Block Strict Feedback Form Research Articles

High-α maneuver under lateral centre of gravity uncertainty: A robust adaptive backstepping control scheme

The present note addresses the novel problem of executing complex aircraft maneuvers under considerable center of gravity (c.g.) uncertainties arising from asymmetrical loading or release of payloads, uneven fuel consumption etc. First, the aircraft flight dynamics under predominantly lateral c.g. movement, is approximated and expressed in a block strict feedback form and thereafter an adaptive backstepping controller is proposed to adapt to the c.g. variations. To alleviate the model uncertainty caused by this model approximation and also to provide robustness to aerodynamic uncertainties in high-alpha regions, a sliding mode control is further integrated with the adaptive backstepping control law. Asymptotic stability conditions of the proposed controller are derived from the first principle using Lyapunov’s method and Barbalat’s lemma. To validate the proposed control scheme, the high-alpha Herbst maneuver is implemented in simulation for the F18-HARV aircraft and the results show that the maneuver performance remains nearly the same under both the nominal and the off-nominal c.g. positions.

Adaptive block backstepping control for a UAV performing lateral maneuvers under lateral c.g. uncertainty

PurposeUnmanned aerial vehicles (UAVs) have wide applications in surveillance and reconnaissance without risking human life. Due to unbalanced payload distribution or in-flight deployment, UAVs may undergo lateral center of gravity (c.g.) variations resulting in an asymmetric dynamic having significant longitudinal and lateral/directional coupling and hence more pronounced nonlinearity. Therefore, automatic control of UAVs becomes extremely difficult when it is forced to perform maneuvers under such imbalance in lateral mass distribution. The purpose of this paper is to design adaptive nonlinear control so that the UAV can perform some useful lateral/directional maneuver under lateral c.g. uncertainty.Design/methodology/approachFirst the nominal lateral/directional dynamics of a fixed-wing UAV is framed into strict feedback form and then the block backstepping approach is used to design the controller to execute horizontal turn and aileron roll maneuvers under no lateral c.g. variation. Thereafter, an adaptive block backstepping controller is designed to adapt to uncertainty in lateral c.g. position considering an approximate model of the asymmetric dynamics. The proposed adaptive scheme is validated against the same two maneuvers as considered for the nominal case.FindingsFirst it is shown that the lateral/directional dynamics of a UAV can be converted to a block strict feedback form for executing some lateral/directional maneuvers. However, it was observed that the maneuver performance suffers significant performance degradation under lateral c.g. variations. To mitigate this issue, a simple and computationally inexpensive adaptive block backstepping scheme is proposed and validated. The adaptation law is further proved to be able to asymptotically estimate the actual c.g. location of the UAV.Practical implicationsThe proposed control scheme allows the UAV to automatically adapt to lateral c.g. variations so that the intended maneuvers are performed without any noticeable loss in maneuver performance.Originality/valueThere are very few works available in the literature that address nonlinear control designs for executing specific lateral/directional maneuvers and, moreover, they consider symmetric UAVs or aircraft only. This paper addresses the practical problem of autonomous maneuvering for UAVs with unbalanced lateral mass distribution leading to shift of c.g. out of its plane of symmetry.

Trajectory Tracking Control of a Class of Underactuated Mechanical Systems with Nontriangular Normal Form Based on Block Backstepping Approach

In this paper, the formulation of a block-backstepping control approach is presented to address the trajectory tracking problem for a general class of nonlinear n degrees of freedom (n-DOF) underactuated mechanical systems (UMSs) in nontriangular normal form. First, the Euler-Lagrange model of the general form of UMSs is transformed into block-strict feedback form. Then, control input for the n-DOF UMS will be obtainable by synthesis of the backstepping approach. Additionally, an integral action is incorporated to the proposed controller to enhance the steady state performance of the overall system and also to improve the trajectory tracking precision of the control system. Lyapunov theory is utilizable to prove the stability and convergence of the overall system. To demonstrate the effectiveness of the designed controller, the proposed control algorithm is applied through numerical simulation for the trajectory tracking of a single-link flexible-link flexible-joint manipulator (SFLFJM) as an UMS with the nontriangular normal form.

Neural Block Control via Integrator Backstepping for a Robotic Arm in Real-Time

This paper presents an online neural identification and control scheme in continuous-time for trajectory tracking of a robotic arm evolving in the vertical plane. A recurrent high-order neural network (RHONN) structure in a block strict-feedback form is proposed to identify online in a series-parallel configuration, using the filtered error learning law, the dynamics of the plant. Based on the RHONN identifier structure, a stabilizing controller is derived via integrator backstepping procedure. The performance of the neural control scheme proposed is tested on a two degrees of freedom robotic arm, of our own design and unknown parameters, powered by industrial servomotors.

Discrete time immersion and invariance adaptive control via partial state feedback for systems in block strict feedback form

This paper presents a new method for the adaptive (tracking) regulation via partial state feedback for a class of discrete-time nonlinear systems in parametric strict-feedback form. A procedure is proposed based on immersion and invariance control approach where the parameter estimator and state observer designs are accomplished simultaneously. The algorithm utilizes discrete-time adaptive backstepping in the controller construction while providing a design without over parametrization. The proposed controller construction guarantees boundedness of the closed-loop trajectories and global (tracking) convergence to the origin of the state of the closed-loop system. The performance of the proposed method is illustrated by simulations.

Adaptive fuzzy control with minimal leaning parameters for electric induction motors

In this paper, an effective adaptive tracking control approach is constructed for the sixth-order induction motor model which is in discrete-time form. The fuzzy logic systems (FLSs) are applied to estimate a control law and used to a block strict feedback form (BSFF) which is in existence of bounded disturbances. Then, a desired optimal control can be achieved. Depend on the Lyapunov analysis approach, for the considered system, the stability is guaranteed, the tracking error can be ensured to a small neighborhood around zero, and the weight estimates can be insured to semi-global uniformly ultimately bounded (SGUUB). An advantage for the controlled system is that the proposed algorithm needs only less parameters which is different from the existing results, therefore, it can reduce the calculation amount. The practicality of the scheme is verified via a simulation.

Design of block backstepping controllers for a class of perturbed multiple inputs and state-delayed systems in semi-strict-feedback form

Based on the Lyapunov stability theorem, an adaptive block backstepping control scheme is proposed in this paper for a class of multi-input systems with mismatched multiple state-delayed perturbations to solve regulation problems. The traditional backstepping control method is modified so that it can be directly applied to systems in block semi-strict-feedback form. The terms in the dynamic equations which do not satisfy the block strict-feedback form are accumulated in the last design step and are suppressed effectively by the adaptive gains, so that the property of asymptotic stability is achieved. Adaptive mechanisms are employed in each of the virtual input controllers as well as the robust controller, hence the least upper bounds of perturbations are not required to be known in advance. A numerical example and a practical application are also given for demonstrating the feasibility of the proposed control scheme.

Nonlinear state feedback controller design for underactuated mechanical system: A modified block backstepping approach

This paper presents the formulation of a novel block-backstepping based control algorithm to address the stabilization problem for a generalized nonlinear underactuated mechanical system. For the convenience of compact design, first, the state model of the underactuated system has been converted into the block-strict feedback form. Next, we have incorporated backstepping control action to derive the expression of the control input for the generic nonlinear underactuated system. The proposed block backstepping technique has further been enriched by incorporating an integral action additionally for enhancing the steady state performance of the overall system. Asymptotic stability of the overall system has been analyzed using Lyapunov stability criteria. Subsequently, the stability of the zero dynamics has also been analyzed to ensure the global asymptotic stability of the entire nonlinear system at its desired equilibrium point. The proposed control algorithm has been applied for the stabilization of a benchmarked underactuated mechanical system to verify the effectiveness of the proposed control law in real-time environment.

Control of an Industrial PA10-7CE Robot Arm Based on Decentralized Neural Backstepping Approach

This paper presents a discrete-time decentralized control strategy for trajectory tracking of a Mitsubishi PA10-7CE robot arm. A high order neural network is used to approximate a decentralized control law designed by the backstepping technique as applied to a block strict feedback form. The weights for each neural network are adapted online by extended Kalman filter training algorithm. The motion of each joint is controlled independently using only local angular position and velocity measurements. The stability analysis for closed-loop system via Lyapunov theory is included. Finally, the simulations results show the feasibility of the proposed scheme.

Dimensional Analysis of Acid Etching Effects on Vertically Grown Carbon Nanofibers Using Atomic Force Microscopy

This paper presents a discrete-time decentralized control scheme for trajectory tracking of a two degrees of freedom (DOF) robot manipulator. A high order neural network (HONN) is used to approximate a decentralized control law designed by the backstepping technique as applied to a block strict feedback form (BSFF). The weights for each neural network are adapted online by an extended Kalman filter training algorithm. The motion for each joint is controlled independently using only local angular position and velocity measurements. The stability analysis for the closed-loop system via the Lyapunov approach is included. Finally, the real-time results show the feasibility of the proposed control scheme robot manipulator.

Decentralized Neural Backstepping Control Applied to a Robot Manipulator

This paper presents a discrete-time decentralized control scheme for trajectory tracking of a two degrees of freedom (DOF) robot manipulator. A high order neural network (HONN) is used to approximate a decentralized control law designed by the backstepping technique as applied to a block strict feedback form (BSFF). The weights for each neural network are adapted online by an extended Kalman filter training algorithm. The motion for each joint is controlled independently using only local angular position and velocity measurements. The stability analysis for the closed-loop system via the Lyapunov approach is included. Finally, the real-time results show the feasibility of the proposed control scheme using a robot manipulator.

Discrete-Time Backstepping Synchronous Generator Stabilization using a Neural Observer

This paper deals with adaptive tracking for discrete-time MIMO nonlinear systems in presence of bounded disturbances, based on a neural observer. A high order neural network structure is used to approximate a control law designed by the backstepping technique, applied to a block strict feedback form (BSFF); besides the observer is based on a recurrent high-order neural network (RHONN), which estimates the state vectors of the unknown plant dynamics. The learning algorithm for both neural networks is based on an Extended Kalman Filter (EKF). The applicability of the proposed approach is tested, via simulations, by its application to synchronous generators control.

Discrete-Time Adaptive Backstepping Nonlinear Control via High-Order Neural Networks

This paper deals with adaptive tracking for discrete-time multiple-input-multiple-output (MIMO) nonlinear systems in presence of bounded disturbances. In this paper, a high-order neural network (HONN) structure is used to approximate a control law designed by the backstepping technique, applied to a block strict feedback form (BSFF). This paper also includes the respective stability analysis, on the basis of the Lyapunov approach, for the whole controlled system, including the extended Kalman filter (EKF)-based NN learning algorithm. Applicability of the scheme is illustrated via simulation for a discrete-time nonlinear model of an electric induction motor.