Ayman El-Badawy

A novel disturbance observer-based backstepping controller with command filtered compensation for a MIMO system

Abstract This paper presents a novel disturbance observer-based trajectory tracking controller based on the integral backstepping approach. To avoid the complexity of analytically calculating derivatives of virtual control signals in the standard backstepping technique, a command filtered backstepping approach is utilized. The proposed control approach is formulated for a class of nonlinear MIMO systems and provides robustness against external disturbances. This approach is applied on an aerodynamic laboratory setup known as the twin rotor MIMO system (TRMS). Stability analysis of the proposed controller is presented using Lyapunov stability arguments and singular perturbation theory. Simulation studies show that the proposed controller successfully allows the system outputs to track arbitrary reference trajectories and reject arbitrary constant disturbances that may occur due to partial actuator failure. The reliability and effectiveness of the approach is validated experimentally by implementation of the proposed controller on a hardware-in-the-loop system.

Quadratic Nonlinear Control of a Self-excited Oscillator

The objective of this work is to demonstrate the feasibility of the use of the nonlinear saturation-based control concept to suppress self-excited vibrations by means of active nonlinear feedback control. The authors use the van der Pol oscillator as the working model for a self-excited system. A saturation phenomenon is induced by tuning the frequency of the under-damped second-order absorber to one-half that of the primary system. Although the authors conclude that we can achieve some level of performance with this control technique, we question its robustness due to the rich dynamics introduced by the controller.

Quadcopter aggressive maneuvers along singular configurations: an energy-quaternion based approach

Automatic aggressive maneuvers with quadcopters are regarded as a highly challenging control problem. The aim is to tackle the singularities that exist in a vertical looping maneuver. Modeling singularities are resolved by writing the equations-of-motion of the quadcopter in quaternion form. Physical singularities due to underactuation are resolved by using an energy-based control. Energy-based control is utilized to overcome the uncontrollability of the quadcopter at physical singular configurations, for instance, when commanding the quadcopter to gain altitude while pitched at 90°. Three looping strategies (circular, clothoidal, and newly developed constant thrust) are implemented on a nonlinear model of the quadcopter. The three looping strategies are discussed along with their advantages and limitations.

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

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 feedback linearization-based control with robustness by integrating it with a disturbance observer. The proposed approach maintains the simplicity of the control structure without ignoring the high nonlinearities existing in the model by considering these nonlinearities as disturbances to be attenuated by the disturbance observer. Thus, the requirement to include complex high-order Lie derivatives in the controller is eliminated even in the presence of the high nonlinearities. Simulation results show that the proposed controller successfully force the quadrotor to follow the desired position and heading trajectories in the presence of different types of disturbances including ignored nonlinear dynamics, wind disturbances and partial actuator failure.

Backstepping trajectory tracking control of a quadrotor with disturbance rejection

This paper presents a trajectory tracking controller based on the backstepping technique. To avoid the increasing complexity of analytically calculating the derivatives of the virtual control signals in standard backstepping control, a command filtered backstepping approach is utilized. The command filtered backstepping controller is modified to include integral action to increase robustness against external disturbances and unmodeled dynamics. The stability proof of the command filtered integral backstepping approach is presented based on Lyapunovs theorem. The controller is implemented on a quadrotor unmanned aerial vehicle in simulation and compared to a standard integral backstepping controller. Simulation results show that the presented controller yields an improvement in the tracking performance of the quadrotor in the presence of constant disturbances and unmodeled actuator dynamics with lower control effort.

Sliding mode disturbance observer-based control of a twin rotor MIMO system

This work proposes a robust tracking controller for a helicopter laboratory setup known as the twin rotor MIMO system (TRMS) using an integral sliding mode controller. To eliminate the discontinuity in the control signal, the controller is augmented by a sliding mode disturbance observer. The actuator dynamics is handled using a backstepping approach which is applicable due to the continuous chattering-free nature of the command signals generated using the disturbance observer based controller. To avoid the complexity of analytically differentiating the command signals, a first order sliding mode differentiator is used. Stability analysis of the closed loop system and the ultimate boundedness of the tracking error is proved using Lyapunov stability arguments. The proposed controller is validated by several simulation studies and is compared to other schemes in the literature. Experimental results using a hardware-in-the-loop system validate the robustness and effectiveness of the proposed controller.

Time domain disturbance observer based control of a quadrotor unmanned aerial vehicle

This paper presents a time domain disturbance observer based controller applied to a quadrotor unmanned aerial vehicle. The quadrotor stabilization performance, in its hovering configuration, in the presence of wind disturbances is studied using simulations. The wind disturbances are simulated using the Dryden wind model. The disturbance observer based controller is compared to a state space integral controller. The integral controller is designed based on a pole placement approach using a Lyapunov-based methodology. Simulation results have shown that the disturbance observer based controller is found to offer superior stabilization performance. In addition, it offers the advantage of simplified gains tuning due to the separation property.

A Study on Coupled Bending and Torsional Vibrations of Wind Turbine Blades

A parametric study is developed to investigate the effect of geometry, material stiffness and the rotational motion on the coupled flapwise bending and torsional vibration modes of a wind turbine blade. The assumed modes method is used to discretize the derived kinetic and potential energy terms. Lagrange’s equations are used to derive the modal equations from the discretized terms, which are solved for the vibration frequencies. The parametric study utilizes dimensional analysis techniques to study the collective influence of the investigated parameters by combining them into few non-dimensional parameters, thus providing deeper insight to the physics of the dynamic response. Results would be useful in providing rules and guidelines to be used in blade design.

Composite Hierarchical Anti-Disturbance Control of a Quadrotor UAV in the Presence of Matched and Mismatched Disturbances

Quadrotor helicopter is an unstable system subject to matched and mismatched disturbances. To stabilize the quadrotor dynamics in the presence of these disturbances, the application of a composite hierarchical anti-disturbance controller, combining a sliding mode controller and a disturbance observer, is presented in this paper. The disturbance observer is used to attenuate the effect of constant and slow time-varying disturbances. Whereas, the sliding mode controller is used to attenuate the effect of fast time-varying disturbances. In addition, sliding mode control attenuates the effect of the disturbance observer estimation errors of the constant and slow time-varying disturbances. In this approach, the upper bounds of the disturbance observer estimation errors are required instead of the disturbances’ upper bounds. The disturbance observer estimation errors are found to be bounded when the disturbance observer dynamics are asymptotically stable and the disturbance derivatives and initial disturbances are bounded. Moreover, due to the highly nonlinear nature of the quadrotor dynamics, the upper bounds of a part of the quadrotor states and disturbance estimates are required. The nonlinear terms in the rotational dynamics are considered as disturbances, part of which is mismatched. This assumption simplifies the control system design by dividing the quadrotor’s model into a position subsystem and a heading subsystem, and designing a controller for each separately. The stability analysis of the closed loop system is carried out using Lyapunov stability arguments. The effectiveness of the developed control scheme is demonstrated in simulations by applying different sources of disturbances such as wind gusts and partial actuator failure.