Showing papers on "Feedback linearization published in 2016"

Stability and Scalability of Homogeneous Vehicular Platoon: Study on the Influence of Information Flow Topologies

Abstract: In addition to decentralized controllers, the information flow among vehicles can significantly affect the dynamics of a platoon. This paper studies the influence of information flow topology on the internal stability and scalability of homogeneous vehicular platoons moving in a rigid formation. A linearized vehicle longitudinal dynamic model is derived using the exact feedback linearization technique, which accommodates the inertial delay of powertrain dynamics. Directed graphs are adopted to describe different types of allowable information flow interconnecting vehicles, including both radar-based sensors and vehicle-to-vehicle (V2V) communications. Under linear feedback controllers, a unified internal stability theorem is proved by using the algebraic graph theory and Routh–Hurwitz stability criterion. The theorem explicitly establishes the stabilizing thresholds of linear controller gains for platoons, under a large class of different information flow topologies. Using matrix eigenvalue analysis, the scalability is investigated for platoons under two typical information flow topologies, i.e., 1) the stability margin of platoon decays to zero as $0(\mbox{1}/N^{2})$ for bidirectional topology; and 2) the stability margin is always bounded and independent of the platoon size for bidirectional-leader topology. Numerical simulations are used to illustrate the results.

Disturbance Observer-Based Antiwindup Control for Air-Breathing Hypersonic Vehicles

Abstract: In this paper, a combination of feedback linearization and disturbance observer-based control (DOBC) is adopted for the design of a state-feedback controller that regulates the velocity and altitude of air-breathing hypersonic vehicles (AHVs) subject to constrained inputs. First, a disturbance observer is established to estimate the overall effect of possible uncertainties and disturbances on the nominal vehicle model which is called the lumped disturbance. Then, a compensation method is proposed based on disturbance observer and feedback linearization control to counteract the mismatched lumped disturbance. Furthermore, a novel antiwindup modification is implemented on the baseline control to handle the possible input saturation. The designed controller addresses the issue of stability robustness with respect to system uncertainties and disturbances, and achieves zero-error tracking with good performance and antiwindup property meanwhile, which is the major merit compared with other existing AHV controllers. Finally, simulation is presented to verify the effectiveness of this control scheme.

Distributed Finite-Time Voltage and Frequency Restoration in Islanded AC Microgrids

Abstract: This paper investigates the distributed finite-time restoration of inverter voltage and frequency terms in an islanded ac microgrid. Formulating networked inverters of ac microgrids as a cooperative multiagent system, the voltage and frequency restoration can be cast as synchronization problems, while the active power sharing can be viewed as a consensus problem. One popular distributed control approach is the neighbor-based linear consensus protocol, where the consensus at the frequency and voltage set points is achieved over an infinite-time horizon with an exponential convergence. To achieve accelerated convergence and better disturbance rejection properties, a distributed finite-time control protocol, based on feedback linearization approach, is proposed for voltage restoration, which synchronizes the voltage term at each inverter to the reference value in finite time period. Then, a finite-time control protocol for both frequency restoration and active power sharing problems is proposed to synchronize the microgrid frequency to the nominal value, and share the active power among inverters based on their ratings in a finite time. Rigorous Lyapunov proofs are provided to establish the upper bounds on the convergence times. Numerical simulation studies verify the effectiveness of the proposed control protocols.

Adaptive neural control for a class of stochastic nonlinear time‐delay systems with unknown dead zone using dynamic surface technique

Abstract: Summary This paper investigates the problem of adaptive control for a class of stochastic nonlinear time-delay systems with unknown dead zone. A neural network-based adaptive control scheme is developed by using the dynamic surface control (DSC) technique and the minimal learning parameters algorithm. The dynamic surface control technique, which can avoid the problem of ‘explosion of complexity’ inherent in the conventional backstepping design procedure, is first extended to the stochastic nonlinear time-delay system with unknown dead zone. The unknown nonlinearities are approximated by the function approximation technique using the radial basis function neural network. For the purpose of reducing the numbers of parameters, which are updated online for each subsystem in the process of approximating the unknown functions, the minimal learning parameters algorithm is then introduced. Also, the adverse effects of unknown time-delay are removed by using the appropriate Lyapunov–Krasovskii functionals. In addition, the proposed control scheme is systematically derived without requiring any information on the boundedness of the dead zone parameters and avoids the possible controller singularity problem in the approximation-based adaptive control schemes with feedback linearization technique. It is shown that the proposed control approach can guarantee that all the signals of the closed-loop system are bounded in probability, and the tracking errors can be made arbitrary small by choosing the suitable design parameters. Finally, a simulation example is provided to illustrate the performance of the proposed control scheme. Copyright © 2015 John Wiley & Sons, Ltd.

Input–Output Feedback Linearization Control With On-Line MRAS-Based Inductor Resistance Estimation of Linear Induction Motors Including the Dynamic End Effects

Abstract: This paper proposes the theoretical framework and the consequent application of the input–output feedback linearization (FL) control technique to linear induction motors (LIMs). LIM, additionally to rotating induction motor, presents other strong nonlinearities caused by the dynamic end effects, leading to a space-vector dynamic model with time-varying inductance and resistance terms and a braking force term. This paper, starting from a recently developed dynamic model of the LIM taking into consideration its end effects, defines a FL technique suited for LIMs, since it inherently considers its dynamic end effects. Additionally, it proposes a technique for the on-line estimation of the inductor resistance, based on model reference adaptive system (MRAS) on-line estimator; it has been exploited for adapting on-line the FL control action versus inductor resistance variations leading to undesirable steady-state tracking errors. The stability of the proposed MRAS on-line estimator has been proven theoretically, adopting the Popov's criterion for hyperstability. The proposed approach has been validated experimentally on a suitably developed test setup, under both no load and loaded conditions. It has been compared firstly with the simplest control structure, which is the scalar $V/f$ control, secondly under the same closed-loop bandwidths of the flux and speed systems, with the industrial standard in terms of high-performance control technique, i.e., field-oriented control.

A Distributed Feedforward Approach to Cooperative Control of AC Microgrids

Abstract: This paper addresses the cooperative control problem of AC microgrids consisting of both voltage-controlled voltage-source inverters and current-controlled voltage-source inverters. The voltage-controlled voltage-source inverters dictate the frequency and voltage of the microgrid and the current-controlled voltage-source inverters provide quick and decoupled active and reactive power support to the microgrid. To handle the nonlinear and heterogeneous dynamics of the inverters, we have developed a distributed feedforward approach based on the cooperative control of multi-agent systems. The proposed controller presents three advantages in comparison with the existing works. First, all the inverters share one communication network, and the locations of the inverters over the communication network can be arbitrarily sited as long as all the inverters are connected. Second, the selection of the control gains does not rely on either the whole microgrid dynamics or the topology of the communication network. Third, the inverters’ dynamics after input-output feedback linearization are allowed to be different. The effectiveness of the proposed controller is verified by the simulation study of a microgrid system for three cases, i.e., frequency and voltage restoration after islanding, active and reactive power adjustment after abrupt load changes and system performance subject to communication link failure and restoration.

Shaping the Energy of Mechanical Systems Without Solving Partial Differential Equations

Abstract: Control of underactuated mechanical systems via energy shaping is a well-established, robust design technique. Unfortunately, its application is often stymied by the need to solve partial differential equations (PDEs). In this technical note a new, fully constructive, procedure to shape the energy for a class of mechanical systems that obviates the solution of PDEs is proposed. The control law consists of a first stage of partial feedback linearization followed by a simple proportional plus integral controller acting on two new passive outputs. The class of systems for which the procedure is applicable is identified imposing some (directly verifiable) conditions on the systems inertia matrix and its potential energy function. It is shown that these conditions are satisfied by three benchmark examples.

Nonlinear System Theory

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Feedback Linearization for Nonlinear Systems With Time-Varying Input and Output Delays by Using High-Gain Predictors

Abstract: This note addresses the problem of feedback linearization for nonlinear systems with time-varying input and output delays. To solve the realization issue of future states, a high-gain-observer is constructed as a predictor. Then, the output feedback predictive control is presented. The stability of the closed-loop system is analyzed by using a Lyapunov-Krasovskii functional. It is demonstrated that by designing the observer gain high enough, the closed-loop system recovers the performance of state feedback control with no time delay. However, the gain of the observer is limited by the time delay. Finally, numerical simulations are given to illustrate the effectiveness of the proposed control.

A Cyber-Enabled Stabilizing Control Scheme for Resilient Smart Grid Systems

Abstract: A parametric controller is proposed for transient stability of synchronous generators after the occurrence of a disturbance in the power grid. The proposed controller based on feedback linearization control theory relies on receiving timely phasor measurement unit (PMU) information from selected parts of the power grid to employ fast acting flywheels that are situated near synchronous generators. The local storage devices aim to balance a swing equation model of the synchronous generator to drive the associated rotor speed to stability. The advantages of the proposed controller include that it is tunable and integrates well with existing governor controls in contrast to other forms of PMU-based control. Further, a comparison is drawn between the proposed controller and recently proposed nonlinear controllers for transient stabilization. Numerical results show the effectiveness and robustness of the proposed controller when applied to the 39-bus 10-generator New England power system.

Fast sliding mode control on air-breathing hypersonic vehicles with transient response analysis:

Abstract: This article studies the tracking control of air-breathing hypersonic vehicles to the reference velocity and the reference altitude with a fast non-linear sliding mode control scheme. By the feedback linearization technology, the longitudinal model of air-breathing hypersonic vehicles is divided into the velocity subsystem and the altitude subsystem. Two lumped tracking error variables are developed based on velocity and altitude subsystems, and non-singular terminal sliding mode control is used so that the two lumped error variables converge to the origin in finite time. During the tracking process, transient properties of non-singular terminal sliding mode control are investigated from the mathematical and theoretical standpoint. The simulation results have shown that the fast non-linear sliding mode control is effective for the tracking control of air-breathing hypersonic vehicles and have demonstrated that the relevant transient response analysis is correct.

A novel sliding mode controller for small-scale unmanned helicopters with mismatched disturbance

Abstract: This paper presents a novel sliding mode control (SMC) strategy based on approximate feedback linearization and enhanced nonlinear disturbance observer for small-scale unmanned helicopters with high-order time-varying matched and mismatched disturbance. The novel SMC method is developed by designing a new sliding surface with the estimation of mismatched disturbance and its derivative. The proposed novel SMC method possesses following two appealing traits. First, it is robust with both matched disturbance and mismatched disturbance. Second, the chattering problem can be attenuated significantly. Moreover, the uniformly ultimately bounded stability of the closed-loop helicopter system is proved by theoretical analysis. Finally, the excellent tracking performance and robustness of the proposed flight control scheme are demonstrated by simulation results.

Optimal Guidance Around Circular Trajectories for Impact-Angle Interception

Abstract: A new linear optimal guidance law for impact-angle interception is presented. The linearization of the nonlinear equations of motion is performed around a nominal circular trajectory, thus allowing the linearization to be valid far from the initial line of sight. The proposed law can be viewed as a generalization of the optimal rendezvous problem. Closed-form expressions for the miss distance, the intercept angle error, and the control effort are derived for the linear model. The transformation from the relative position and the relative velocity (with respect to the circular trajectory) to the relative inscribed angle and the relative inscribed angle rate is presented. Using this transformation, the implementation of the optimal impact-angle guidance law based on the inscribed angle is derived. The application in various scenarios enforcing different impact angles is studied via nonlinear simulations, and it is shown that, for the investigated parameters, the proposed law performs better when compared to...

Global Stabilization of a Class of Nonminimum-Phase Nonlinear Systems by Sampled-Data Output Feedback

Abstract: In this technical note, global asymptotic stabilization by sampled-data output feedback is investigated for a class of nonminimum-phase nonlinear systems. Under a global Lipschitz condition imposing on both zero dynamics (i.e., the so-called driven system) and the driving system, together with a lower-triangular form, we prove that the nonminimum-phase system is globally stabilizable by a sampled-data dynamic output compensator that is composed of a nonlinear observer and a linear controller, both in discrete-time. The sampled-data feature makes the proposed output feedback controller easier for digital implementation.

Efficient Computation of Inverse Dynamics and Feedback Linearization for VSA-Based Robots

Abstract: We develop a recursive numerical algorithm to compute the inverse dynamics of robot manipulators with an arbitrary number of joints, driven by variable stiffness actuation (VSA) of the antagonistic type. The algorithm is based on Newton-Euler dynamic equations, generalized up to the fourth differential order to account for the compliant transmissions, combined with the decentralized nonlinear dynamics of the variable stiffness actuators at each joint. A variant of the algorithm can be used also for implementing a feedback linearization control law for the accurate tracking of desired link and stiffness trajectories. As in its simpler versions, the algorithm does not require dynamic modeling in symbolic form, does not use numerical approximations, grows linearly in complexity with the number of joints, and is suitable for online feedforward and real-time feedback control. A Matlab/C code is made available.

Disturbance observer-based feedback linearization control of an unmanned quadrotor helicopter

Abstract: Feedback linearization is widely used for the purpose of quadrotor control. Unfortunately, feedback linearization is highly sensitive to any quadrotor model uncertainties. This paper provides feedb...

Tracking Control of Ball Screw Drives Using ADRC and Equivalent-Error-Model-Based Feedforward Control

Abstract: This paper proposes a novel disturbance-rejection tracking controller for ball screw feed drives. First, active-disturbance-rejection control (ADRC) and proportional-integral (PI) control are employed to ensure the performance of the closed-loop system. In this control framework, the extended state observer estimates and compensates for unmodeled dynamics, parameter perturbations, variable cutting load, and other uncertainties, which improves the disturbance-rejection performance and robustness of the system. Then, based on ADRC feedback linearization, a novel equivalent-error-model-based feedforward controller is designed to further improve the tracking performance of the system. This equivalent error model is independent of the mechanical model, simple to design and easy to tune. Simulations and experimental results demonstrate that the proposed control method has better tracking performance and robustness against the internal and external disturbances compared with the conventional P-PI controller.

Adaptive Fuzzy Control of a Class of MIMO Nonlinear System With Actuator Saturation for Greenhouse Climate Control Problem

Abstract: This paper presents an indirect adaptive fuzzy control scheme for a class of MIMO non-affine nonlinear systems with unknown dynamics and actuator saturation for greenhouse climate control problems. The objective is to implement output tracking control on nonlinear systems. Using feedback linearization, control inputs with known control gains are first synthesized by well-modeled dynamics of the system, and Taylor series expansion is used to transform unknown non-affine dynamics into the corresponding affine forms. Fuzzy logic systems (FLS) are introduced to estimate the unknown nonlinearity of the transformed affine system and the saturation nonlinearity due to the actuator constraint. The control inputs corresponding to nonlinearity are constructed based on the estimations. By introducing a robust control term, estimation errors and external disturbances are well handled, so as to guarantee the stability when tracking the control process. The control gain estimation obtained by FLS is modified to avoid singularity. Lyapunov stability analysis is performed to derive the adaptive law. To validate the effectiveness of the proposed control scheme, we apply it to a greenhouse climate control problem. The ventilation rate in the greenhouse model is unknown; therefore, it is estimated by FLS. The simulation exhibits satisfactory results, in which the temperature and humidity inside the greenhouse are well tracked.

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

Abstract: Summary This paper describes a delay-range-dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time-delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay-range-dependent and delay-dependent stabilization problems for linear and nonlinear time-delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay-rate-independent condition for control of nonlinear systems in the presence of input saturation with unknown delay-derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L2 gain reduction from disturbance to output is devised to address the problem of the stabilization of input-constrained nonlinear time-delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time-delay network and a large-scale chemical reactor under input saturation and varying interval time-delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.

A Review of Control Algorithms for Autonomous Quadrotors

Abstract: The quadrotor unmanned aerial vehicle is a great platform for control systems research as its nonlinear nature and under-actuated configuration make it ideal to synthesize and analyze control algorithms. After a brief explanation of the system, several algorithms have been analyzed including their advantages and disadvantages: PID, Linear Quadratic Regulator (LQR), Sliding mode, Backstepping, Feedback linearization, Adaptive, Robust, Optimal, L1, H-infinity, Fuzzy logic and Artificial neutral networks. The conclusion of this work is a proposal of hybrid systems to be considered as they combine advantages from more than one control philosophy.