Second-order Actuator Dynamics Research Articles

A Flexible MATLAB/Simulink Simulator for Robotic Floating-base Systems in Contact with the Ground: Theoretical Background and Implementation Details

This paper presents an open-source MATLAB/Simulink physics simulator for rigid-body articulated systems, including manipulators and floating-base robots. Thanks to MATLAB/Simulink features like MATLAB system classes and Simulink Function blocks, the presented simulator combines a programmatic and block-based approach, resulting in a flexible design in the sense that different parts, including its physics engine, robot-ground interaction model, and state evolution algorithm are simply accessible and editable. Moreover, through the use of Simulink dynamic mask blocks, the proposed simulator supports robot models integrating open-chain and closed-chain kinematics with any desired number of links interacting with the ground. This simulator can also integrate second-order actuator dynamics. Furthermore, the simulator benefits from a one-line installation and an easy-to-use Simulink interface.

Adaptive Control for a Class of Multi-Input Multi-Output Plants With Arbitrary Relative Degree

In this paper, a new adaptive output-feedback controller for a class of multi-input multi-output linear plant models with relative degree three or higher is developed. The adaptive controller includes a baseline design based on observers and parameter adaptation based on a modified closed-loop reference model. The overall design guarantees stability and tracking performance in the presence of large parametric uncertainties that are common in aircraft models with actuator dynamics. The requisite controller has a computational complexity that is an order of magnitude lower than that of a classical model reference adaptive controller. The proposed adaptive controller is evaluated using a model of a very flexible aircraft with second-order actuator dynamics and parametric uncertainties, and demonstrates stable command tracking behavior in scenarios that cause the failure of an linear quadratic regulator controller and an adaptive controller with a first-order actuator model.

A Method to Compensate Interaction between Actuator Dynamics and Control Allocator under Incremental Nonlinear Dynamic Inversion Controller

When designing flight control allocator for an over-actuated flight system, actuator dynamics, generally, are assumed to be ideal since the bandwidths of actuators are much larger than the frequency of aircraft. However, under incremental nonlinear dynamic inversion controller, the interaction between the constrained control allocation frame and actuator dynamics can cause serious consequence. In this work, a method is developed to compensate for actuator dynamics in s-domain analysis. Here, first-order and second-order actuator dynamics are taken into consideration as more complicated actuator dynamics can be combined by these two simplified models. This method solves for gains, which post-processe the output of control allocation frame. The gains are terse in form and are easy to be calculated, which means that it can be implemented into typical flight computer. Simulation results show proposed method can significantly compensate the flaw caused by actuator dynamics.

Fuzzy Constrained Predictive Optimal Control of High Speed Train with Actuator Dynamics

We investigate the problem of fuzzy constrained predictive optimal control of high speed train considering the effect of actuator dynamics. The dynamics feature of the high speed train is modeled as a cascade of cars connected by flexible couplers, and the formulation is mathematically transformed into a Takagi-Sugeno (T-S) fuzzy model. The goal of this study is to design a state feedback control law at each decision step to enhance safety, comfort, and energy efficiency of high speed train subject to safety constraints on the control input. Based on Lyapunov stability theory, the problem of optimizing an upper bound on the cruise control cost function subject to input constraints is reduced to a convex optimization problem involving linear matrix inequalities (LMIs). Furthermore, we analyze the influences of second-order actuator dynamics on the fuzzy constrained predictive controller, which shows risk of potentially deteriorating the overall system. Employing backstepping method, an actuator compensator is proposed to accommodate for the influence of the actuator dynamics. The experimental results show that with the proposed approach high speed train can track the desired speed, the relative coupler displacement between the neighbouring cars is stable at the equilibrium state, and the influence of actuator dynamics is reduced, which demonstrate the validity and effectiveness of the proposed approaches.

Satellite Attitude Control Using Analytical Solutions to Approximations of the Hamilton-Jacobi Equation

The solution to the Hamilton-Jacobi equation associated with the nonlinear ℋ∞ control problem is approximated using a Taylor series expansion. A recently developed analytical solution method is used for the second-, third-, and fourth-order terms. The proposed controller synthesis method is applied to the problem of satellite attitude control with attitude parameterization accomplished using the modified Rodrigues parameters and their associated shadow set. This leads to kinematical relations that are polynomial in the modified Rodrigues parameters and the angular velocity components. The proposed control method is compared with existing methods from the literature through numerical simulations. Disturbance rejection properties are compared by including the gravity-gradient and geomagnetic disturbance torques. Controller robustness is also compared by including unmodeled first- and second-order actuator dynamics, as well as actuation time delays in the simulation model. Moreover, the gap metric distance induced by the unmodeled actuator dynamics is calculated for the linearized system. The results indicated that a linear controller performs almost as well as those obtained using higher-order solutions for the Hamilton-Jacobi equation and the controller dynamics.

A Decentralized Fault-Tolerant Control System for Accommodation of Failures in Higher-Order Flight Control Actuators

In this paper, an effective integrated failure detection and identification (FDI) and fault-tolerant control (FTC) technique is developed for a class of nonlinear systems actuated by actuators that may undergo several different types of failures. Assuming that the actuator dynamics are fast, a baseline controller is designed and, using the singular perturbation arguments, shown to achieve the control objective. Typical failures in flight control actuators are considered next, and online FDI algorithms are derived for second-order actuator dynamics with non-measurable actuator rates, and third-order actuator dynamics when only output of the actuator is measurable. The FDI subsystem is decentralized in that an observer is run at each of the actuators, and the parameter estimates are adjusted using only the local information. The major issue of how to use this information to reconfigure the control law and assure the stability of the resulting closed-loop control system is addressed. An adaptive fault-tolerant controller that uses the parameter estimates from the FDI subsystem at every instant is designed next. It is demonstrated that all the signals in the system are bounded and that the tracking error converges to zero asymptotically despite multiple simultaneous actuator failures even in the case of second or third order actuator dynamics. The properties of the proposed FDI-FTC algorithms are evaluated through piloted simulations of the F/A-18 aircraft.

Compensation of Actuator Dynamics in Nonlinear Missile Control

This brief presents an approach to the compensation of the actuator dynamics in nonlinear missile control. In general, actuator dynamics are not considered in nonlinear missile control systems. Here, we analyzed the influences of actuator dynamics on the nonlinear missile controller and found that the second-order actuator dynamics showed risks of potentially destabilizing the overall system. Thus, to accommodate for the influence of the actuator dynamics, a compensator is proposed where the information of the nonlinear control input and the actual fin deflection is incorporated. We also conducted performance and stability analysis for the proposed control system, including actuator dynamics. We were able to confirm the validity of the proposed approach based on simulation results for the first- and second-order actuator dynamics.