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Flight testbeds with multiple unmanned aerial vehicles (UAVs) are especially important to support research on multi-vehicle-related algorithms. The existing platforms usually lack a generic and complete solution allowing for software and hardware design. For such a purpose, this paper presents the design and implementation of a comprehensive multi-camera-based testbed for 3-D tracking and control of UAVs. First, the testbed software consists of a multi-camera system and a ground control system, which performs image processing, camera calibration, 3-D reconstruction, pose estimation, and motion control. In the multi-camera system, the positions and orientations of UAVs are first reconstructed by using epipolar geometric constraints and triangulation methods and then filtered by an extended Kalman filter (EKF). In the ground control system, a classical proportional–derivative (PD) controller is designed to receive the navigation data from the multi-camera system and then generates control commands to the target vehicles. Then, the testbed hardware employs smart cameras with field-programmable gate array (FPGA) modules to allow for real-time computation at a frame rate of 100 Hz. Lightweight quadcopter Parrot Bebop drones are chosen as the target UAVs, which does not require any modification to the hardware. Artificial infrared reflective markers are asymmetrically mounted on target vehicles and observed by multiple infrared cameras located around the flight region. Finally, extensive experiments are performed to demonstrate that the proposed testbed is a comprehensive and complete platform with good scalability applicable for research on a variety of advanced guidance, navigation, and control algorithms.

An adaptive smooth unsaturated bistable stochastic resonance (ASUBSR) system for bearing fault signal detection is established. Based on the problem of output saturation and poor low-frequency suppression performance of classical bistable stochastic resonance (CBSR) system, an SUBSR with unsaturated characteristics is proposed. An ASUBSR system is designed by extracting the envelope spectrum of the input signal and resampling it to satisfy the adiabatic approximation condition, combining high-pass filter to filter out low-frequency interference, and using genetic algorithm to select the optimal system parameters. Through simulations and experiments, we found that the system can effectively suppress the interference of low-frequency and high-frequency, indicates that the system performs like a band-pass filter, and the output signal-to-noise ratio is better than that of the CBSR system. The proposed ASUBSR system has great application in the field of fault detection of rolling bearings.

Designing a controller for the docking maneuver in Probe-Drogue Refueling (PDR) is an important but challenging task, due to the complex system model and the high precision requirement. In order to overcome the disadvantage of only feedback control, a feedforward control scheme known as Iterative Learning Control (ILC) is adopted in this paper. First, Additive State Decomposition (ASD) is used to address the tight coupling of input saturation, nonlinearity and the property of NonMinimum Phase (NMP) by separating these features into two subsystems (a primary system and a secondary system). After system decomposition, an adjoint-type ILC is applied to the Linear Time-Invariant (LTI) primary system with NMP to achieve entire output trajectory tracking, whereas state feedback is used to stabilize the secondary system with input saturation. The two controllers designed for the two subsystems can be combined to achieve the original control goal of the PDR system. Furthermore, to compensate for the receiver-independent uncertainties, a correction action is proposed by using the terminal docking error, which can lead to a smaller docking error at the docking moment. Simulation tests have been carried out to demonstrate the performance of the proposed control method, which has some advantages over the traditional derivative-type ILC and adjoint-type ILC in the docking control of PDR. Keywords: Additive state decomposition, Adjoint operator, Docking control, Iterative learning control, Probe-drogue refueling, Stable inversion

There exist at least two viewpoints on the internal model principle (IMP), namely the cancelation viewpoint and the geometrical viewpoint. However, neither of them is applicable to repetitive contr...

Microgrid (MG) usually operates in medium/low-voltage systems, where the line impedance parameters are mainly resistive, and traditional P–f / Q–U droop control is no longer applicable. When the virtual complex impedance method is adopted, the resistance component of line impedance can be counteracted by a virtual negative resistance. Unfortunately, the improper design of the virtual negative resistance will result in an unstable system due to the problem of line impedance parameter drift and estimation error. According to the line parameters characteristics of the off-grid MG with medium/low voltage, the P–U / Q–f droop control is adopted in this study, where the virtual complex impedance composed of a virtual negative inductance and a virtual resistance is introduced in the control loop. The virtual negative inductance is used to reduce the power coupling caused by the inductive component of the system impedance. The virtual resistance is implemented to enhance the resistive component and adjust the impedance matching degree for raising the accuracy of power sharing. However, the power sharing is still affected by the system hardware parameters; meanwhile, the voltage deviation caused by the droop control and the virtual impedance exists. In this study, a novel voltage stabilization and power sharing control method based on the virtual complex impedance is investigated to achieve accurate power sharing without the impact of hardware parameters variations and to improve the voltage quality. Moreover, the small-signal model of the inverter-based off-grid MG with the proposed controller is established, which can be utilized to analyze the stability and dynamic performance of the system. Meanwhile, the control parameters can be sequentially determined. Analysis shows that the strategy is robust against the line-impedance parameter drift and the estimation error and has a large stability margin and fast dynamic-response speed. Finally, numerical simulations and experimental results are provided to verify the effectiveness of the proposed control method in comparison with traditional frameworks.

Contraction mapping methods do not need to know about the concrete form of plant models like the Lyapunov method. This is the biggest advantage over other methods in the field of iterative learning control for example. However, it is difficult to use such a tool to analyze repetitive control systems. This paper proposes a contraction mapping method based on spectral theory to design a saturated repetitive controller for a class of nonlinear systems, where the derived necessary and sufficient condition on the spectral radius can reduce the conservatism as much as possible. The feasibility of our work is demonstrated through a robotic manipulator tracking example.

With a focus on the problems of active power sharing and voltage deviation of parallel-connected inverters in an islanded micro-grid (MG), in this study, the power-voltage droop controller and the inner voltage regulator are redesigned based on a total sliding-mode control (TSMC) technique. As for the power-voltage droop control loop, a droop control relation error between the active power and the point-of-common-coupling (PCC) voltage amplitude is defined. Then, the TSMC scheme is adopted to reach the new droop control relation, where the active power sharing and voltage amplitude recovery can be achieved simultaneously. Owing to the faster dynamic response and strong robustness provided by the TSMC framework, high-precision active power sharing during transient state also can be ensured without the influence of line impedances. The power allocation error can be improved by more than 81.2% and 50% than the conventional and proportional-integral (PI)-based droop control methods, respectively, and the voltage deviation rate can be reduced to 0.16%. Moreover, a small-signal model of the TSMC-based droop-controlled system is established, and the influences of control parameters on the system stability and the dynamic response are also investigated. The effectiveness of the proposed control method is verified by numerical simulations and experimental results.

In Semi-Autonomous Control (SAC), a multicopter’s attitude stabilization or hover is realized by the autopilot, while position control is often manually realized by a remote pilot with a Radio Control (RC) transmitter. The SAC is based on the attitude controller and position controller designed in the previous chapters. This chapter will involve three modes (stabilize mode, altitude hold mode, loiter mode) of SAC of multicopters. Readers will gradually master this part of the knowledge through three step-by-step experiments, namely, basic, analysis and design experiments from shallow to deep. In the basic experiment, readers will repeat the simulation of the stabilize mode and observe its control performance. In the analysis experiment, readers will change the stabilize mode to altitude hold mode and then analyze their difference. Finally, in the design experiment, readers will further realize the loiter mode and design a state machine to switch among the three modes.

The state estimation [13] is fundamental because it denotes the base for control and decision-making. This chapter introduces the principle and method of attitude estimation in detail via three step-by-step experiments from shallow to deep, namely a basic experiment, an analysis experiment, and a design experiment.

The objective of Chap. 8 is to estimate flight state accurately. In this chapter, it is assumed that the attitude of the multicopter has been estimated accurately. Feedback signals used in the controllers are the estimated values. However, for simplicity, true values are used instead of feedback according to the separation principle. The purpose of this chapter is to enable the multicopter to maintain a specific attitude. The performance of the attitude controller directly determines whether or not the multicopter can fly smoothly; further it is also the basis of position control, which will be discussed in Chap. 10. Control performance is determined by the rise time, overshoot, settling time, steady-state error in the time domain, and the cut-off frequency and stability margin in the frequency domain.

The position control described in this chapter is concerned with set-point control, which is the basic issue in the trajectory tracking and path following problems. The experimental flow of set-point position controller design is similar to that of the attitude controller design. This chapter introduces the design principles and methods of constructing a position controller for multicopters. It is expected that readers can gradually master this part through three step-by-step experiments, namely basic, analysis and design experiments. In the basic experiment, readers will repeat the simulation of the position control of a multicopter to understand how a set-point position controller works. In the analysis experiment, readers will adjust the PID parameters of the set-point position controller so that the multicopter exhibits good control performance in the time domain. In the design experiment, readers will design compensators based on well-known principles of automatic control, allowing multicopters to achieve good control performance in the frequency domain.

In a probe–drogue aerial refueling system, the drogue is affected not only by wind disturbances but also by strong disturbances from the tanker vortex and receiver forebody bow wave. Along with the aerodynamic disturbances acting on the receiver aircraft, it is difficult for the probe to capture the moving drogue in the docking stage. This paper studies the model of the probe–drogue aerial refueling system under aerodynamic disturbances, and proposes docking control method based on iterative learning control to compensate for the docking errors caused by aerodynamic disturbances. For receiver aircraft with different maneuverability, three control strategies are proposed to achieve a trade-off between safety and control precision. Furthermore, a practical method is proposed to predict the initial value of the learning controllers, which can significantly improve the iterative learning speed of the proposed methods. Finally, simulations demonstrate that the proposed control methods are simple and efficient for the docking control of autonomous probe–drogue aerial refueling.

In the previous chapter, continuous-time filtered repetitive control (FRC, or filtered repetitive controller, which is also designated as FRC), was proposed using an additive-state-decomposition-based method for nonlinear systems. In this chapter, the sampled-data FRC is proposed for the same nonlinear system, but with a different problem under the additive-state-decomposition-based tracking control framework [1].

The internal model principle (IMP) was first proposed by Francis and Wonham [2, 3]. It states that if any exogenous signal can be regarded as the output of an autonomous system, then the inclusion of this signal model, namely, internal model, in a stable closed-loop system can assure asymptotic tracking or asymptotic rejection of the signal. Until now, to the best of the authors’ knowledge, there exist at least two viewpoints on IMP. In the early years, for linear time-invariant (LTI) systems, IMP implies that the internal model is to supply closed-loop transmission zeros which cancel the unstable poles of the disturbances and reference signals. This is called cancelation viewpoint here and only works for problems able to be formulated in terms of transfer functions. In the mid-1970s, Francis and Wonham proposed the geometric approach [4] to design an internal model controller [2, 3]. The purpose of internal models is to construct an invariant subspace for the closed-loop system and make the regulated output zero at each point of the invariant subspace. This is called geometrical viewpoint here.

The adaptive-control-like method utilizes Lyapunov-based design techniques to develop feedforward to compensate for unknown disturbance. Moreover, the designed controllers depend on the concrete forms of the Lyapunov functions. The Lyapunov-based design technique is a good choice for nonlinear RC problems. However, in most cases, no general method exists for constructing Lyapunov functions for ordinary problems. Contraction mapping is a widely used tool for iterative learning control (ILC, or iterative learning controller, which is also designated as ILC). Using this tool, the ILC design is straightforward and uniform without requiring Lyapunov functions. Inspired by this concept, a contraction mapping-based RC design is proposed for a class of nonlinear systems in this chapter.

Linear time-invariant (LTI) systems are systems that are both linear and time-invariant. A system is considered linear if the output of the system is scaled by the same amount as the input given to the system. Moreover, this system follows the superposition principle, which implies that the sum of all the inputs will be the sum of the outputs of the individual inputs. Time-invariant systems are systems in which the output caused by a particular input does not change with time and only depends on when that input was applied. This class of systems is very important in the control field where many mature tools and methods exist. Before discussing nonlinear systems, the results of LTI systems must be reviewed to allow for the easy introduction of repetitive control (RC, or repetitive controller, which is also designated as RC) for nonlinear systems. On the other hand, any RC methods applicable to nonlinear systems should be first applicable to LTI systems. Therefore, it is necessary to apply these methods to LTI systems first and then move onto nonlinear systems. Moreover, some RC methods for nonlinear systems are an extended form or a combination of the methods in LTI systems. Therefore, it is important and necessary to first be aware of the RC methods for LTI systems. LTI systems often employ two types of models, i.e., transfer function models and state-space models. This chapter aims to answer the following question: How do you design a repetitive controller for LTI systems based on transfer function models and state-space models?

A direct method for solving the repetitive control (RC, or repetitive controller; also abbreviated as RC) problem for nonlinear systems is to transform them into linear time-invariant (LTI) systems using feedback linearization. Existing design methods that facilitate RC design can be used directly on transformed systems; however, some nonlinear systems cannot be linearized. Therefore, transformed systems are often subject to nonlinearities—assumed to be weak in this chapter—such as Lipschitz conditions or sector conditions. This chapter aims to answer the following question: How is RC applied to linearized systems subject to weak nonlinearities?

Error dynamics are often required for nonlinear systems using an adaptive-control-like method. However, this requirement restricts the applications of repetitive control (RC, or repetitive controller, which is also designated as RC) and fails to emphasize the special features and importance of RC. Moreover, it is difficult and also computationally expensive to derive error dynamics for nonminimum-phase nonlinear systems, especially when the internal dynamics are subject to an unknown disturbance. Therefore, there are very few RC works on nonminimum-phase nonlinear systems.

An adaptive-control-like method is the leading repetitive control (RC, or repetitive controller, also RC) method for nonlinear systems. Before using this method, a tracking problem for nonlinear systems needs to be converted into a rejection problem for nonlinear error dynamics subject to periodic disturbance. This conversion reduces the difficulties of the original problem. Furthermore, the periodic disturbance is considered as an unknown parameter that needs to be learned. As discussed in Chap. 4, the stability is enhanced by introducing a low-pass filter in RC for linear systems, resulting in a filtered repetitive controller (FRC, or filtered repetitive control, which is also designated as FRC). Similarly, it is also necessary to introduce a filter into RC for nonlinear systems. However, the theory on FRC proposed in [1] is derived in the frequency domain and can be applied only with difficulty, if at all, to nonlinear systems.

The main problem in control theory is controlling the output of a system to achieve the asymptotic tracking of desired signals and/or asymptotic rejection of disturbances. Among the existing approaches to asymptotic tracking and rejection, tracking via an internal model, which can handle the exogenous signal (The term “exogenous signal” is used to refer to both the desired signal and the disturbance when there is no need to distinguish them.) from a fixed family of functions of time, is one of the important approaches [1]. The basic concept of tracking via the internal model originated from the internal model principle (IMP) [2, 3]. The IMP states that if any exogenous signal can be regarded as the output of an autonomous system, then the inclusion of this signal model, i.e., the internal model, in a stable closed-loop system can ensure asymptotic tracking and asymptotic rejection of the signal. Given that the exogenous signals under consideration are often nonvanishing, the characteristic roots of these autonomous systems that generate these exogenous signals are neutrally stable. To produce asymptotic tracking and asymptotic rejection, if a given signal has a certain number of harmonics, then a corresponding number of neutrally stable internal models (one for each harmonic) should be incorporated into the closed-loop based on the IMP. Repetitive control (RC, or repetitive controller, also abbreviated as RC) is a specialized tracking method via an internal model for the asymptotic tracking and rejection of general T-periodic signals [4].

This paper presents an additive-state-decomposition-based attitude tracking control method for a class of bank-to-turn aerial vehicles subject to unknown disturbances and nonlinear coupling. This method ‘additively’ decomposes the original tracking problem into two more tractable problems, namely a tracking problem for a deterministic nonlinear ‘primary’ system, and a disturbance rejection problem for a linear time-invariant ‘secondary’ system. Based on the decomposition, a backstepping controller is designed for the primary system to track the reference attitude signal, and a proportional-integral controller is applied to the secondary system to compensate for the disturbances. Finally, the two designed controllers are combined to achieve the original control objective. By using additive state decomposition, the proposed control method with two degrees of freedom can consider tracking task and disturbance rejection task respectively. Simulation results illustrate that the proposed controller can track the reference attitude signal and compensate for disturbances meanwhile. Additionally, the ASD-based controller outperforms the traditional backstepping controller in the presence of unknown disturbances and input delay, and the robustness of the full system can be improved by adjusting the controller parameters of the secondary system.

In order to ensure the normal operation and increase the safety, reliability and mission dependability of quadcopters, the fault detection and diagnosis is very important. In this paper, the problem of fault detection and diagnosis is investigated for the homogenous quadcopter team subject to non-negligible wind disturbance. However, it is difficult to accurately diagnose the fault, because it is coupled with the wind disturbance, whose effect is difficult to eliminate. For this problem, first, the observability is analyzed for the sum effect of the fault and the wind disturbance of one quadcopter, for the fault of one quadcopter, and for the fault of the homogenous quadcopter team, respectively. By analysis, the fault in the situation of the homogenous quadcopter team is observable under some reasonable assumptions. Based on this, a procedure is further proposed to detect and diagnose the fault for the homogenous quadcopter team, eliminating the effect of the wind disturbance. Finally, the simulation demonstrates the effectiveness of the proposed procedure.

Multicopters have been attracting increasing attention in recent years, while it is significant to consider the flight safety of multicopters in the presence of propulsor faults or failures. Therefore, this paper presents a methodology to analyze the controllable probability of a multicopter with arbitrary configurations based on controllability theory and an available control authority index. The methodology is then used to analyze the controllable probability of multicopters with different propulsor numbers and configurations to show its effectiveness. Based on the controllable probability results, an optimal configuration method is given.

To study the problem of improving transient tracking performance for nonlinear systems, this paper proposes an additive-state-decomposition-based control method for a class of nonlinear nonminimum phase (NMP) systems. This method ‘additively’ decomposes the original problem into two more tractable problems, namely a tracking problem for a linear time-invariant NMP ‘primary’ system and a state stabilisation problem for a certain nonlinear ‘secondary’ system. Then, controller for each system is designed respectively by employing existing methods, i.e. the linear quadratic regulator (LQR) method for the primary system and the backstepping method for the secondary system. Next, these two controllers are combined together to achieve the original tracking goal. Furthermore, the adjustment of weighting matrix Q in the LQR regulates the transient response of the closed-loop nonlinear system. Finally, two illustrative examples are provided to demonstrate the effectiveness of the proposed method.

In this technical note, an additive-state-decomposition-based iterative learning control (ILC) method is proposed. Based on this method, the output feedback ILC problem is solved for a class of nonminimum phase (NMP) nonlinear systems with input saturation. This method is to “additively” decompose the output feedback ILC problem into two more tractable subproblems, namely an output feedback ILC problem for a linear time invariant (LTI) system and a state-feedback stabilization problem for a nonlinear system with input saturation. Then, a controller can be designed for each subproblem separately using existing methods, and the two designed controllers are combined together to achieve the original control goal. An illustrative example demonstrates the effectiveness of the proposed method.

In this paper, an auxiliary modeling method for system identification is proposed for multicopter dynamic modeling. By utilizing an auxiliary controller called damper during the modeling and identification process, the unstable attitude angle and angular rate channels of multicopters can turn to be stable so as to obtain the parameterized dynamic model without safety problems led by traditional methods and large-space requirement. Through an application to an indoor fixed quadcopter system, simulation results demonstrate the feasibility of the proposed method for the multicopter dynamic modeling.

International audience; This paper proposes a xed-time differentiator running in parallel with a feedbacklinearization-based controller, which allows quadrotors to track a given trajectory.The xed-time differentiator estimates outputs' derivatives in a prede ned conver-gence time, largely compensating for initial condition problems and solving the delayproblem. Combined with a state reconstruction step, a whole observer-estimator-controller scheme for trajectory tracking problem of quadrotors can be constructed.Also, an LMI optimization-based algorithm to tune parameters of the differentiatoris also developed here. The high performance of the proposed model is illustratedby simulation results.

Aerial refueling is capable of increasing the endurance and flight range of aircraft. However, during the docking phase of aerial refueling, the docking risk increases as the receiver aircraft approaches the tanker aircraft. A high docking risk indicates docking failure or even flight collision. In order to guarantee docking reliability and safety, a stochastic approximation method is proposed to predict the docking success probability during the docking phase of aerial refueling. If the success probability is lower than the specified value, the receiver aircraft needs to increase its relative distance from the tanker aircraft to reduce the risk. In our method, a stochastic differential equation is used to model the relative motion between the receiver and tanker aircrafts, where the receiver aircraft flies along a predefined flight path with influence of additive wind perturbations. The correlation between the magnitude of wind perturbations and the distance between the receiver and tanker aircrafts is considered. Then, based on the established relative motion model, the probability that the receiver aircraft enters the target set during a given time interval is predicted by the Markov chain stochastic approximation method. The docking success probability is computed by propagating the transition probabilities of the Markov chain backwards starting from the target set during the time interval. Comparing with the widely used Monte Carlo method in previous studies, our method demonstrates substantial effectiveness and efficiency.

Summary The generator design for causal ideal internal dynamics (IID), namely, solving IID, is a fundamental problem in a nonminimum-phase output tracking process. In this paper, for a class of unstable matrix differential equations, a new causal IID generator is proposed, whose parameters are partly chosen via H2/H∞ optimization. Compared with existing similar design schemes, it is applicable to matrix differential equations with singular system matrices. Also, it requires less computation, avoids taking higher order derivatives, and can be easily extended to treat slowly time-varying matrix differential equations without the need for extra computation. Copyright © 2016 John Wiley & Sons, Ltd.

Based on the additive-state-decomposition (ASD) dynamic inversion design, a proportional-integral controller is designed to stabilize a class of multi-input multi-output (MIMO) systems subject to nonparametric time-varying uncertainties with respect to both state and input. By ASD and a new definition of output, the considered uncertain system is transformed into a first-order system, in which all original uncertainties are lumped into a new disturbance at the new defined output. Subsequently, the dynamic inversion control is applied to reject the lumped disturbance. Performance analysis of the resulting closed-loop dynamics shows that the stability can be ensured. Finally, to demonstrate its effectiveness, the proposed controller design is applied to two existing problems by numerical simulation. Furthermore, in order to show its practicability, the proposed controller design is also performed on a real quadrotor to stabilize its attitude when its inertia moment matrix is subject to a large uncertainty.

In this paper, a saturated D-type iterative learning control (ILC) method is proposed for multicopter trajectory tracking based on the additive state decomposition (ASD) method. By using the ASD method, the multicopter nonlinear horizontal channel with input saturation is divided into a linear primary system and a nonlinear secondary system. The ILC method for linear systems can be used directly in the linear primary system to track desired trajectories. A state feedback is applied to stabilize the nonlinear secondary system. Then, the above two controllers are combined to achieve the control goal. Simulation results demonstrate the feasibility of the proposed method for the multicopter trajectory tracking problem with input saturation and other nonlinearities.

Microgrid (MG) usually operates in medium/low voltage systems, where the line impedance parameters are mainly resistive, and traditional P-f/Q-U droop control is no longer applicable. According to the line parameters characteristics of the off-grid MG with medium/low voltage, the P-U/Q-f droop control is adopted in this study, where the virtual complex impedance composed of a virtual negative inductance and a virtual resistance is introduced in the control loop. The virtual negative inductance is used to reduce the power coupling caused by the inductive component of the system impedance. The virtual resistance is implemented to enhance the resistive component and adjust the impedance matching degree for raising the accuracy of power sharing. However, the power sharing is still affected by the system hardware parameters, meanwhile, the voltage deviation caused by the droop control and the virtual impedance exists. In this study, a novel voltage stabilization and power sharing control method based on the virtual complex impedance is investigated to achieve accurate power sharing without the impact of hardware parameters variations and to improve the voltage quality. Numerical simulations are provided to verify the effectiveness of the proposed control method in comparison with traditional frameworks.

This paper studies the model of the probe-drogue aerial refueling system under aerodynamic disturbances, and proposes a docking control method based on terminal iterative learning control to compensate for the docking errors caused by aerodynamic disturbances. The designed controller works as an additional unit for the trajectory generation function of the original autopilot system. Simulations based on our previously published simulation environment show that the proposed control method has a fast learning speed to achieve a successful docking control under aerodynamic disturbances including the bow wave effect., Comment: Accepted by Journal of Guidance, Control, and Dynamics

The repetitive control (RC) or repetitive controller problem for nonminimum phase nonlinear systems is both challenging and practical. In this paper, we consider an RC problem for the translational oscillator with a rotational actuator (TORA), which is a nonminimum phase nonlinear system. The major difficulty is to handle both a nonminimum phase RC problem and a nonlinear problem simultaneously. For such purpose, a new RC design, namely the additive-state-decomposition-based approach, is proposed, by which the nonminimum phase RC problem and the nonlinear problem are separated. This makes RC for the TORA benchmark tractable. To demonstrate the effectiveness of the proposed approach, a numerical simulation is given.

Net recovery is an advanced accurate-point recovery way for small fixed-wing unmanned aerial vehicles (UAVs), especially in limited recovery fields or naval vessels. In order to perform recovery successfully, the aerial vehicle must satisfy certain conditions to shut down the engine so that it can glide into the net without a crash. In this paper, an aircraft longitudinal dynamic model is taken into consideration. Given the initial position, we aim to obtain the feasible initial speed of the aircraft. This problem is formulated as an optimal control problem and then solved by Pseudo-Spectral methods. The simulation results show the initial state in the computational flight envelope can perform successful net recovery task.

In practice, the lift that a propeller produces is composed of theoretical value and fluctuation, which results in vibration in aircraft. This paper will analyze the effect of the fluctuation on the quadcopter. In order to reduce the vibration caused by the fluctuation, an improved Additive-State-Decomposition-Based (ASDB) dynamic inversion stabilized controller is proposed. To show its effectiveness, the proposed controller is compared with the traditional ASDB dynamic inversion stabilized controller in numerical simulations. Simulation results show that a better damping performance for lift fluctuation is achieved with the improved ASDB dynamic inversion stabilized controller. Then the continuous-time controller is further discretized by Tustin transformation method with prewarping to be a digital controller in different sampling time, and the ideal sampling time is found out to trade off cost and performance of the digital controller.

On the basis of the coordinate frames and attitude representations in Chap. 5, forces on a multicopter will be taken into account and dynamic models for filtering and control will be established.

Control is an enabling technology, the essence of which is the feedback. Unstable multicopters can become stable with the help of feedback control. However, it is not enough to be just stable.

The state of a multicopter may not be measured directly by existing sensors. For example, since the speed of a multicopter is very low, its accurate value is difficult to be measured directly.

Stability and controllability are the basic properties of a dynamical system. Since a multicopter without control feedback is unstable, an autopilot is required to guarantee its stability and further make the multicopter hover automatically without any need for an external intervention.

This paper considers the controllability analysis and fault tolerant control problem for a class of hexacopters. It is shown that the considered hexacopter is uncontrollable when one rotor fails, even though the hexacopter is over-actuated and its controllability matrix is row full rank. According to this, a fault tolerant control strategy is proposed to control a degraded system, where the yaw states of the considered hexacopter are ignored. Theoretical analysis indicates that the degraded system is controllable if and only if the maximum lift of each rotor is greater than a certain value. The simulation and experiment results on a prototype hexacopter show the feasibility of our controllability analysis and degraded control strategy., Comment: 21 pages, 7 figures, submitted to Journal of Intelligent & Robotic Systems

SUMMARY 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.

Besides parametric uncertainties and disturbances, unmodelled dynamics and time delay at the input are often present in practical systems, and cannot always be ignored. This paper aims to solve the problem of output feedback tracking control for a class of non-linear uncertain systems subject to unmodelled high-frequency gains and time delay in the input. By additive state decomposition, the uncertain system is transformed to an uncertainty-free system, in which the uncertainties, disturbances and effects of unmodelled dynamics along with time delay are lumped into a new disturbance at the output. Subsequently, additive state decomposition is used to decompose the transformed system to simplify the tracking controller design. The proposed control scheme is applied to three benchmark examples to demonstrate its effectiveness.

In this paper, a new concept of iterative learning control (ILC), namely consolidated ILC (CILC), is introduced. An iterative learning control system is subject to data interrupt when the system output is restricted within a certain area. Data interrupt means that the system output is interrupted at a certain moment due to output restrictions. The output data from this moment to the end of the trail duration cannot be obtained, which is the biggest difference from the classical ILC problems. The ILC problems with data interrupt caused by output restrictions are called CILC problems. The idea to solve the CILC problems is to obtain the complete output data gradually as the number of iterations increases. First of all, three CILC problems in practice are presented as well as the intermittent ILC problems and the relationship between them. The CILC problems are formulated later and the uniform restriction is given. A specific linear case is also studied. According to the simulation results, it is possible to achieve the convergence of the specific system as well as to control the convergence rate by using a proper algorithm.

This paper shows further results on the output feedback tracking problem for a class of uncertain nonminimum phase nonlinear systems, where a state-based uncertainty is involved. Through a new additive state decomposition process, this uncertainty is divided into two parts which are assigned to the two decomposed subsystems, respectively. Then the controller is designed and its stability is analyzed by the nonlinear small-gain theorem. Finally, to demonstrate the effectiveness of the proposed method, an illustrative example is given.