights the main novelty : (1) The inherent uncertainties imply that more serious unknowns and time-variations are allowed in the nonlineartities and the control coefficients of the NMASs. (2) The inherent disturbances mean that the upper bound of the disturbances is unknown. To compensate the inherent uncertainties and disturbances, time-varying protocols are proposed by integrating time-varying technique and sliding mode method. Based on the proposed protocols, the finite-time leader-following consensus and finite-time containment are achieved under directed graph. Finally, the validation of the proposed protocols is verified by two examples.     

Robust adaptive output feedback control of a class of discrete‐time nonlinear systems with nonlinear uncertainties and unknown control directions

In this paper, robust adaptive output feedback control is studied for a class of discrete‐time nonlinear systems with functional nonlinear uncertainties of the Lipschitz type and unknown control directions. In order to construct an output feedback control, the system is transformed into the form of a nonlinear autoregressive moving average with eXogenous inputs (NARMAX) model. In order to avoid the noncausal problem in the control design, future output prediction laws and parameter update laws with the dead‐zone technique are constructed on the basis of the NARMAX model. With the employment of the predicted future outputs, a constructive output feedback adaptive control is proposed, where the discrete Nussbaum gain technique and the dead‐zone technique are used in parameter update laws. The effect of the functional nonlinear uncertainties is compensated for, such that an asymptotic tracking performance is achieved, whereas other signals in the closed‐loop systems are guaranteed to be bounded. Simulation studies are performed to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust tracking control for a class of MIMO nonlinear systems with measurable output feedback

This paper proposes a robust output feedback controller for a class of nonlinear systems to track a desired trajectory. Our main goal is to ensure the global input-to-state stability (ISS) property of the tracking error nonlinear dynamics with respect to the unknown structural system uncertainties and external disturbances. Our approach consists of constructing a nonlinear observer to reconstruct the unavailable states, and then designing a discontinuous controller using a back-stepping like design procedure to ensure the ISS property. The observer design is realized through state transformation and there is only one parameter to be determined. Through solving a Hamilton–Jacoby inequality, the nonlinear control law for the first subsystem specifies a nonlinear switching surface. By virtue of nonlinear control for the first subsystem, the resulting sliding manifold in the sliding phase possesses the desired ISS property and to certain extent the optimality. Associated with the new switching surface, the sliding mode control is applied to the second subsystem to accomplish the tracking task. As a result, the tracking error is bounded and the ISS property of the whole system can be ensured while the internal stability is also achieved. Finally, an example is presented to show the effectiveness of the proposed scheme. Copyright © 2007 John Wiley & Sons, Ltd.     

Sliding mode output‐feedback causal output tracking for a class of discrete‐time nonlinear systems

The output tracking (OT) of arbitrary references in discrete‐time (DT) nonlinear systems is addressed by designing an output‐feedback control. A set of difference‐algebraic equations is proposed as an exact solution of the problem. Using a novel technique of approximating DT functions, the system disturbance and steady states, characterized by tracking error identically zero, for both the system state and the control input, are represented as signals generated by a disturbed dynamic system. Using the mentioned dynamics, the control system is extended. Then, a state observer is proposed to estimate the resulting extended system state. Finally, a DT sliding mode controller is designed to achieve the approximate OT. Simulations show the effectiveness of the proposed control scheme.     

Robust adaptive multi-task tracking control of redundant manipulators with dynamic and kinematic uncertainties and unknown disturbances

In this paper, a novel adaptive multi-priority controller for redundant manipulators is proposed to accomplish the multi-task tracking when kinematic/dynamic uncertainties and unknown disturbances exist. Prioritized redundancy resolution in kinematic level is incorporated into this passivity-based control framework. The kinematic and dynamic parameter adaptations are driven by both tracking error and prediction error. Moreover, the tracking information from both primary and subtasks are all utilized to accelerate the parameter estimation when the tasks are independent, whereas the inevitable tracking error of the subtasks due to algorithmic singularities is properly eliminated in the adaptation laws when the tasks are dependent. Potential ill-conditioned solution of the pseudoinverse is avoided using an improved singularity-robust inverse of the projected Jacobian. Along with the improvement of the multi-task tracking performance, smoothness of the commanded torques is still guaranteed for easy application. Measurements of the noisy joint acceleration and task velocity are avoided. The controller is mathematically derived based on Lyapunov stability analysis. Simulation results of the two cases are presented to verify the effectiveness and superiority of the proposed controller.     

Adaptive tracking control of MIMO nonlinear nonminimum phase system with unknown input nonlinearity

This paper proposes a nonlinear adaptive control for output tracking of multi‐input multi‐output nonlinear nonminimum phase system with input nonlinearity. The parameters of the input nonlinearity are assumed to be unknown. This problem is challenging, not only because of the unstable internal dynamics of nonminimum phase system, but also the existence of the unknown input nonlinearity. The partially linearized model of the original system is obtained through input/output linearization, and a states tracking model is constructed based on the computed ideal internal dynamics. A nonlinear adaptive controller, which can guarantee the bounded of output tracking error in the existence of unknown input nonlinearity, is proposed. Finally, a numerical simulation on vertical takeoff and landing aircraft is given to show the effectiveness of the proposed control methods.     

Robust adaptive control of a class of nonlinear strict-feedback discrete-time systems with exact output tracking

In this paper, adaptive control is studied for a class of single-input–single-output (SISO) nonlinear discrete-time systems in strict-feedback form with nonparametric nonlinear uncertainties of the Lipschitz type. To eliminate the effect of the nonparametric uncertainties in an unmatched manner, a novel future states prediction is designed using states information at previous steps to compensate for the effect of uncertainties at the current step. Utilizing the predicted future states, constructive adaptive control is developed to compensate for the effects of both parametric and nonparametric uncertainties such that global stability and asymptotical output tracking is achieved. The effectiveness of the proposed control law is demonstrated in the simulation.     

Output feedback sliding‐mode control with unmatched disturbances,an ISS approach

The robustness properties of a first‐order sliding‐mode controller are combined with those of an added linear term in order to obtain a closed loop that shows input‐to‐state stability with respect to matched and unmatched disturbances, of which an upper bound might not be known, using only output information. The output under consideration can have any relative degree. Also, a transformation of the state into a novel output normal form is presented. The zero dynamics are considered unstable and perturbed, so a methodology for defining an observer and a virtual control for it is presented. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust control of a family of uncertain nonminimum‐phase systems via continuous‐time and sampled‐data output feedback

The problem of global robust stabilization is studied by both continuous‐time and sampled‐data output feedback for a family of nonminimum‐phase nonlinear systems with uncertainty. The uncertain nonlinear system considered in this paper has an interconnect structure consisting of a driving system and a possibly unstable zero dynamics with uncertainty, ie, the uncertain driven system. Under a linear growth condition on the uncertain zero dynamics and a Lipschitz condition on the driving system, we show that it is possible to globally robustly stabilize the family of uncertain nonminimum‐phase systems by a single continuous‐time or a sampled‐data output feedback controller. The sampled‐data output feedback controller is designed by using the emulated versions of a continuous‐time observer and a state feedback controller, ie, by holding the input/output signals constant over each sampling interval. The design of either continuous‐time or sampled‐data output compensator uses only the information of the nominal system of the uncertain controlled plant. In the case of sampled‐data control, global robust stability of the hybrid closed‐loop system with uncertainty is established by means of a feedback domination method together with the robustness of the nominal closed‐loop system if the sampling time is small enough.     

Distributed finite-time trajectory tracking control for multiple nonholonomic mobile robots with uncertainties and external disturbances

This paper investigates the distributed finite-time trajectory tracking control for a group of nonholonomic mobile robots with time-varying unknown parameters and external disturbances. At first, the tracking error system is derived for each mobile robot with the aid of a global invertible transformation, which consists of two subsystems, one is a first-order subsystem and another is a second-order subsystem. Then, the two subsystems are studied respectively, and finite-time disturbance observers are proposed for each robot to estimate the external disturbances. Meanwhile, distributed finite-time tracking controllers are developed for each mobile robot such that all states of each robot can reach the desired value in finite time, where the desired reference value is assumed to be the trajectory of a virtual leader whose information is available to only a subset of the followers, and the followers are assumed to have only local interaction. The effectiveness of the theoretical results is finally illustrated by numerical simulations.     

Robust output tracking for heterogeneous double-integrator dynamics with external disturbance

This paper studies the robust output tracking for heterogeneous double-integrator dynamics with external disturbance. It is assumed that there exist interactions among agents and their neighbours. All the agents have non-identical dynamics with others, and all the system matrices are unknown. A state feedback control protocol with only neighbours information is proposed based on a distributed compensator for non-identical dynamics and an internal-model compensator for the unknown parts. By the algebraic graph theory and matrix theory, sufficient conditions are given to guarantee that all the outputs of the agents converge to the reference output as time tends to infinity. Finally, two numerical simulations are provided to illustrate the effectiveness of the theoretical results.     

输出重定义方法设计垂直/短距起降飞机高度控制器

垂直/短距起降飞机是一类典型的非最小相位系统.系统的负调特性使得飞机高度响应比较缓慢,并且会在初始阶段响应为负,从而出现不期望的掉高现象.针对该问题,本文设计了新的最小相位输出预估控制器,通过调节近似输出零点的方法提高系统的动态响应;对于负调部分,采用两步参数整定的方法设计PID控制器,达到抑制负调的作用.最后,对飞机的高度俯仰控制进行了仿真验证,结果表明设计的控制器对飞机高度初始负调具有明显的抑制作用,并且缩短了回复上升所需的时间.     

非匹配扰动干扰下的无人直升机轨迹跟踪控制

针对小型无人直升机在飞行过程中容易受到非匹配扰动影响的特点,本文设计了一种基于新型滑模控制方法的轨迹跟踪控制器.首先,建立了无人直升机系统的非线性数学模型,并对该模型进行近似反馈线性化处理,同时将模型分为位置和偏航两个子系统;然后,利用扩展扰动观测器对复合扰动以及非匹配扰动的各阶导数的估计值,设计新型时变滑模面,得到滑模控制律,并给出了控制系统的稳定性分析;最后,仿真结果验证了控制方法的有效性和优越性.该新型滑模控制方法的优越性主要体现在:对非匹配扰动具有较强的鲁棒性,以及能有效地抑制抖振现象.