Generalized Dynamic Inversion Research Articles

Rotary inverted pendulum control using neuro-adaptive robust generalized dynamic inversion

The objective of this research is to design a robust control system for trajectory tracking of the under-actuated Rotary Inverted Pendulum (RIP). The focus is on achieving semi-global asymptotic stability in the absence of knowledge about the RIP geometric and inertia parameters. The control design commences by formulating differential servo constraint dynamics (VCD) that encapsulates the control objectives for the RIP. The baseline generalized dynamic inversion (GDI) control law is derived by inverting the VCD for the control voltage input using the Moore–Penrose generalized inverse. To enhance robustness against modeling uncertainties and exogenous disturbances, a sliding mode control (SMC) element is integrated within the GDI control system, resulting in the robust GDI (RGDI) control system. Furthermore, an adaptive estimator that is based on Radial Basis Function Neural Networks (RBF-NN) is adopted to eliminate the dependency of the RGDI control system on the RIP mathematical model. The weighting matrices of the RBF-NN are updated with the aid of a Lyapunov control function. The proposed control system offers robust solution and guarantees semi-global asymptotic stability to the unstable equilibria of the RIP dynamics in the absence of a mathematical model. The proposed control system’s performance is evaluated through computer simulations and experimental tests on a real RIP system. Comparative analyses with traditional SMC and linear quadratic control methodologies are conducted to show the effectiveness of the proposed approach.

Improving MRAC Transient Response Using Generalized Dynamic Inversion and Nullspace Parametrization

We demonstrate how the transient response of Model Reference Adaptive Control (MRAC) is improved by utilizing Generalized Dynamic Inversion (GDI) and the corresponding nullspace parametrization in the powerful Greville formula. The proposed approach neither alters the reference model structure, nor it modifies it through feedback. Rather, the proposed approach utilizes the control redundancy in matching the reference model for the purpose of designing an MRAC control law that yields good transient closed loop adaptive control response. The adaptive GDI-MRAC control law is composed of two parts: a particular part that enforces the reference model dynamics, and an auxiliary part that is affine in a null control vector. The particular and the auxiliary parts of the adaptive control law are confined in the range space of the transposed control matrix and its orthogonal complement nullspace, respectively. The null control vector is projected onto the nullspace of the control matrix via a nullprojection matrix. Hence, the null control vector design does not interfere with the reference model following, yet it can be designed via state feedback to improve closed loop state transient response. An improved Lyapunov control function is used to design the adaptation gains such that asymptotic vanishing of the state error dynamics is guaranteed. Extensive simulations are conducted to demonstrate the efficacy of the proposed method.

Autonomous Underwater Vehicles Attitude control using Neuro-Adaptive Generalized Dynamic Inversion

A novel two loops control architecture is presented for motion control of Autonomous Underwater Vehicle (AUVs). The outer (slow) positional loop incorporates classical Proportional-Derivative control to generate reference pitch and yaw tilting commands based on the positional errors. The reference attitude commands are fed to the inner (fast) attitude control loop, which utilizes Neuro-Adaptive Generalized Dynamic Inversion (NAGDI) control to generate the elevator and rudder deflections. The baseline Generalized Dynamic Inversion (GDI) control composed of particular and auxiliary parts. The particular part is designed by dynamically scaled generalized inversion of the attitude error dynamics, and the auxiliary part is constructed via a Lyapunov control function to provide global asymptotic stability to the angular body rate dynamics. A discontinuous control based on the concept of Sliding Mode Control (SMC) theory is augmented with baseline GDI. The modulation gain of discontinuous term is made adaptive to avoid chattering. Furthermore, online estimation of the unknown nonlinear attitude dynamics is achieved through radial basis function neural networks to obtain the resultant NAGDI control law. The proposed control law guarantees semi-global practically stable attitude tracking. Computer simulations are conducted on a six degrees of freedom simulator of the Monterey Bay Aquarium Research Institute AUV under nominal and perturbed marine environments.

Positional control of rotary servo cart system using generalized dynamic inversion

This paper presents the design approach of Generalized Dynamic Inversion (GDI) for angular position control of SRV02 rotary servo base system. In GDI, linear first order constraint differential equations are formulated based on the deviation function of angular position and its rate, and its inverse is calculated using Moore-Penrose Generalized Inverse to realize the control law. The singularity problem related to generalized inversion is solved by the inclusion of dynamic scaling factor that will guarantee the boundedness of the elements of the inverted matrix and stable tracking performance. Numerical simulations and real-time experiment are performed to evaluate the tracking performance and robustness capabilities of the proposed control law considering nominal and perturbed model dynamics. For comparative analysis, the results of GDI is compared with conventional PID control. Simulation and experimental results demonstrate better angular position tracking for the square-wave and sinusoidal waveforms, which reveals the superiority, and agility of GDI control over conventional PID.

Robust launch vehicle’s generalized dynamic inversion attitude control

PurposeTo design a robust attitude control system for the ascent flight phase of satellite launch vehicles (SLVs).Design/methodology/approachThe autopilot is based on generalized dynamic inversion (GDI). Dynamic constraints are prescribed in the form of differential equations that encapsulate the control objectives, and are generalized inverted using the Moore-Penrose Generalized Inverse (MPGI) based Greville formula to obtain the control law. The MPGI is modified via a dynamic scaling factor for assuring generalized inversion singularity-robust tracking control. An additional sliding mode control (SMC) loop is augmented to robustify the GDI closed-loop system against model uncertainties and external disturbances.FindingsThe robust GDI control law allows for two cooperating controllers that act on two orthogonally complement control spaces: one is the particular controller that realizes the dynamic constraints, and the other is the auxiliary controller that is affined in the null control vector, and is used to enforce global closed-loop stability.Practical implicationsOrthogonality of the particular and the auxiliary control subspaces ensures noninterference of the two control actions, and thus, it ensures that both actions work toward a unified goal. The robust control loop increases practicality of the GDI control design.Originality/valueThe first successful implementation of GDI to the SLV control problem.

Robust Generalized Dynamic Inversion Control of Autonomous Underwater Vehicles

This paper presents the Robust Generalized Dynamic Inversion (RGDI) control system for Autonomous Underwater Vehicles (AUV)s. The outer (position) and the inner (attitude) loops of the control system utilize Generalized Dynamic Inversion (GDI) of two pre-specified asymptotically stable dynamics of the inertial position coordinates and the attitude angles, respectively. The outer loop provides the pitch and yaw tilting commands to the inner loop, which in turns generates values of the corresponding control surface deflections by which the vehicle’s position is controlled. Sliding mode control-based elements are included in the particular parts of the two GDI control loops, and they work to robustify the GDI control system against instabilities and performance deterioration due to unmodeled nonlinearities, parametric variations, and unknown bounded disturbances. A Lyapunov stability analysis of the proposed RGDI control law is presented, and a detailed six degrees of freedom mathematical model of the Monterey Bay Aquarium Research Institute AUV is used to evaluate the controller performance. Numerical simulations are conducted under both nominal and perturbed conditions to demonstrate robustness of the control design.

Generalized Dynamic Inversion based Attitude Control of Autonomous Underwater Vehicles

Abstract: A novel Generalized Dynamic Inversion (GDI) based two-loops structured control system is proposed for position and attitude control of Autonomous Underwater Vehicles (AUVs). The outer (position) loop utilizes Proportional-Derivative (PD) control of the sway and heave position error variables and provides the reference roll and pitch attitude angles to the inner loop. The inner (attitude) loop utilizes GDI control of a prescribed asymptotically stable dynamics of the attitude angles errors from their desired values, and provides the required control surface deflections such that the desired path of the vehicle is tracked. The GDI singularity avoidance is achieved by augmenting a dynamic scaling factor in the Moore-Penrose generalized inverse. The involved null control vector is constructed to be linear in the roll and pitch angular velocities, and the proportionality gain matrix is designed via a control Lyapunov function such that global closed loop stability of the internal dynamics is guaranteed. A detailed six degrees of freedom mathematical model of the Monterey Bay Aquarium Research Institute (MBARI) AUV is used to evaluate performance of the proposed control design, and numerical simulations are conducted to demonstrate its effectiveness and robustness under nominal conditions and in the presence of disturbances and parametric variations.

Fault Tolerant Control of Aircraft Actuating Surfaces using Generalized DI and Integral SM Control

The paper introduces a new fault tolerant control structure against control surface failure, made by a combined use of Generalized Dynamic Inversion (GDI) control and Integral Sliding Mode control (ISMC). The null-control vector in the GDI-based control law parameterizes all the possible control functions that drive the aircraft trajectories to the sliding surface. A simple choice of the null-control vector is made, and is shown to yield closed-loop system stability for the nominal actuator scenario. The small gain theorem is employed to provide an explicit lower limit on the actuator efficiency matrix in the event of faults/failures. The efficacy of the proposed method in tolerating control surface actuator failure is demonstrated on the ADMIRE benchmark model.

Aircraft Multi-Constrained Generalized Dynamic Inversion Control

The new and evolving paradigm of generalized dynamic inversion (GDI) is applied to aircraft maneuvering control design, through the development of a new multiple constraint formulation. The flexibility of GDI in utilizing nullspace of the controls coefficient matrix is exploited to eliminate the problems of excessive control effort and limited performance that are associated with classical dynamic inversion. Scalar deviation functions of the aircraft state error variables are differentiated along the aircraft mathematical model solution trajectories, and linear time varying stable dynamics in these deviation functions are manipulated to obtain linear algebraic constraint equations in the control vector. The constraint equations are inverted using the Greville formula, resulting in the control law. The particular part of the control law drives the states to their desired values, and the auxiliary part acts to stabilize the vehicles inner dynamics by means of the null-control vector. The null-control vector is constructed via a novel class of positive semidefinite Lyapunov functions and nullprojected Lyapunov equations. The closed loop control system is assessed by performing a fully coordinated simultaneous heading-velocity change maneuver. The new type of GDI control laws shows to require low control effort, in addition to providing excellent transient response and reasonable steady-state tracking accuracy.