scholarly journals Robust Linear Quadratic Regulator via Sliding Mode Guidance for Spacecraft Orbiting a Tumbling Asteroid

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Peng Zhang ◽  
Tianhao Ma ◽  
Bo Zhao ◽  
Bo Dong ◽  
Yuanchun Li
Keyword(s):  
Feedback Linearization ◽  
Actuator Saturation ◽  
Sliding Mode ◽  
Linear Quadratic Regulator ◽  
Transition Process ◽  
The Body ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
Control Scheme ◽  
The Stability

Aiming to ensure the stability of the spacecraft with multiuncertainties and mitigate the threat of the initial actuator saturation, a Robust Linear Quadratic Regulator (RLQR) via sliding mode guidance (SMG) for orbiting a tumbling asteroid is proposed in this paper. The orbital motion of the spacecraft near a tumbling asteroid is modelled in the body-fixed frame considering the sun-relative effects, and the orbiting control problem is formulated as a stabilization of a nonlinear time-varying system. RLQR based on the adaptive feedback linearization is proposed to stabilize the spacecraft orbiting with the uncertainties of the asteroid’s rotation and gravitational field. In order to avoid the initial actuator saturation, SMG is applied to generate the transition process trajectory of the closed-loop system. The effectiveness of the proposed control scheme is verified by the simulations of orbiting the asteroid Toutatis 4179.

scholarly journals Mathematical Modelling and Control of a Two-Wheeled PUMA-LikeVehicle

2016 ◽  
Vol 6 (2) ◽  
pp. 11 ◽  
Author(s):  
Khaled M Goher
Keyword(s):  
Mathematical Modelling ◽  
Sliding Mode ◽  
Impact Load ◽  
State Space Model ◽  
Linear Quadratic Regulator ◽  
The Body ◽  
Pole Placement ◽  
General Motors ◽  
Linear Quadratic ◽  
And Control

<p class="1Body">This paper presents mathematical modelling and control of a two-wheeled single-seat vehicle. The design of the vehicle is inspired by the Personal Urban Mobility and Accessibility (PUMA) vehicle developed by General Motors® in collaboration with Segway®. The body of the vehicle is designed to have two main parts. The vehicle is activated using three motors; a linear motor to activate the upper part in a sliding mode and two DC motors activating the vehicle while moving forward/backward and/or manoeuvring. Two stages proportional-integral-derivative (PID) control schemes are designed and implemented on the system models. The state space model of the vehicle is derived from the linearized equations. Controller based on the Linear Quadratic Regulator (LQR) and the pole placement techniques are developed and implemented. Further investigation of the robustness of the developed LQR and the pole placement techniques is emphasized through various experiments using an applied impact load on the vehicle.</p>

Fault tolerant control using integral sliding modes with control allocation along the null-space

2020 ◽  
Vol 42 (11) ◽  
pp. 2011-2019
Author(s):  
Chengcheng Ma ◽  
Chunsheng Liu ◽  
Jiazhen Yao
Keyword(s):  
Actuator Saturation ◽  
Fault Tolerant ◽  
Sliding Mode ◽  
Null Space ◽  
Fault Tolerant Control ◽  
Control Allocation ◽  
Control Scheme ◽  
Small Gain ◽  
Actuator Constraints ◽  
The Stability

In this paper, a new fault tolerant control scheme with control allocation is presented. The pseudo-inverse along the null-space control allocation is applied to the fault tolerant control system to handle the actuator constraints. The stability of the overall closed-loop system is proved via the small gain theory. The null-space vector is viewed as uncertainty, and is disposed by an integral sliding mode controller and a robust controller. The simulation results show that the new method can solve both failure scenarios and actuator saturation problems well.

Delayed Reference Control of a Two-Mass Elastic System

2004 ◽  
Vol 10 (1) ◽  
pp. 135-159 ◽  
Author(s):  
P Gallina ◽  
Alberto Trevisani
Keyword(s):  
Elastic System ◽  
Linear Quadratic Regulator ◽  
Primary Concern ◽  
Linear Quadratic ◽  
Mass System ◽  
Control Scheme ◽  
Optimal Linear ◽  
Reference Parameter ◽  
The Stability

An innovative non-time-based control scheme for path tracking and vibration control of a two-mass system is introduced in this paper. The basic idea of the scheme, called delayed reference control (DRC), is to make the path reference of the system be a function of an action reference parameter which depends both on time and a variable which plays the role of a time delay. By suitably computing the value of the delay on the basis of the vibration measured, such vibration can be actively suppressed while an independent position regulator ensures an accurate tracking of the desired path. The DRC scheme is therefore suitable for those applications, in particular in the robotic field, where a pre-defined path through space must be followed precisely while the time taken to carry out the task is not a primary concern. In this paper the stability of the system is investigated, and numerical results are provided to assess the performance of the proposed method, compared to that of an optimal linear quadratic regulator.

scholarly journals Polynomial Linear Quadratic Gaussian and Sliding Mode Observer for a Quadrotor Unmanned Aerial Vehicle

2005 ◽  
Vol 17 (4) ◽  
pp. 483-495 ◽  
Author(s):  
Abdellah Mokhtari ◽  
◽  
Abdelaziz Benallegue ◽  
Abdelkader Belaidi ◽  
◽  
...  
Keyword(s):  
Feedback Linearization ◽  
Actuator Saturation ◽  
Sliding Mode ◽  
Mimo System ◽  
Tracking Error ◽  
Sliding Mode Observer ◽  
Exact Linearization ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Output State

A polynomial Linear quadratic Gaussian method is used to compute a controller which is mixed with feedback linearization to control altogether a non linear Quadrotor UAV. A dual criterion involving the minimization of the error and control signal variances is analyzed. The introduction of the feedback linearization is seen to be useful to transform the MIMO system into a non interacting one. This will facilitate the computation of spectral factorization where the behavior is like SISO system. An algorithm is developed in this context. A sliding mode observer is added to feedback loop to estimate the unmeasured states necessary to the inner loop controller. The convergence of output state vector is obtained despite the non-robustness exact linearization when uncertainties on system parameters and disturbances occur. However the sensitivity and complementary sensitivity are presented to confirm the performance and robustness theory and validate the efficiency of results. The weighting functions choice is analyzed through frequency domain. The whole observer-estimator-control constitutes an original suggestion of control system with minimum sensors used. The robustness study has been realized on simulation taking into account uncertainties, disturbances, with a corrupted measured state by noise, and the actuator saturation. The results obtained show the convergence in finite time of estimated values and a satisfying tracking error of desired trajectories.

Sliding Mode Control of a 2D Torsional MEMS Micromirror with Sidewall Electrodes

2013 ◽  
Vol 3 (1) ◽  
pp. 16-26
Author(s):  
Hui Chen ◽  
Manu Pallapa ◽  
Weijie Sun ◽  
Zhendong Sun ◽  
John T. W. Yeow
Keyword(s):  
Sliding Mode Control ◽  
Closed Loop ◽  
Sliding Mode ◽  
Loop System ◽  
Closed Loop System ◽  
Parameter Uncertainties ◽  
External Disturbances ◽  
Mode Control ◽  
Control Scheme ◽  
The Stability

This paper presents a sliding mode control scheme to improve the positioning performance of a 2-Degree-of-freedom (DOF) torsional MEMS micromirror with sidewall electrodes. The stability of closed-loop system is proved by Lyapunov stability theorem under the existence of bounded parameter uncertainties and external disturbances. Furthermore, the performance of the closed-loop system is illustrated by experimental and simulation results which verify that the feasibility and effectiveness of the proposed scheme. The results demonstrated that the torsional MEMS micromirror with the proposed sliding mode controller has a good transient response and tracking performance.

Design and comparison of LQR and a novel robust backstepping controller for supercavitating vehicles

2016 ◽  
Vol 39 (2) ◽  
pp. 149-162 ◽  
Author(s):  
Xiaoyu Zhang ◽  
Yanhui Wei ◽  
Yuntao Han ◽  
Tao Bai ◽  
Kemao Ma
Keyword(s):  
Actuator Saturation ◽  
Control Design ◽  
Linear Quadratic Regulator ◽  
Underwater Vehicles ◽  
Friction Drag ◽  
Linear Quadratic ◽  
Supercavitating Vehicles ◽  
Lqr Control ◽  
Control Scheme ◽  
Backstepping Controller

Traditional underwater vehicles are limited in speed due to dramatic friction drag on the hull. Supercavitating vehicles exploit supercavitation as a means to reduce drag and increase their underwater speed. Compared with fully wetted vehicles, the non-linearity in the modelling of cavitator, fin and in particular the planing force make the control design of supercavitating vehicles more challenging. Dominant non-linearities associated with planing force are taken into account in the model of supercavitating vehicles in this paper. Two controllers are proposed to realize stable system dynamics and tracking responses, a linear quadratic regulator (LQR) control scheme and a robust backstepping control (RBC) scheme. The proposed backstepping procedure, in association with integral filters technique, exploits the possibility of avoiding the overparameterization problem existing in the classical backstepping process. In particular, the achieved stability is robust to modelling errors in supercavitating vehicles. Compared with the LQR control scheme, the RBC scheme is seen to increase the robustness with saturation compensation algorithm, which can be useful for avoiding actuator saturation in magnitude.

Stability Analysis of a Bilateral Teleoperating System

1993 ◽  
Vol 115 (3) ◽  
pp. 419-426 ◽  
Author(s):  
Y. Strassberg ◽  
A. A. Goldenberg ◽  
J. K. Mills
Keyword(s):  
Feedback Linearization ◽  
Closed Loop ◽  
Tracking Error ◽  
Degree Of Freedom ◽  
Closed Loop System ◽  
Control Scheme ◽  
Feedback Linearization Control ◽  
Small Gain ◽  
The Stability ◽  
Three Degree Of Freedom

In this paper the stability of a control scheme for bilateral master-slave teleoperation is investigated. Given the nominal models of the master and slave dynamics, and using an approximate feedback linearization control, based on the earlier work of Spong and Vidyasagar, 1987, a robust closed-loop system (position and force) can be obtained with a multiloop version of the small gain theorem. It is shown that stable bilateral teleoperating systems can be achieved under the assumption that the deviation of the models from the actual systems satisfies certain norm inequalities. We also show that, using the proposed scheme, the tracking error (position/velocity and force/torque) is bounded and it can be made arbitrarily small. The control scheme is illustrated using the simulation of a three-degree-of-freedom master-slave teleoperator (three-degree-of-freedom master and three-degree-of-freedom slave).

scholarly journals A Review on Comparative Remarks, Performance Evaluation and Improvement Strategies of Quadrotor Controllers

Technologies ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 37
Author(s):  
Rupal Roy ◽  
Maidul Islam ◽  
Nafiz Sadman ◽  
M. A. Parvez Mahmud ◽  
Kishor Datta Gupta ◽  
...  
Keyword(s):  
Feedback Linearization ◽  
Sliding Mode ◽  
Control Strategies ◽  
Approximation Error ◽  
Linear Quadratic Regulator ◽  
Industrial Applications ◽  
Training Data ◽  
Linear Quadratic ◽  
Challenges And Opportunities ◽  
Control Technologies

The quadrotor is an ideal platform for testing control strategies because of its non-linearity and under-actuated configuration, allowing researchers to evaluate and verify control strategies. Several control strategies are used, including Proportional-Integral-Derivative (PID), Linear Quadratic Regulator (LQR), Backstepping, Feedback Linearization Control (FLC), Sliding Mode Control (SMC), and Model Predictive Control (MPC), Neural Network, H-infinity, Fuzzy Logic, and Adaptive Control. However, due to several drawbacks, such as high computation, a large amount of training data, approximation error, and the existence of uncertainty, the commercialization of those control technologies in various industrial applications is currently limited. This paper conducts a thorough analysis of the current literature on the effects of multiple controllers on quadrotors, focusing on two separate approaches: (i) controller hybridization and (ii) controller development. Besides, the limitations of the previous works are discussed, challenges and opportunities to work in this field are assessed, and potential research directions are suggested.

Robust stabilization control of a spatial inverted pendulum using integral sliding mode controller

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ishan Chawla ◽  
Vikram Chopra ◽  
Ashish Singla
Keyword(s):  
Inverted Pendulum ◽  
Sliding Mode ◽  
Robust Stabilization ◽  
Linear Quadratic Regulator ◽  
Humanoid Robots ◽  
Sliding Mode Controller ◽  
Linear Quadratic ◽  
Integral Sliding Mode ◽  
Wide Range ◽  
Lqr Controller

AbstractFrom the last few decades, inverted pendulums have become a benchmark problem in dynamics and control theory. Due to their inherit nature of nonlinearity, instability and underactuation, these are widely used to verify and implement emerging control techniques. Moreover, the dynamics of inverted pendulum systems resemble many real-world systems such as segways, humanoid robots etc. In the literature, a wide range of controllers had been tested on this problem, out of which, the most robust being the sliding mode controller while the most optimal being the linear quadratic regulator (LQR) controller. The former has a problem of non-robust reachability phase while the later lacks the property of robustness. To address these issues in both the controllers, this paper presents the novel implementation of integral sliding mode controller (ISMC) for stabilization of a spatial inverted pendulum (SIP), also known as an x-y-z inverted pendulum. The structure has three control inputs and five controlled outputs. Mathematical modeling of the system is done using Euler Lagrange approach. ISMC has an advantage of eliminating non-robust reachability phase along with enhancing the robustness of the nominal controller (LQR Controller). To validate the robustness of ISMC to matched uncertainties, an input disturbance is added to the nonlinear model of the system. Simulation results on two different case studies demonstrate that the proposed controller is more robust as compared to conventional LQR controller. Furthermore, the problem of chattering in the controller is dealt by smoothening the controller inputs to the system with insignificant loss in robustness.

A computationally efficient adaptive robust control scheme for a quad-rotor transporting cable-suspended payloads

2021 ◽  
pp. 095441002110136
Author(s):  
Nasim Ullah ◽  
Irfan Sami ◽  
Wang Shaoping ◽  
Hamid Mukhtar ◽  
Xingjian Wang ◽  
...  
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Adaptive Robust Control ◽  
Computationally Efficient ◽  
Control Scheme ◽  
Control Schemes ◽  
Adaptive Laws ◽  
Unknown Disturbances ◽  
The Stability

This article proposes a computationally efficient adaptive robust control scheme for a quad-rotor with cable-suspended payloads. Motion of payload introduces unknown disturbances that affect the performance of the quad-rotor controlled with conventional schemes, thus novel adaptive robust controllers with both integer- and fractional-order dynamics are proposed for the trajectory tracking of quad-rotor with cable-suspended payload. The disturbances acting on quad-rotor due to the payload motion are estimated by utilizing adaptive laws derived from integer- and fractional-order Lyapunov functions. The stability of the proposed control systems is guaranteed using integer- and fractional-order Lyapunov theorems. Overall, three variants of the control schemes, namely adaptive fractional-order sliding mode (AFSMC), adaptive sliding mode (ASMC), and classical Sliding mode controllers (SMC)s) are tested using processor in the loop experiments, and based on the two performance indicators, namely robustness and computational resource utilization, the best control scheme is evaluated. From the results presented, it is verified that ASMC scheme exhibits comparable robustness as of SMC and AFSMC, while it utilizes less sources as compared to AFSMC.

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