Ideal Internal Dynamics Research Articles

Anti-Windup Robust Backstepping Control for an Underactuated Reusable Launch Vehicle

The attitude control of an underactuated reusable launch vehicle (RLV) in the reentry phase involving nonminimum phase problem and control input constraints is investigated in this article. To address the nonminimum phase problem, an approach combining output redefinition and robust backstepping is proposed, where a synthetic output is constructed using the combination of the original output and the internal states to obtain stable zero dynamics, and then robust backstepping is performed on the new output. Besides, the ideal internal dynamics are obtained by using optimal bounded inversion, which are incorporated into the controller as the reference trajectories for the internal states to improve the output tracking accuracy. To cope with the control input constraints, a simple and useful anti-windup strategy is proposed by using feedback error clipping, which is shown to be very effective in mitigating control input saturation. Numerical simulations are given to validate the effectiveness of the proposed method.

Output Tracking of Uncertain Nonminimum Phase Systems by Experience Replay

The precision output tracking problem of multi-input-multi-output (MIMO) uncertain nonlinear nonminimum phase systems is investigated in this paper. The challenge lies in the difficulty in solving the ideal internal dynamics (IID), which is a bounded solution for the uncertain zero dynamics. First, the experience replay technique is applied to identify the uncertain parameters in the zero dynamics. It uses the recorded past data concurrently with current data which can greatly speed up the identification convergence. With the identified parameters, a novel approach called optimal bounded inversion is proposed to obtain the IID by solving a trajectory optimization problem using GPOPS-II. The boundedness of the IID is guaranteed by setting state constraints and the feasibility is achieved by minimizing the initial condition mismatch. Moreover, a piecewise IID updating scheme is adopted to reduce the computational burden. The benchmark nonminimum phase system, a vertical take-off and landing (VTOL) aircraft is used to validate the effectiveness of the proposed method.

Robust Adaptive Fuzzy Tracking Control for Uncertain MIMO Nonlinear Nonminimum Phase System

Parameter uncertainty and unmodeled dynamics are inevitable for an actual nonlinear system, and are hard to deal with in control design, especially when the internal dynamics of this nonlinear system are unstable. The control design for a multiinput multioutput nonlinear nonminimum phase system with parameter uncertainty and unmodeled dynamics is discussed in this paper. The internal dynamics of nonminimum phase system are unstable, the control of this kind of system is challenging. Ideal internal dynamics (IID) based controller design method are utilized here, and a partially linearized model is constructed. A state tracking model is constructed on account of the partially linearized model and IID. Then the robust fuzzy controller design problem is discussed and a fuzzy logical system is utilized to identify the parameter uncertainty and unmodeled dynamics. A robust adaptive fuzzy controller is proposed for the stability of the nonlinear nonminimum phase system with parameter uncertainty and unmodeled dynamics. Finally, by simulations on vertical takeoff and landing aircraft, the availability of the presented adaptive fuzzy controller is validated.

Robust Adaptive Fuzzy Control for HFV With Parameter Uncertainty and Unmodeled Dynamics

This paper proposes a robust adaptive fuzzy tracking controller for a hypersonic flight vehicle (HFV) subject to both parametric uncertainties and unmodeled dynamics. First, the nonlinear model of HFV is input/ouput linearization and the internal dynamics of HFV are established. Second, the ideal internal dynamics (IID) are calculated and then an IID-based controller designing method is utilized. With considering parameter uncertainties and unmodeled dynamics, a full state tracking error system is built. Fuzzy logical system (FLS) is utilized to identify the nonlinear system with parameter uncertainty and unmodeled dynamics. An adaptive fuzzy controller is proposed to guarantee the stability of the whole system with parameter uncertainty and unmodeled dynamics. Comparison simulations show remarkable efficiency of the proposed method.

Nonlinear adaptive tracking control of non-minimum phase hypersonic flight vehicles with unknown input nonlinearity

A nonlinear adaptive controller design method for output tracking of hypersonic flight vehicles (HFVs) subject to input nonlinearity is proposed in this paper. The parameters of the input nonlinearity are assumed to be unknown. This problem is challenging because of the complex nonlinearity of HFVs and the existence of the unknown input nonlinearity. The nonlinear model of HFVs is linearized, and the internal dynamics of this model are constructed. Since the internal dynamics of HFVs are non-minimum, an ideal internal dynamics (IID)-based control strategy is utilized and a states tracking model is constructed based on the computed IID. Then a nonlinear adaptive control strategy is designed to guarantee the bounded of output tracking error in the existence of unknown input nonlinearity. Comparison simulation results are provided to verify the available of the proposed method.

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

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

Adaptive sliding mode control of non‐linear non‐minimum phase system with input delay

This study proposes an adaptive sliding mode control (SMC) design method for multi-input multi-output non-linear non-minimum phase system with input delay. The problem is challenging, not only because of the unstable internal dynamics of the non-minimum phase system, but also the existence of input delay. The partially linearised model of the original non-linear system is obtained through input/output linearisation, and a state tracking model is constructed based on the computed ideal internal dynamics. A filtered tracking error is introduced to handle the input delay. A SMC strategy is proposed for the stability of filtered tracking error system, and an adaptive law is designed to estimate the upper bound of perturbations. Finally, comparison simulation results on vertical takeoff and landing aircraft are provided to verify the efficiency of the proposed method.

Approximate stable system centre approach to output tracking of non-minimum phase nonlinear systems

This paper proposes a novel method to approximate the ideal internal dynamics state trajectories which coincide with accurate output tracking for known non-minimum phase nonlinear systems. The proposed approach resembles the stable system centre method, but uses a lower order dynamic system than the stable system centre to generate an approximation of the ideal internal dynamics state trajectories. This approximate stable system centre is used to construct a sliding mode based output tracking controller which can achieve improved transient response at the cost of some tracking accuracy in comparison to the use of the stable system centre. The effectiveness of the proposed approach has been demonstrated considering the position control of a two-wheeled robot and has been found to be promising.

Adaptive variable structure control of input delay non-minimum phase hypersonic flight vehicles

An adaptive variable structure control strategy is proposed for the output tracking control of input delay non-minimum hypersonic flight vehicles. The problem is challenging because of the complex nonlinearity of hypersonic flight vehicles and the existence of input delay. The nonlinear model of hypersonic flight vehicles is partially linearized, and a state tracking model is constructed based on the ideal internal dynamics of hypersonic flight vehicles. A filtered tracking error is introduced to handle the input delay. A variable structure control strategy is proposed for the stability of filtered tracking error system, and an adaptive law is established for the unknown perturbations. Finally, the effectiveness of the proposed control method is shown by the simulation results.

A new generator of causal ideal internal dynamics for a class of unstable linear differential equations

SummaryThe 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 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.

Output-feedback dynamic surface control for a class of nonlinear non-minimum phase systems

In this paper, an output-feedback tracking controller is proposed for a class of nonlinear non-minimum phase systems. To keep the unstable internal dynamics bounded, the method of output redefinition is applied to let the stability of the internal dynamics depend on that of redefined output, thus we only need to consider the new external dynamics rather than internal dynamics in the process of designing control law. To overcome the explosion of complexity problem in traditional backstepping design, the dynamic surface control (DSC) method is firstly used to deal with the problem of tracking control for the nonlinear non-minimum phase systems. The proposed output-feedback DSC controller not only forces the system output to asymptotically track the desired trajectory, but also drives the unstable internal dynamics to follow its corresponding bounded and causal ideal internal dynamics, which is solved via stable system center method. Simulation results illustrate the validity of the proposed output-feedback DSC controller.

Fuzzy stable inversion-based output tracking for nonlinear non-minimum phase system and application to FAHVs

In this paper, a novel fuzzy stable inversion-based output tracking control for multi-input multi-output (MIMO) nonlinear non-minimum phase system is investigated. By applying input/output linearization, the nonlinear system is transformed into a standard form. By applying T–S fuzzy based non-causal inversion approach, more reliable ideal internal dynamics (IID) of the nonlinear system are obtained. The output tracking problem is transformed into a state tracking one, then the T–S fuzzy model technology, which can get a more practical description than simple linearization, is utilized to approach the complex nonlinearity of the internal dynamics. A fuzzy controller design method is proposed for the constructed T–S fuzzy model. The proposed method can improve the control performance of the stable inversion based method, and can be easily solved by standard numerical algorithms. Moreover, the proposed control scheme is applied to solve the output tracking problem of flexible air-breathing hypersonic vehicles (FAHVs).

Output Tracking Control for Nonminimum Phase Flexible Air-Breathing Hypersonic Vehicle Models

AbstractBased on the nonlinear stable inversion approach, an exact output tracking control law is designed for flexible air-breathing hypersonic vehicles (FAHVs). This problem is challenging because of the inherent couplings between the propulsion system, the airframe dynamics, and the presence of strong flexibility effects. Because of the complex nonlinear dynamics of the vehicles, a control-oriented model, which can retain the dominant features of the higher-fidelity model, is adopted for the control design. With respect to velocity and altitude as the regulated outputs, a partially linearized model of FAHVs is obtained through input/output linearization. Then the internal dynamics of FAHVs model are constructed and the stability of the zero dynamics are discussed. Based on the noncausal stable inversion approach, the ideal internal dynamics of FAHVs are computed. A state tracking model is derived from the output tracking problem, and an optimal controller is designed. The stability of the closed-loop s...

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

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

Robust output tracking control for a velocity‐sensorless vertical take‐off and landing aircraft with input disturbances and unmatched uncertainties

SUMMARYIn this paper, we develop a nonlinear controller to achieve output tracking for a nonminimum phase vertical take‐off and landing aircraft without velocity measurements. To attenuate the effects of input disturbances and unmatched uncertainties, auxiliary control inputs are introduced in the state observer. Then by taking the aircraft lateral movement into consideration, a control law is proposed to force the vertical take‐off and landing aircraft to asymptotically track the desired trajectories even in the presence of unexpected changes of the trajectories, while driving the unstable internal dynamics to follow the bounded and causal ideal internal dynamics via the stable system center method. Numerical simulation results illustrate the effectiveness and robustness of the proposed controller. Copyright © 2012 John Wiley & Sons, Ltd.

Robust control of a nonlinear non-minimum phase supersonic flight vehicle based on stable system center

Design and synthesis of a nonlinear time-varying and non-minimum phase supersonic flight vehicle longitudinal dynamics control for g-commands output tracking are presented. Differential geometric approach utilized to outline system relative degree and unstable internal dynamics explored based on the vehicle dynamics transformation into a nonlinear normal form. Unstable internal dynamics are then invoked to identify ideal state reference profiles leading to a desired output-tracking problem. Compensated internal dynamics converged to a solution on the system center manifold for ideal internal dynamics asymptotically. Finally, sliding mode control employed based on an appropriate sliding manifold to track the reference input while being robust against uncertainties. Simulation results are performed and effectiveness of the designed approach demonstrated.

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

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

Robust output tracking control of VTOL aircraft without velocity measurements

AbstractIn this paper, we develop a nonlinear controller to achieve causal output tracking for a non-minimum phase vertical take-off and landing (VTOL) aircraft without velocity measurements. Due to the presence of disturbances, auxiliary control inputs are introduced in the state observer to attenuate their effects. By decomposing the original system into one minimum phase and one non-minimum phase subsystems, the corresponding sub-control laws are respectively designed. After control transformation, the resulting controller not only forces the VTOL aircraft to asymptotically track the desired trajectories, but also drives the unstable internal dynamics to follow the causal ideal internal dynamics solved via stable system center method. Numerical simulation results illustrate the effectiveness of the proposed controller.