Robust Trajectory‐Tracking Control of a PVTOL under Crosswind

This work proposes a robust controller to solve the trajectory‐tracking control problem of planar vertical take‐off and landing (PVTOL) aircraft under crosswind. The controller combines input–output feedback linearization and active disturbance rejection control techniques. The former linearizes the PVTOL dynamics and the latter actively estimates and compensates for the crosswind effects. Numerical simulations assess the effectiveness of the proposed approach.     

Robust nonlinear control of atomic force microscope via immersion and invariance

This paper reports an immersion and invariance (I&I)–based robust nonlinear controller for atomic force microscope (AFM) applications. The AFM dynamics is prone to chaos, which, in practice, leads to performance degradation and inaccurate measurements. Therefore, we design a nonlinear tracking controller that stabilizes the AFM dynamics around a desired periodic orbit. To this end, in the tracking error state space, we define a target invariant manifold, on which the system dynamics fulfills the control objective. First, considering a nominal case with full state measurement and no modeling uncertainty, we design an I&I controller to render the target manifold exponentially attractive. Next, we consider an uncertain AFM dynamics, in which only the displacement of the probe cantilever is measured. In the framework of the I&I method, we recast the robust output feedback control problem as the immersion of the output feedback closed‐loop system into the nominal full state one. For this purpose, we define another target invariant manifold that recovers the performance of the nominal control system. Moreover, to handle large uncertainty/disturbances, we incorporate the method of active disturbance rejection into the I&I output feedback control. Through Lyapunov‐based analysis of the closed‐loop stability and robustness, we show the semiglobal practical stability and convergence of the tracking error dynamics. Finally, we present a set of detailed, comparative software simulations to assess the effectiveness of the control method.     

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.     

Position feedback global tracking control of EL systems: a statetransformation approach

The contribution of this paper is a dynamic position feedback global tracking controller for fully actuated Euler-Lagrange (EL) systems. The properties we show for the closed loop system are uniform stability and exponential convergence, global in the initial tracking errors and semiglobal in the initial estimation errors. The novelty of our approach is that our observer and control design are based on a new model for EL systems which is linear in the immeasurable velocities. This model is shown to fit robot manipulators. We also provide some simulation results     

Robust Stabilization of Nonlinear PVTOL Aircraft with Parameter Uncertainties

In this work, the stabilization control problem is investigated for the planar vertical take‐off and landing (PVTOL) aircraft with unknown model parameters. To cope with the challenges caused by non‐minimum phase and parametric uncertainties, a new appropriate output, different from the general centroid position output, is carefully constructed to ensure the zero dynamics asymptotically stable, then the sliding‐mode technique is applied to design a state feedback control law. The proposed robust control law is proved able to asymptotically stabilize the PVTOL aircraft to the desired fixed position with null velocities and roll angle despite the unknown model parameters. Simulation examples illustrate the effectiveness of the proposed control algorithm.     

Adaptive actuator failure compensation for multivariable feedback linearizable systems

A feedback linearization‐based adaptive control scheme is developed for multivariable nonlinear systems with redundant actuators subject to uncertain failures. Such an adaptive controller contains a direct adaptive actuator failure compensator to compensate the uncertain actuator failure, a nonlinear feedback to linearize the nonlinear dynamics, and a linear feedback to stabilize the linearized system. The key new design feature is the estimation of both the failure patterns and the failure values, for direct adaptive actuator failure compensation, newly developed for multivariable feedback linearizable nonlinear systems. With direct control signal adaptation, the adaptive failure compensation design ensures closed‐loop stability and asymptotic output tracking in the presence of actuator failure uncertainties. Simulation results from an application to attitude control of a near‐space vehicle dynamic model are presented to verify the desired system performance with adaptive actuator failure compensation. Copyright © 2015 John Wiley & Sons, Ltd.     

Approximate finite‐time control for a class of uncertain nonlinear systems with dynamic compensation

In this work, a new robust nonlinear feedback control method with dynamic active compensation is proposed; the active control method has been applied to an integral series of finite‐time single‐input single‐output nonlinear system with uncertainty. In further tracking the closed‐loop stability and nonlinear uncertainty, an extended state observer has been employed to solve the immeasurability and nonlinear uncertainty within a nonlinear system. A singular perturbation theory has been used to solve for the finite‐time stability of the closed‐loop system; furthermore, numerical simulations showed that the robust nonlinear feedback controller tracked the uncertainty in a nonlinear Duffing‐type oscillator and has proven the effectiveness of the approximate finite‐time control strategy proposed. By using an approximate finite‐time control approach with active compensation, the uncertainty in a nonlinear system could be accurately estimated and controlled. Copyright © 2017 John Wiley & Sons, Ltd.     

A general analysis and control framework for process systems with inventory recycling

In this work, we generalize our previous results concerning the impact of material recycling and energy recovery on plant dynamics and control. We define a generic class of integrated process systems, in which an extensive quantity that obeys conservation laws is recovered from the process output and recycled to the process feed; the operation of the system is assumed to be subject to time‐varying, measurable disturbances. We establish, in this general case, that integration is conducive to the emergence of a two‐time‐scale dynamic behavior and derive reduced‐order models for the dynamics in each time scale. Subsequently, we postulate a hierarchical control framework that exploits these dynamics results in the design of coordinated fast and slow feedback/feedforward controllers and formulate a stability result for the closed‐loop system. We demonstrate these concepts on a case study concerning an energy‐integrated process. Copyright © 2013 John Wiley & Sons, Ltd.     

Approximate trajectory tracking of input‐disturbed PVTOL aircraft with delayed attitude measurements

In this paper, we address the flight‐trajectory tracking problem of an input‐disturbed planar vertical take‐off and landing (PVTOL) aircraft with delayed attitude measurements. By applying the first‐order Padé approximation to deal with the time delay functions, the problem is reduced to the output tracking of a new non‐minimum‐phase system without delay. A tracking controller, consisting of a linear static‐state feedback term, a switching control term and a nonlinear auxiliary input term, is proposed for robust stabilization of the output‐tracking errors together with the internal dynamics. Numerical simulations are performed to show the main results. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust output regulation and the preservation of polynomial closed‐loop stability

In this paper, we study the robust output regulation problem for distributed parameter systems with infinite‐dimensional exosystems. The main purpose of this paper is to demonstrate the several advantages of using a controller that achieves polynomial closed‐loop stability, instead of a one stabilizing the closed‐loop system strongly. In particular, the most serious unresolved issue related to strongly stabilizing controllers is that they do not possess any known robustness properties. In this paper, we apply recent results on the robustness of polynomial stability of semigroups to show that, on the other hand, many controllers achieving polynomial closed‐loop stability are robust with respect to large and easily identifiable classes of perturbations to the parameters of the plant. We construct an observer based feedback controller that stabilizes the closed‐loop system polynomially and solves the robust output regulation problem. Subsequently, we derive concrete conditions for finite rank perturbations of the plant's parameters to preserve the closed‐loop stability and the output regulation property. The theoretical results are illustrated with an example where we consider the problem of robust output tracking for a one‐dimensional heat equation.Copyright © 2013 John Wiley & Sons, Ltd.     

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.     

基于饱和方法的直升机镇定设计

考虑直升机的镇定问题. 通过把直升机的部分动态视为非线性扰动下的积分器链, 并进一步转化为前馈型系统, 然后运用饱和设计方法, 给出了直升机镇定控制器的设计. 并用 Lyapunov 方法证明了闭环系统的全局渐近稳定性. 本文设计方法简单, 无需前推、反推技巧, 也无需小增益分析. 与现存的控制器设计相比, 本文的控制律形式简单. 数例仿真表明了方法的有效性.     

Finite‐time tracking control of a nonholonomic mobile robot

In this paper, the finite‐time tracking problem is investigated for a nonholonomic wheeled mobile robot in a fifth‐order dynamic model. We consider the whole tracking error system as a cascaded system. Two continuous global finite‐time stabilizing controllers are designed for a second‐order subsystem and a third‐order subsystem respectively. Then finite‐time stability results for cascaded systems are employed to prove that the closed‐loop system satisfies the finite‐time stability. Thus the closed‐loop system can track the reference trajectory in finite‐time when the desired velocities satisfy some conditions. In particular, we discuss the control gains selection for the third‐order finite‐time controller and give sufficient conditions by using Lyapunov and backstepping techniques. Simulation results demonstrate the effectiveness of our method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A periodic approach for input‐delay problems: Application to network controlled systems affected by polytopic uncertainties

This paper deals with robust stability and stabilization of linear discrete‐time systems subject to uncertainties and network constraints. In network control systems, the control loop is closed over a network, which induces additional dynamics to the original control loop such as delays, sampling, and quantization among many others. This paper focuses on networked induced delays due to unreliable network for which packet losses may occur. An equivalent periodic‐like representation of the resulting system is proposed. This allows first to revisit existing results in this framework and second to take model uncertainties into account by analyzing the closed‐loop model by means of a recent method based on robust control for discrete‐time time‐varying systems. Stability analysis and dynamic state‐feedback stabilization are characterized via new conditions, whose conservatism is extensively discussed. Effectiveness of the proposed methodology is illustrated by numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust nonlinear ship course‐keeping control by H∞ I/O linearization and μ‐synthesis

In this paper, the H_∞ input/output (I/O) linearization formulation is applied to design an inner‐loop nonlinear controller for a nonlinear ship course‐keeping control problem. Due to the ship motion dynamics are non‐minimum phase, it is impossible to use the ordinary feedback I/O linearization to resolve. Hence, the technique of H_∞ I/O linearization is proposed to obtain a nonlinear H_∞ controller such that the compensated nonlinear system approximates the linear reference model in I/O behaviour. Then a μ‐synthesis method is employed to design an outer‐loop robust controller to address tracking, regulation, and robustness issues. The time responses of the tracking signals for the closed‐loop system reveal that the overall robust nonlinear controller is able to provide robust stability and robust performance for the plant uncertainties and state measurement errors. Copyright © 2002 John Wiley & Sons, Ltd.     

Dynamic modeling and nonlinear tracking control of a novel modified quadrotor

In this article, a nonlinear tracking controller is designed based on Lyapunov stability for a novel aerial robot. The proposed 6‐rotor configuration improves stability and payload lifting capacity of the robot compared with conventional quadrotors while avoiding further complexities in the robot dynamics and steering principles. The dynamical model of the robot is derived using Newton‐Euler method. The model represents a nonlinear, coupled, and underactuated system. The proposed control strategy includes 2 main parts: an attitude controller and a position controller. Both the attitude and position controls are Lyapunov‐based nonlinear tracking controllers that guarantee the asymptotic convergence of the states' tracking errors to zero. Simulation results are presented to illustrate appropriate performance of the closed‐loop system in terms of position/attitude tracking even in the presence of wind disturbance.     

Model reference adaptive control of discrete‐time piecewise linear systems

This article presents a switched model reference adaptive controller for discrete‐time piecewise linear systems. In the spirit of the work by Landau in the late seventies, proof of asymptotic stability of the closed‐loop error system is obtained, recasting its dynamics as a feedback system and showing the feedforward and the feedback paths are both passive. The challenge is that both paths can be piecewise linear. Numerical results show excellent performance of the proposed controller even in the face of sudden variations of the plant parameters. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive neural network control of bilateral teleoperation with unsymmetrical stochastic delays and unmodeled dynamics

In this paper, adaptive NN control is proposed for bilateral teleoperation system with dynamic uncertainties, unknown external disturbances, and unsymmetrical stochastic delays in communication channel to achieve transparency and robust stability. Compared with previous passivity‐based teleoperation framework, the communication delays are unsymmetrical and stochastic. By partial feedback linearization using nominal dynamics, the nonlinear dynamics of the teleoperation system are transformed into two subsystems: local master/slave dynamics control and time‐delay motion tracking. By integrating Markov jump systems and adaptive parameters updating, adaptive NN control strategy is developed. The stability of the closed‐loop system and the boundedness of tracking errors are proved using Lyapunov–Krasovskii functional synthesis under specific linear matrix inequalities conditions. The proposed adaptive NN control is robust against motion disturbances, parametric uncertainties, and unsymmetrical stochastic delay, which effectiveness is validated by extensive simulation studies. Copyright © 2013 John Wiley & Sons, Ltd.     

A modified dynamic surface approach for control of nonlinear systems with unknown input dead zone

This paper focuses on the robust output precise tracking control problem of uncertain nonlinear systems in pure‐feedback form with unknown input dead zone. By designing an extended state observer, the states unmeasurable problem in traditional feedback control is solved, and the lumped uncertainty, which is caused by system unknown functions and input dead zone, is estimated. In order to apply separation principle, finite‐time extended state observer is designed to obtain system states and estimate the lumped uncertainty. Then, by introducing tracking differentiator, a modified dynamic surface control approach is developed to eliminate the ‘explosion of complexity’ problem and guarantee the tracking performance of system output. Because tracking differentiator is a fast precise signal filter, the closed‐loop control performance is significantly improved when it is used in dynamic surface control instead of first‐order filters. The L _∞ stability of the whole closed‐loop system, which guarantees both the transient and steady‐state performance, is shown by the Lyapunov method and initialization technique. Numerical and experiment examples are performed to illustrate our proposed control scheme with satisfactory results. Copyright © 2013 John Wiley & Sons, Ltd.     

Arbitrarily fast and robust tracking by feedback

The output of a singe-input-single-output linear feedback system with more than one pole in excess over the zeros in the loop transmission cannot track arbitrarily fast its input (by the root locus). In this work we extend the linear feedback so that some of the open loop poles may depend on the open loop gain; we call this new class quasi-linear feedback systems. We then derive time domain, pole-zero, and frequency domain conditions which ensure arbitrarily fast and robust tracking by quasi-linear feedback, for an arbitrary number of poles in excess over the zeros. We prove that in a particular case these conditions are equivalent, and that the boundedness in frequency of the closed loop transfer function is no longer necessary for achieving arbitrarily fast tracking. The robustness is to external disturbances and initial conditions, and the open loop has to be minimum phase. Some examples are presented which illustrate these results. They also show that this good performance can be obtained with a reduced control effort, and that quasi-linear feedback can alleviate the limitation on performance of non-minimum phase open loops.