Robust Linear Quadratic Regulator Research Articles

Vibration Control of Flexible Arm Based on Adaptive Robust Sliding Mode Control and LQR Control

Vibration Control of Flexible Arm Based on Adaptive Robust Sliding Mode Control and LQR Control

Adaptive Elite Ant Lion Optimizer tuned optimal controller for underactuated systems

The issue of stabilization and ensuring the correct path is followed in the cart-inverted pendulum underactuated system is being addressed. In the construction of a robust Linear Quadratic Regulator (LQR) optimum controller, the optimization algorithms are best suited for tuning the LQR weighing matrices which are usually obtained by cumbersome trial and error methods. In this study, a novel Adaptive Elite Ant Lion Optimizer (AE-ALO) is suggested to tune the weighing matrices of the optimum controller. Aiming at the foible of ALO's imbalanced exploration for some intricate optimization problems, and influenced by Adaptive Particle Swarm Optimization (APSO), the amended location of antlions in ALO's elitism operator is enhanced, yielding the Adaptive Elite-ALO (AE-ALO). The proposed AE-ALO tested in 12 standard benchmark functions outperforms the existing algorithms interms of global exploration and is then used to tune the LQR weighing matrices such that the trajectory tracking error is minimized. The suggested controller's viability is demonstrated in Quanser's IP02 benchmark Cart-inverted pendulum system. The study found that using the method proposed resulted in a 10.97 % decrease in the ISE of trajectory tracking while stabilizing the pendulum in the unstable upright position, as compared to using ALO and APSO tuned LQR control schemes.

Attitude modelling and real-time robust control of a 3-DoF quadcopter UAV test bench

Abstract In this work, a three degrees-of-freedom (3-DoF) static quadcopter unmanned aerial vehicle (UAV) test-rig of a pendulum-type configuration is custom-designed, developed, instrumented, and interfaced with a PC. The rig serves as a test bed to develop high-fidelity mathematical models as well as to investigate autopilot designs and real-time closed-loop controllers’ performances. The Simulink Desktop Real-Time software is employed for the quadcopter’s attitude signals acquisition and real-time implementation of closed-loop controllers on a target microcontroller hardware. The mathematical models for pitch, roll, and yaw axes are derived via the first principle and validated with the experimental linear system identification (SI) techniques. Subsequently, employing the multi-parameter root contour technique, the classical proportional integral derivative (PID) controllers are designed and implemented in real-time on the quadcopter UAV test rig. This served as a benchmark controller for comparing it with an integral-based linear quadratic regulator (LQR) controller. Further, to improve the transient response of the LQR controller, a novel robust integral-based LQR controller with a feedforward term (LQR-FF) is implemented, which shows much superior performance than the benchmark and basic LQR controller. This work thus will act as a precursor for a more complex 3-DoF autopilot design of an untethered quadcopter.

LQR-Based Suspension for Heavy Vehicles Considering the Time-Varying Characteristics of Vehicle–Road Interaction

The rapidly increasing demand for heavy vehicles in the transportation sector has led to more severe road damage and significantly higher road maintenance costs. Investigation of active suspension system incorporating vehicle–road interaction (VRI) can provide effective means to reduce the road damage and improve the ride comfort of vehicles. In this paper, an active vehicle suspension controller based on the strongly stable and robust linear–quadratic regulator (LQR) principle is developed for the time-varying VRI system. The coupled system is modeled by a quarter-car traveling on the road modeled by an Euler–Bernoulli beam resting on a viscoelastic foundation. Two types of road irregularities, deterministic sine wave and random, are considered in the numerical studies. A time-frozen technique, by which the linear time-varying system is converted to a time sequence of time-invariant systems, is applied to solve for the coupled responses. Three variables, the dynamic tire load, vehicle body acceleration, and suspension relative displacement, are used to assess the effectiveness of the LQR-based controller in comparison to the passive suspension system. The performance of the active control is investigated for different vehicle speeds, vehicle loads, and road profiles. Numerical studies show that the controller can effectively reduce the road damage and improve the ride comfort, with a slight increase in the suspension relative displacement. This work lays a useful foundation in the problem formulation and system parameter influences for future vehicle suspension design and road damage mitigation including VRI.

Robust and intelligent control of quadrotors subject to wind gusts

AbstractThe combination of artificial neural networks with advanced control techniques has shown great potential to reject uncertainties and disturbances that affect the quadrotor during trajectory tracking. However, it is still a complex and little‐explored challenge. In this sense, this work proposes the development of robust and intelligent architectures for position control of quadrotors, improving flight performance during trajectory tracking. The proposed architectures combine a robust linear quadratic regulator (RLQR) with deep neural networks (DNNs). In addition, a comparative study is performed to evaluate the performance of the proposed architectures using three other widely used controllers: linear quadratic regulator (LQR), proportional‐integral‐derivative (PID), and feedback linearization (FL). The architectures were developed using the robot operating system (ROS), and the experiments were performed with a commercial quadrotor, the ParrotTM Bebop 2.0. Flights were performed by applying wind gusts to the aircraft's body, and the experimental results showed that using neural networks combined with controllers, robust or not, improves quadrotors' flight performance.

Spherical robot: A novel robot for exploration in harsh unknown environments

AbstractThe authors propose a complete software and hardware framework for a novel spherical robot to cope with exploration in harsh and unknown environments. The proposed robot is driven by a heavy pendulum covered by a fully enclosed spherical shell, which is strongly protected, amphibious, anti‐overturn and has a long‐battery‐life. Algorithms for location and perception, planning and motion control are comprehensively designed. On the one hand, the authors fully consider the kinematic model of a spherical robot, propose a positioning algorithm that fuses data from inertial measurement units, motor encoder and Global Navigation Satellite System, improve global path planning algorithm based on Hybrid A* and design an instruction planning controller based on model predictive control (MPC). On the other hand, the dynamic model is built, linear MPC and robust servo linear quadratic regulator algorithm is improved, and a speed controller and a direction controller are designed. In addition, based on the pose and motion characteristics of a spherical robot, a visual obstacle perception algorithm and an electronic image stabilisation algorithm are designed. Finally, the authors build physical systems to verify the effectiveness of the above algorithms through experiments.

Hybrid Dynamical Modeling and Control of Permanent Magnet Synchronous Motors: Hardware-in-the-Loop Verification

The stabilization of a permanent magnet synchronous motor using digital controllers requires the design of both the feedback law and an appropriate sampling frequency. Moreover, the design approach must be robust against existing uncertainties, such as disturbances and parameter variations. In this paper, we develop a stabilizing state feedback nonlinear control scheme for the permanent magnet synchronous motor. Moreover, we consider the case where the feedback signal is transmitted over a digital platform, and we derive the stabilizing sampling frequency, such that the stability of the closed-loop system is maintained. We design the controller by emulation, where the closed-loop stability is first established in continuous time; we then take into account the effect of sampling. The feedback law consists of two parts: feedback linearization and robust linear quadratic regulator for the linearized mode. The robustness is achieved by augmenting the state space model, with additional states representing the tracking errors of the motor speed and the motor current. Then, to cope with sampling, we estimate the maximally allowable sampling interval to reduce the sampling frequency while preserving the closed-loop stability. The overall system is modeled as a hybrid dynamical system, which allows handling both the continuous-time and discrete-time dynamics. The effectiveness of the proposed technique is illustrated by simulation and verified experimentally using a hardware-in-the-loop setup. Upon implementing the proposed approach, the obtained sampling interval was around 91 ms, making it suitable for digital implementation setups.

Robust regulation of discrete-time systems subject to parameter uncertainties and state delay

This paper deals with the robust recursive regulation problem of uncertain discrete-time linear systems subject to unknown state delays. The variation rate between two consecutive delays is considered bounded. The parameter matrices are affected by norm-bounded uncertainties. Applying the lifting method and modeling the delay as a Markov chain, systems with state delays are converted to augmented delay-free Markovian jump linear systems. Then, a robust recursive linear quadratic regulator is obtained, solving an optimization problem through robust regularized least-squares approaches. The solution is given in terms of algebraic Riccati equations. We assess the proposed regulator through a numerical example and compare its performance with other robust control approaches.

Improving the Stability of Semi Trailer Articulated Vehicles

The transportation of industrial products is an important function of every industry involved in mass production. This is mostly done with the use of semi trailer articulated vehicles. The dynamics characteristic of these vehicles differs from those of other vehicles, and their accidents are fatal and destructive leading to lost of lives and valuable properties. Therefore, there is a need for continuous research and improvement of the stability of these vehicles. This paper aimed at reviewing literatures on improvement of stability of this vehicle in order to ensure safety of lives and properties. Driver Assistance Systems (DAS) such as Semitrailer Differential Braking Technique (SDBT), Roll Stability Control (RSC) system, Electronic Stability Control (ESC) system, Active Yaw Control (AYC) system, Linear Quadratic Regulator (LQR) controller, Robust LQR (RLQR), were noted as an efficient method for combating the vehicle instability and loss of control. It was noted that the RWA is an important parameter for determining the rollover propensity of this vehicle., while a driver model would be of great important to investigate the interaction between the driver and Driver Assistance Systems (DAS).

Robust LQR Design Method for the Aero-Engine Integral Constant Pressure Drop Control Valve with High Precision

The closed-loop constant pressure drop control valve is widely used in aero-engine fuel servo metering systems. However, the available constant pressure drop control valve cannot realize servo tracking without static error and, often, a high proportional gain is used to reduce the static error and improve the servo tracking performance, which reduces the stability margin. In this paper, an integral constant pressure drop control valve is designed, which consists of an integral controller and a stabilizing controller. Moreover, a robust LQR design method is proposed to complete the design task. Firstly, the controlled plant’s state–space model is derived, and the augmented model with tracking error is established based on the robust servo system design theory. Secondly, a servo controller with dual functions of integral control and stabilization control is constructed and decoupled, in which the stabilizing controller guarantees the asymptotic stability as well as the anti-disturbance performance, and the integral controller realizes the servo tracking without static error. Finally, based on the robust LQR design method, two key design parameters, including the integral control gain and the stabilization control gain, are designed to complete the design task. The simulation results indicate that, even when suffering 50 mm2 metered flow area step disturbance and 1 MPa inlet pressure step change, the designed integral constant pressure drop control valve can realize the function of servo tracking without static error. The static error is almost 0, the settling time is within 0.01 s, the overshoot is within 10%, and the phase margin is more than 55°.

Robust servo linear quadratic regulator controller based on state compensation and velocity feedforward of the spherical robot: Theory and experimental verification

There are few studies on the lateral motion of spherical robots. In this article, a new algorithm is proposed to solve the problem of low control accuracy of the lateral motion. A single lateral motion model is established, and the optimal solution of the linear quadratic regulator in infinite time domain is obtained. Aiming at the problems of longitudinal velocity and lateral angle coupling and low control precision, state compensation and velocity feedforward are carried out, and an improved robust servo linear quadratic regulator control algorithm is proposed. Experiments show that the proposed lateral control algorithm has strong adaptability and robustness to changing speeds and lateral angles, and the control effect is stable and reliable.

Robust LQR control based on multidimensional particle swarm optimization for enhancing the dynamic performance of poultry house system

Robust LQR control based on multidimensional particle swarm optimization for enhancing the dynamic performance of poultry house system

Seamless Operation of Master–Slave Organized AC Microgrid With Robust Control, Islanding Detection, and Grid Synchronization

In this article, islanding detection, control, grid synchronization, and power share techniques have been considered for the seamless operation of ac microgrid in grid-connected mode, islanded mode, and during the transition between both modes. A master–slave organization coordinates the power distribution among microgrid sources. The control scheme of each source is designed with a nested loop robust linear quadratic regulator and mixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{2}/H_{\infty }$</tex-math></inline-formula> optimal controller. The islanding detection algorithm is developed with synchro-extraction transform and optimal support vector machine (OSVM). An optimal linear Kalman filter-based synchronous reference frame phase locked loop (OLKF-SRFPLL) method is considered for the reconnecting of the microgrid to the utility grid. For optimal parameter tuning in the OSVM and LKF-SRFPLL methods, a particle swarm optimization technique is used. The seamless operation of the proposed ac microgrid system is verified in MATLAB/SIMULINK, and the practical feasibility is verified with an experimental photo-type setup and dSPACE 1202 control kit. Simulation and experimental results are presented to illustrate the seamless operation of the proposed ac microgrid system.

Optimisation of robust and LQR control parameters for discrete car model using genetic algorithm

Active suspension systems are the main feature in modern cars and will be the main stream in the future. The optimisation of their performances requires many studies about the different types of controllers. Robust H-infinity and linear quadratic regulator (LQR) controllers are used to control the suspension system and to reduce the vibrations in the car and to improve handling. A half car discrete model is considered in this research to study the effects on passengers owing to different road profiles. The weights of robust H-infinity and LQR controllers are obtained using genetic algorithm on a half car model with two different types of common road disturbance. The design parameters of both the active controllers vary with various road profiles. This proves that particular design parameters in robust and LQR controller do not have the ability to adapt to the variations in road surface. Furthermore, active controllers significantly improve the performance of the system in all aspects when compared to passive systems.

Gearshift Control in Engagement Process of Dual-Motor Coaxial Propulsion System for Electric Bus

Considering single-motor drive system cannot meet the requirements of high-performance electric buses for Beijing Winter Olympics, a dual-motor coaxial propulsion system based on single planet gear set is developed. At the same time, a shift control method based on hierarchical linear quadratic regulator (HLQR) algorithm is designed to improve the poor shift quality caused by the rapid change of output shaft speed in the shift process. In this method, the upper controller adopts robust tracking linear quadratic regulator algorithm to control the speed change rate of the output shaft in the process of gear shifting, so as to reduce the load of gear shifting actuator in the process of gear shifting; the lower controller adopts disturbance suppression linear quadratic regulator algorithm to control the shifting force and improve the adaptability of the system to disturbance conditions Through simulation analysis, the performances of hierarchical linear quadratic regulator algorithm, optimal control algorithm based on variational method and PI algorithm in the process of gear shifting were comparatively analyzed. Simulation results showed that the hierarchical linear quadratic regulator algorithm exhibited a better performance in gear control than the other two algorithms. In addition, a large number of bench test results also proved that compared with PI algorithm, hierarchical linear quadratic regulator algorithm reduced vehicle impact by 19.17% and reduced the shift force by 32.48% in the sacrifice of shift time by 5.03%.

Disturbance Observer-Based Robust Control of a Quadrotor Subject to Parametric Uncertainties and Wind Disturbance

We propose a disturbance observer-based controller to deal with the trajectory tracking problem of a quadrotor subject to parametric uncertainties and wind disturbance. The design is based on the combination of a recursive robust linear-quadratic regulator and a Kalman filter. Robust regulation deals with uncertainties of state and input matrices of the quadrotor in order to minimize, mainly, its trajectory tracking error. Filtering aims to estimate wind disturbance based on an augmented state-space model of the quadrotor. We finish the approach with a compensation controller whose task is to perform disturbance attenuation. We develop indoor experiments where a wind disturbance source provides a measurable speed pattern. We provide a comparative study among the robust control approach proposed with a feedback linearization controller, a proportional-integral-derivative controller, and a nominal linear-quadratic regulator.

Robust LQR and LQR-PI control strategies based on adaptive weighting matrix selection for a UAV position and attitude tracking control

Unmanned aerial vehicles (UAVs) are subject to the wind and other environmental disturbances that can destabilize them. The high performance and robustness of the Linear Quadratic Regulator (LQR) controllers ensure the ability to reduce the deviations in state trajectories with minimum control effort. In this paper, the weighting matrices are adjusted automatically via a novel method implemented through state variables matrix of the quadrotor together with a preference factor. This proposed factor is determined by the designer via penalizing or rewarding a certain state of the quadrotor out of others so that the model insufficiencies against disturbances are compensated. The effectiveness of the proposed method of selecting these matrices is evaluated for the cases of LQR and LQR with a PI controller. They were evaluated with respect to the convergence of state variables to their reference values within a specific time and compliance with their desired performance characteristics. The experimental results revealed that both control strategies could stabilize the quadrotor in the desired position and attitude with better performance and robustness characteristics. The results also showed that the LQR-PI control method is a more reliable and effective approach in achieving higher tracking performances compared to the LQR only.

A Hybrid Linear Quadratic Regulator Controller for Unmanned Free-Swimming Submersible

An unmanned free-swimming submersible (UFSS) is designed to perform certain tasks in water without interposing humans. The vehicle’s control is achieved by integrating mathematical (analog) and non-mathematical (embedded) controllers. The main goal of integrated controllers is to overcome the environmental disturbances and noise of the sensor data. These disturbances, as well as the noise data, are generated during steering, diving, and speed control. The amplitude of disturbances and noise varies with the depth and intensity of water waves. This article presents a robust hybrid linear quadratic regulator (HLQR) controller for UFSS. The presented controller targets the desired state of the UFSS in the presence of a disturbing environment. The hybrid approach is achieved by employing: (1) two linear quadratic regulators or controllers and (2) a mathematical structure of the Riccati equation. Consequently, the proposed HLQR controller is integrated into the UFSS system to evaluate the response in terms of settling time, rise time, overshoot, and steady-state error. Furthermore, the robustness of the HLQR is investigated by considering the feedback to step response and hydrodynamic disturbances. The implementation results reveal that the proposed controller outperforms state of the art controllers, such as proportional-integral-derivative and lead-compensator controllers.

Adaptive immersion and invariance induced optimal robust control of unmanned surface vessels with structured/unstructured uncertainties

This paper addresses the path-tracking performance improvement of unmanned surface vessels (USVs) through a novel adaptive immersion and invariance (I&I) based robust adaptive control algorithm. The substantial drawback related to the control of USVs is the uncertain dynamics of the vessel, and unexpected environmental disturbances due to surges or crosswinds that promote the instability. The asymptotic stability of the closed-loop USV system is guaranteed based on the I&I stability theory, and the adaptation laws for the uncertain parameters are derived accordingly. The design variables of I&I algorithm are varied in a convex optimization problem with constraints on the control inputs. The robustness of the proposed algorithm is further assessed for the target USV subject to uncertain hydrodynamic damping in surge, sway and yaw. The performance of the proposed control algorithm is tested against benchmark schemes of disturbance observer-based composite nonlinear feedback (DO-CNF) and robust LQR (RLQR). The results are suggestive of the improved performance of the USV to follow the intended trajectory while guaranteeing optimality in the sense of actuation constraints.

Feedback-linearization based robust relatively optimal trajectory tracking controller for 3-DOF helicopter

This paper proposes a feedback linearization-based robust trajectory tracking controller for the elevation and pitch axes of three degrees of freedom (3-DOF) helicopter. The 3-DOF helicopter is a benchmark system that operates on the same principle of operation as that of a tandem-rotor helicopter. Accurate control of this laboratory set up in the presence of external disturbances is a sophisticated problem as it is easily affected by external disturbances due to its low weight. Hence, to ensure efficient trajectory tracking performance in the presence of uncertainties and disturbances a nonlinear disturbance observer is integrated with a feedback linearization (FL) based relatively optimal trajectory tracking controller (ROTTC). Feedback linearization of the nonlinear model results in a decoupled linear error dynamics for each axis, which is used for the design of the ROTTC. The stability of the 3-DOF helicopter in the presence of estimation error and parameter uncertainties is analyzed using the Lyapunov method. A comparison study with an FL-based robust linear quadratic regulator (RLQR) method illustrates the superiority of the proposed method in terms of tracking error and disturbance estimation. The efficacy of the proposed controller to accommodate external disturbances is demonstrated with real-time implementation on the 3-DOF helicopter with a strong wind disturbance as well as an impulse disturbance.