Aggressive Longitudinal Aircraft Path Tracking Using Nonlinear Control

We study the problem of converting a trajectory tracking controller to a path tracking controller for a nonlinear non-minimum phase longitudinal aircraft model. The solution of the trajectory tracking problem is based on the requirement that the aircraft follows a given time parameterized trajectory in inertial frame. In this paper we introduce an alternative nonlinear control design approach called path tracking control. The path tracking approach is based on designing a nonlinear state feedback controller that maintains a desired speed along a desired path with closed loop stability. This design approach is different from the trajectory tracking approach where aircraft speed and position are regulated along the desired path. The path tracking controller regulates the position errors transverse to the desired path but it does not regulate the position error along the desired path. First, a trajectory tracking controller, consisting of feedforward and static state feedback, is designed to guarantee uniform asymptotic trajectory tracking. The feedforward is determined by solving a stable noncausal inversion problem. Constant feedback gains are determined based on LQR with singular perturbation approach. A path tracking controller is then obtained from the trajectory tracking controller by introducing a suitable state projection.     

A HIL Testbed for Initial Controller Gain Tuning of a Small Unmanned Helicopter

A Hardware-In-The-Loop (HIL) testbed design for small unmanned helicopters which provides a safe and low-cost platform to implement control algorithms and tune the control gains in a controlled environment is described. Specifically, it allows for testing the robustness of the controller to external disturbances by emulating the hover condition. A 6-DOF nonlinear mathematical model of the helicopter has been validated in real flight tests. This model is implemented in real-time to estimate the states of the helicopter which are then used to determine the actual control signals on the testbed. Experiments of the longitudinal, lateral and heading control tests are performed. To minimize the structural stress on the fuselage in case of controller failure or a subsystem malfunction, a damping system with a negligible parasitic effect on the dynamics of the helicopter around hover is incorporated. The HIL testbed is capable of testing the helicopter in hover, as well as on any smooth trajectories such as cruise flight, figure-8, etc. Experimentally tuning the controller on the HIL testbed is described and results in a controller which is robust to the external disturbances, and achieves an accuracy of ±2.5 cm in the position control on the longitudinal and lateral trajectory tracking, and ±5 deg accuracy around the yaw axis on the heading trajectory tracking.     

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.     

Trajectory linearization based output tracking control of an unmanned tandem helicopter with variance constraints

An output tracking control problem for an unmanned tandem rotor helicopter with variance constraints is investigated in this paper. A modified Trajectory Linearization Control (TLC) is proposed to stabilize a nonlinear continuous-time flight dynamics system of the tandem helicopter. The tracking controller structure of TLC is designed by using two-time-scale nonlinear dynamic inversion. The base control law of the translational and attitude loops is designed in a pseudo-inversion feedforward controller to deal with nonlinear features of the plant and a proportional integral controller to stabilize the linear slowly time-variant error system resulted from the nonlinear flight system. Furthermore, a feasible TLC strategy is designed to meet a performance index set including steady trajectory tracking error variance and desired Parallel D-spectrum (PD-) eigenvalues to achieve good flight quality. The Variance-constrained Trajectory Linearization Control (VCTLC) is designed to realize the desired steady tracking precision and agile capability. Flight simulation results show the VCTLC method is feasible and effective in attitude and altitude tracking.     

主旋翼升力和机身姿态受限的模型直升机非线性控制（英文）

A nonlinear control is proposed for trajectory tracking of a 6-DOF model-scaled helicopter with constraints on main rotor thrust and fuselage attitude. In the procedure of control design, the mathematical model of helicopter is simplified into three subsystems: altitude subsystem, longitudinal-lateral subsystem and attitude subsystem. The proposed control is developed by combining the sub-controls for the corresponding subsystems. The sub-controls for altitude subsystem and longitudinal-lateral subsystem are designed with hyperbolic tangent functions to satisfy the constraints; the sub-control for attitude subsystem is based on backstepping technique such that fuselage attitude tracks the virtual control for longitudinallateral subsystem. It is proved theoretically that tracking errors are ultimately bounded, and control constraints are satisfied.Performances of the proposed controller are demonstrated by simulation results.     

主旋翼升力和机身姿态受限的模型直升机非线性控制

针对主旋翼升力和机身姿态受限的6自由度模型无人直升机的轨迹跟踪控制问题设计了一种非线性控制器.在控制器设计过程中,直升机的数学模型被简化为三个子系统: 姿态子系统,纵-侧向子系统和高度子系统,所设计的控制器由针对这三个子系统的子控制器组成.纵-侧向和高度子控制器基于双曲正切函数进行设计,以保证满足受限条件; 姿态子控制器利用反步法设计,使得机身姿态能够跟踪纵-侧向和高度子系统的虚拟控制.本文在理论上证明了闭环系统跟踪误差最终有界,并且控制器满足受限条件.仿真结果证实了所设计控制器的性能.     

From the Test Benches to the First Prototype of the muFly Micro Helicopter

The goal of the European project muFly is to build a fully autonomous micro helicopter, which is comparable to a small bird in size and mass. The rigorous size and mass constraints infer various problems related to energy efficiency, flight stability and overall system design. In this research, aerodynamics and flight dynamics are investigated experimentally to gather information for the design of the helicopter’s propulsion group and steering system. Several test benches are designed and built for these investigations. A coaxial rotor test bench is used to measure the thrust and drag torque of different rotor blade designs. The effects of cyclic pitching of the swash plate and the passive stabilizer bar are studied on a test bench measuring rotor forces and moments with a 6–axis force sensor. The gathered knowledge is used to design a first prototype of the muFly helicopter. The prototype is described in terms of rotor configuration, structure, actuator and sensor selection according to the project demands, and a first version of the helicopter is shown. As a safety measure for the flight tests and to analyze the helicopter dynamics, a 6DoF vehicle test bench for tethered helicopter flight is used.     

Nonlinear adaptive model following control for a 3-DOF tandem-rotor model helicopter

This paper considers two-input, two-output nonlinear adaptive model following control of a 3-DOF (degree-of-freedom) tandem rotor model helicopter. The control performance is studied by real time implementation of the control algorithms in an actual helicopter testbed. Since the decoupling matrix of the model helicopter is singular, the system is not decouplable by static state feedback, and it is challenging to design a feedback control system. Dynamic state feedback is applied. The controller is designed using a nonlinear structure algorithm. Furthermore, a parameter identification scheme is introduced in the closed-loop system to improve the control performance. Three identification methods are discussed.     

Model‐assisted extended state observer and dynamic surface control–based trajectory tracking for quadrotors via output‐feedback mechanism

In this paper, an output‐feedback trajectory tracking controller for quadrotors is presented by integrating a model‐assisted extended state observer (ESO) with dynamic surface control. The quadrotor dynamics are described by translational and rotational loops with lumped disturbances to promote the hierarchical control design. Then, by exploiting the structural property of the quadrotor, a model information–assisted high‐order ESO that relies only on position measurements is designed to estimate not only the unmeasurable states but also the lumped disturbances in the rotational loop. In addition, to account for the problem of “explosion of complexity” inherent in hierarchical control, the output feedback–based trajectory tracking and attitude stabilization laws are respectively synthesized by utilizing dynamic surface control and the corresponding estimated signals provided by the ESO. The stability analysis is given, showing that the output‐feedback trajectory tracking controller can ensure the ultimate boundedness of all signals in the closed‐loop system and make the tracking errors arbitrarily small. Finally, flight simulations with respect to an 8‐shaped trajectory command are performed to verify the effectiveness of the proposed scheme in obtaining the stable and accurate trajectory tracking using position measurements only.     

共轴式无人直升机建模与鲁棒跟踪控制

针对共轴式无人直升机非线性、强耦合的动力学特性,本文提出了一种基于动态反馈线性化方法的鲁棒跟踪控制策略.首先根据叶素理论、Pitt-Peters动态入流模型、上下旋翼气动干扰分析建立了共轴式无人直升机的数学模型.然后对于高度-姿态子系统,通过扩展状态变量对其进行了动态反馈线性化,分析了零动态特性.根据内环期望跟踪特性对解耦后的子系统进行极点配置.通过设计鲁棒补偿器实现了对高度与姿态指令的鲁棒跟踪.在此基础上,针对水平面内的位置子系统设计了外环比例微分(proportional-derivative,PD)控制器以实现位置跟踪.最后,通过内环跟踪仿真验证了反馈线性化方法良好的解耦特性,通过干扰条件下的轨迹跟踪仿真验证了所设计控制器具有较好的控制性能与鲁棒性.     

Sliding mode control of singularly perturbed systems and its application in quad-rotors

This paper presents a sliding mode control scheme for tracking control of nonlinear singularly perturbed systems in the presence of model errors and external disturbances. A dual-loop feedback control is developed to provide accurate tracking capability and sufficient robustness to system uncertainties. A sliding mode controller is proposed in the outer-loop feedback design such that the plant states are stabilised for given reference trajectories, while an additional robust controller is designed in the inner loop to increase the adaptability to uncertainties, and reduce the effect of unmodelled high-frequency dynamics on plant dynamics. An appealing feature of the control scheme is the attenuation of chattering. The effectiveness and merits of the new control scheme developed are shown via a verification example of velocity control of a quad-rotor.     

Nonlinear asymptotic attitude tracking control of an underactuated 3-degree-of-freedom helicopter using neural network feedforward term

This paper proposes a new asymptotic attitude tracking controller for an underactuated 3-degree-of-freedom (DOF) laboratory helicopter system by using a nonlinear robust feedback and a neural network (NN) feedforward term. The nonlinear robust control law is developed through a modified inner-outer loop approach. The application of the NN-based feedforward is to compensate for the system uncertainties. The proposed control design strategy requires very limited knowledge of the system dynamic model, and achieves good robustness with respect to system parametric uncertainties. A Lyapunov-based stability analysis shows that the proposed algorithms can ensure asymptotic tracking of the helicopter’s elevation and travel motion, while keeping the stability of the closed-loop system. Real-time experiment results demonstrate that the controller has achieved good tracking performance.     

Adaptive output feedback control of uncertain nonlinear systems using single-hidden-layer neural networks

We consider adaptive output feedback control of uncertain nonlinear systems, in which both the dynamics and the dimension of the regulated system may be unknown. However, the relative degree of the regulated output is assumed to be known. Given a smooth reference trajectory, the problem is to design a controller that forces the system measurement to track it with bounded errors. The classical approach requires a state observer. Finding a good observer for an uncertain nonlinear system is not an obvious task. We argue that it is sufficient to build an observer for the output tracking error. Ultimate boundedness of the error signals is shown through Lyapunov's direct method. The theoretical results are illustrated in the design of a controller for a fourth-order nonlinear system of relative degree two and a high-bandwidth attitude command system for a model R-50 helicopter.     

Adaptive neural output feedback tracking control for a class of nonlinear systems

In this paper, an adaptive neural output feedback control scheme based on backstepping technique and dynamic surface control (DSC) approach is developed to solve the tracking control problem for a class of nonlinear systems with unmeasurable states. Firstly, a nonlinear state observer is designed to estimate the unmeasurable states. Secondly, in the controller design process, radial basis function neural networks (RBFNNs) are utilised to approximate the unknown nonlinear functions, and then a novel adaptive neural output feedback tracking control scheme is developed via backstepping technique and DSC approach. It is shown that the proposed controller ensures that all signals of the closed-loop system remain bounded and the tracking error converges to a small neighbourhood around the origin. Finally, two numerical examples and one realistic example are given to illustrate the effectiveness of the proposed design approach.     

TORQUE AND FLUX TRACKING OF INDUCTION MOTORS

The problem of torque tracking and rotor flux norm regulation of induction motors perturbed by an unknown constant load torque was recently solved with an observer-based controller in Reference 5. In this paper we extend this result to treat the practically important case when the rotor flux norm is required to follow a time-varying reference. The controller design follows the passivity-based approach and proceeds in two steps: first, we define a target closed-loop dynamics compatible with the physical model of the motor that delivers the desired rotor flux and torque. Second, we propose a nonlinear dynamic output feedback controller that ensures this behaviour is asymptotically achieved. A proof of global tracking is given under the assumption of known motor parameters. Some key features of our physically based design are that the control law does not require measurement of rotor variables, is always well defined and does not rely on (intrinsically nonrobust) nonlinear dynamics cancellation. A corollary of our main result is the proof that a slight modification of the classical indirect field-oriented controller ensures global tracking for current-fed machines. © 1997 by John Wiley & Sons, Ltd.     

Investigations on the Hybrid Tracking Control of an Underactuated Autonomous Underwater Robot

The problem of trajectory tracking control of an underactuated autonomous underwater robot (AUR) in a three-dimensional (3-D) space is investigated in this paper. The control of an underactuated robot is different from fully actuated robots in many aspects. In particular, these robot systems do not satisfy Brockett's necessary condition for feedback stabilization and no continuous time-invariant state feedback control law exists that makes a specified equilibrium of the closed-loop system asymptotically stable. The uncertainty of hydrodynamic parameters, along with the coupled, nonlinear dynamics of the underwater robot, also makes the navigation and tracking control a difficult task. The proposed hybrid control law is developed by combining sliding mode control (SMC) and classical proportional–integral–derivative (PID) control methods to reduce the tracking errors arising out of disturbances, as well as variations in vehicle parameters like buoyancy. Here, a trajectory planner computes the body-fixed linear and angular velocities, as well as vehicle orientations corresponding to a given 3-D inertial trajectory, which yields a feasible 6-d.o.f. trajectory. This trajectory is used to compute the control signals for the three available controllable inputs by the hybrid controller. A supervisory controller is used to switch between the SMC and PID control as per a predefined switching law. The switching function parameters are optimized using Taguchi design techniques. The effectiveness and performance of the proposed controller is investigated by comparing numerically with classical SMC and traditional linear control systems in the presence of disturbances. Numerical simulations using the full set of nonlinear equations of motion show that the controller does quite well in dealing with the plant nonlinearity and parameter uncertainties for trajectory tracking. The proposed controller response shows less tracking error without the usually present control chattering. Some practical features of this control law are also discussed.     

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.     

An Approximate Backstepping Based Trajectory Tracking Control of a Gun Launched Micro Aerial Vehicle in Crosswind

This paper considers the question of obtaining a nonlinear trajectory tracking control law for a comprehensive design of a Gun Launched Micro Aerial Vehicle (GLMAV) despite unknown aerodynamic efforts. To this purpose, a nonlinear mathematical model of the GLMAV is firstly presented for hover and near hover flight conditions. Then, an approximate backstepping control law is derived, allowing the trajectory tracking and the stabilization of the vehicle’s position and orientation while on-line estimating the unknown aerodynamics efforts. The main idea of the control law is to separate the controller into a position controller in cascade with an orientation controller. The control design will be extended such that the interconnection term between the cascaded sub-systems is minimised. Finally, numerical simulations are used to demonstrate the control law’s good performance.