LQR Controller Research Articles

Data-Driven Control Method Based on Koopman Operator for Suspension System of Maglev Train

The suspension system of the Electromagnetic Suspension (EMS) maglev train is crucial for ensuring safe operation. This article focuses on data-driven modeling and control optimization of the suspension system. By the Extended Dynamic Mode Decomposition (EDMD) method based on the Koopman theory, the state and input data of the suspension system are collected to construct a high-dimensional linearized model of the system without detailed parameters of the system, preserving the nonlinear characteristics. With the data-driven model, the LQR controller and Extended State Observer (ESO) are applied to optimize the suspension control. Compared with baseline feedback methods, the optimization control with data-driven modeling reduces the maximum system fluctuation by 75.0% in total. Furthermore, considering the high-speed operating environment and vertical dynamic response of the maglev train, a rolling-update modeling method is proposed to achieve online modeling optimization of the suspension system. The simulation results show that this method reduces the maximum fluctuation amplitude of the suspension system by 40.0% and the vibration acceleration of the vehicle body by 46.8%, achieving significant optimization of the suspension control.

The Two-Wheeled Robot: Experimental Evaluation of Two Controllers

Abstract In this paper we present the theoretical and experimental comparison of two digital controllers intended for stabilization of a two-wheeled robot. The properties of an LQG controller and an LQR controller with H ∞ filter are evaluated. Using the μ-analysis, we show that both controllers ensure robust stability of the closed-loop system in the presence of unstructured uncertainty. The results from the closed-loop system experimental evaluation confirm the precise work of both controllers.

Design of Robust Centralized PID Optimized LQR Controller for Temperature Control in Single-Stage Refrigeration System

Design of Robust Centralized PID Optimized LQR Controller for Temperature Control in Single-Stage Refrigeration System

Intelligent vehicle lateral control strategy research based on feedforward + predictive LQR algorithm with GA optimisation and PID compensation

Targeting the lateral motion control problem in the intelligent vehicle autopilot structural system, this paper proposes a feedforward + predictive LQR algorithm for lateral motion control based on Genetic Algorithm (GA) parameter optimisation and PID steering angle compensation. Firstly, based on the vehicle dynamics tracking error model, the intelligent vehicle LQR lateral motion controller as well as the feedforward controller are designed, and upon which the predictive controller is added to eliminate the system lag.Subsequently, exploiting the advantage that the PID algorithm is not model-based, a PID steering angle compensation controller that can directly control and correct the lateral error is designed. Second, a LQR controller based on path tracking deviation is designed by using the parameter rectification method of genetic algorithm (GA), which optimizes the control parameters of the lateral motion controller and improves the adaptivity of the control accuracy. Finally, Based on the Carsim-Simulink co-simulation platform, the simulation validation and analysis of double lane change (DLC) test and circular condition test (CCT) are carried out, and the results indicate that compared with the other two LQR controllers, the optimised controllers improved more than 50% in lateral error and heading error control, and the vehicle sideslip angle and vehicle yaw rate are in the range of −0.05° to 0.05° and − 0.15 rad/s to 0.10 rad/s, and it showed improved performance in tracking accuracy and satisfied vehicle stability constrains.

Adaptive Robust Servo LQR Control for Aircraft Under a Wide Range of Icing Conditions

Adaptive Robust Servo LQR Control for Aircraft Under a Wide Range of Icing Conditions

Balancing and Trajectory-Tracking by LQR Control for Linear Triple-Linked Pendubot

Pendubot is a popular single input-multi output (SIMO) in laboratories to test control algorithms. In this paper, we focus on a developed model of pendubot – linear triple-linked pendubot (LTLP) and propose LQR to control this model. Through simulation, link 1 is kept balanced, kept following trajectories when link 2, 3 is kept upward under LQR control. Thence, besides balancing well this model at TOP position, our algorithm also makes system tracking sine and pulse trajectories well.

Development of state space models for underwater gliders equipped with embedded actuators in vertical and horizontal planes

Nowadays, underwater gliders (UGs) are known as efficiency vehicles to observe and quantify water properties concerning marine environments, seabed characteristics, and water depths. The development of appropriate dynamic and state space models is necessary for designing an effective control system. This study aims to develop state space models for UGs equipped with embedded actuators based on a non-linear dynamic model that takes into account the hydrodynamic characteristics of the body and wings. The method involves utilizing sensitivity analysis and assumptions to construct two distinct state space models, along with the linearization of the non-linear model in horizontal and vertical plane motions. The presented models are compared with simulation and experiment results to enhance validity. Furthermore, the linear models, when compared with the non-linear model and experimental tests, exhibit suitable performance. The results indicate the maximum observed differences of −9.7% in the period of the first cycle, −12.02% in the yaw angle, and 15.5% in the advance length between linear and non-linear models during zigzag, course-changing, and helical maneuvers, respectively. Through the presented linear models, LQR controllers are designed for the SUT glider and are subjected to testing in a real-world environment, experiencing suitable performance.

Optimal design of robust control for belt conveyor systems based on fuzzy dynamic model and Nash game

An optimized robust control method is proposed in this paper to deal with the disturbances of nonlinear factors such as uncertainty in belt conveyor and to realize the speed control of belt conveyor. By controlling the subsystems to track the same desired speed, belt breaks and overlaps caused by varying belt speeds from one section to another are limited. First, a fuzzy model is developed by applying fuzzy set theory to describe uncertainties of belt conveyor such as masses, stiffness, damping and frictions. Second, a robust control is designed for the nominal system and compensating for the uncertainty. With the robust control, the belt conveyor system is proved to be uniformly bounded and uniformly ultimately bounded by the Lyapunov approach. Third, the parameters of controller are optimized based on a non-cooperative game approach. The optimal solution is the Nash equilibrium. Optimal solution allows the controller system to perform better and decrease the cost of control. Finally, by comparing with LQR control and different parameters, the feasibility of robust control and the rationality of the optimal parameters are proven.

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

PLC-based Implementation of Stochastic Optimization Method in the Form of Evolutionary Strategies for PID, LQR, and MPC Control

PLC-based Implementation of Stochastic Optimization Method in the Form of Evolutionary Strategies for PID, LQR, and MPC Control

Active suspension LQR control based on modified differential evolutionary algorithm optimization

Active suspension LQR control based on modified differential evolutionary algorithm optimization

A new model for compressor surge and stall control

This paper compares the bifurcations and closed-loop performances of two compressor models, Moore-Greitzer (MG) and a developed model based on MG (Shahriyari Khaleghi, SK). First, both models are linearized about two equilibrium points (pure surge and fully-developed rotating stall), and the perturbed state-space dynamics and input matrices are obtained. The compressor unstable regions are then identified using an eigenvalue and global bifurcation analysis. Furthermore, optimal LQR controllers are designed, and the performances of closed-loop systems are compared. The LQRs are designed to control the compression system near the peak pressure rise by suppressing surge or stall. Results reveal that if the initial operating point is in the positive slope region of the compressor characteristic and the initial amplitude of the disturbances is small, the LQR controller can stabilize the compressor in both models. However, when the disturbances are intensive, the two models respond differently: although the SK model damps a fair range of disturbances and predicts instability for excessively powerful disturbances, the MG model always damps them, even when extremely intense. Without a controller in the MG model, initial disturbances (even very large) can never grow and are always damped in the compressor’s negative slope region (obviously, the same applies to the controller). However, pending the amplitude of the disturbances (in the absence of a controller), the disturbances in the SK model may be damped or grow. The SK model can successfully control the instabilities if the disturbances are small. Nonetheless, the controller fails to dampen the instabilities for extreme disturbances, which is consistent with reality.

Active Flutter Suppression of a Wing Section in the Subsonic, Sonic and Supersonic Regimes by the H∞ Control Method

This paper compares various procedures for determining the optimal control law for a wing section in compressible flow. The flow regime includes subsonic, sonic and supersonic flows. For the evolution of the system in the Laplace plane, the present method makes use of the exact unsteady aerodynamic forces in this plane once the control law is established. This is a great advantage over other results previously published, where the unsteady aerodynamics in the Laplace plane are merely approximations of the curve-fitted values in the frequency domain (imaginary axis). A comparison of different control techniques like pole placement, LQR and H-infinity control demonstrates that the H-infinity controller is the optimal choice, exhibiting an H-infinity norm approximately two orders of magnitude lower than the LQR case. Furthermore, the H-infinity controller demonstrates lower pole values than those of the pole placement and LQR compensator, showing the advantage of the H-infinity controller in terms of economic efficiency.

LQR controller design for affine LPV systems using reinforcement learning

In this paper, a data-driven sub-optimal state feedback is designed for a continuous time linear parameter varying (LPV) system using reinforcement learning. Time-varying parameters lie in a poly top and the system matrix has an affine representation for the parameters. Two novels, on-policy and off-policy algorithms, are proposed using available data from vertex systems of polytop to minimise a performance index and admit a common Lyapunov function (CLF). A convex optimisation problem is derived for each iteration based on Lyapunov inequality. Algorithms yield stabilising feedback gain in each iteration and convergence to a common lyapunov function. We demonstrate the efficacy of the proposed method by simulation of two case studies.

Integrated control of anti-rollover for high-mobility emergency rescue vehicles

In this paper, an integrated anti-rollover control strategy is proposed to solve the rollover stability problem of emergency rescue vehicles. The integrated anti-rollover control is performed on the Active suspension system and the multi-axle steering system. Firstly, establish an eleven-degree-of-freedom coupled dynamic model for the vehicle; Secondly, the H∞/generalized H2 output feedback controller for Active suspension is designed, and the multi-axle steering LQR controller is designed; The upper level coordinated fuzzy controller is designed again, and the integrated control strategy of anti-rollover is used to integrate the Active suspension system and the multi-axle steering system. The test results show that, compared with the uncontrolled vehicle, the root mean square value of the lateral load transfer rate of the vehicle under integrated control decreased by 14.3%, 12%, and 10.9%; the root mean square values of lateral acceleration decreased by 26.8%, 22.8%, and 27.4%, respectively; the root mean square values of roll angle decreased by 27.7%, 25.2%, and 29.1%, respectively; respectively in the three-vehicle tests, and the proposed integrated control strategy for rollover prevention effectively improved the rollover prevention ability of emergency rescue vehicles.

Optimizing LQR controllers: A comparative study

Linear Quadratic Regulator is one of the most common ways to control a linear system. Despite Linear Quadratic Regulator’s (LQR) strong performance and solid resilience, developing these controllers have been challenging, largely because there is no reliable way to choose the Q and R weighing matrices. In this regard a deterministic method is used for choosing them in this paper, providing the designers a precise control over performance variables. An Artificial Bee Colony (ABC) optimisation is also used to find the sub-optimal gain matrices along with an analytical approach based on neural networks. A comparative study of the three approaches is performed using MATLAB simulations. These three approaches are applied on an inverted pendulum–cart system due to its complexity and dexterity. The results show that all the three methods show comparable performances with the proposed analytical method being slightly better in terms of transient characteristics.

Study of Q-learning and deep Q-network learning control for a rotary inverted pendulum system

The rotary inverted pendulum system (RIPS) is an underactuated mechanical system with highly nonlinear dynamics and it is difficult to control a RIPS using the classic control models. In the last few years, reinforcement learning (RL) has become a popular nonlinear control method. RL has a powerful potential to control systems with high non-linearity and complex dynamics, such as RIPS. Nevertheless, RL control for RIPS has not been well studied and there is limited research on the development and evaluation of this control method. In this paper, RL control algorithms are developed for the swing-up and stabilization control of a single-link rotary inverted pendulum (SLRIP) and compared with classic control methods such as PID and LQR. A physical model of the SLRIP system is created using the MATLAB/Simscape Toolbox, the model is used as a dynamic simulation in MATLAB/Simulink to train the RL agents. An agent trainer system with Q-learning (QL) and deep Q-network learning (DQNL) is proposed for the data training. Furthermore, agent actions are actuating the horizontal arm of the system and states are the angles and velocities of the pendulum and the horizontal arm. The reward is computed according to the angles of the pendulum and horizontal arm. The reward is zero when the pendulum attends the upright position. The RL algorithms are used without a deep understanding of the classical controllers and are used to implement the agent. Finally, the outcome indicates the effectiveness of the QL and DQNL algorithms compared to the conventional PID and LQR controllers.

Vibration control of FGM plate using optimally placed piezoelectric patches

The aim of this study is to propose a methodology to actively control the vibration of functionally graded plates, with the help of piezoelectric actuators and sensors. The study relays on the classical plate theory to analytically formulate the governing equation of motion, which is then expanded to derive a space state equation of the model. The material properties of the FG plate are assumed to vary along the thickness direction. In order to improve the damping effectiveness, the location of the piezoelectric sensors and actuators is optimally determined using the H2 norm. The necessary control voltage was determined based on optimal LQR and LQG controllers.

On designing a configurable UAV autopilot for unmanned quadrotors.

Unmanned Aerial Vehicles (UAVs) and quadrotors are being used in an increasing number of applications. The detection and management of forest fires is continually improved by the incorporation of new economical technologies in order to prevent ecological degradation and disasters. Using an inner-outer loop design, this paper discusses an attitude and altitude controller for a quadrotor. As a highly nonlinear system, quadrotor dynamics can be simplified by assuming several assumptions. Quadrotor autopilot is developed using nonlinear feedback linearization technique, LQR, SMC, PD, and PID controllers. Often, these approaches are used to improve control and to reject disturbances. PD-PID controllers are also deployed in the tracking and surveillance of smoke or fire by intelligent algorithms. In this paper, the efficiency using a combined PD-PID controllers with adjustable parameters have been studied. The performance was assessed by simulation using matlab Simulink. The computational study conducted to assess the proposed approach showed that the PD-PID combination presented in this paper yields promising outcomes.

Performance analysis of fuzzy-LQR and fuzzy-LQG controllers for active vehicle suspension systems

Suspension systems in vehicles are crucial to both ride quality and driving security. The challenge of creating an effective control mechanism for automotive active suspension systems is addressed in this work. In the event of unforeseen road disturbances, the active suspension systems are intended to deliver a more pleasant ride and good handling. Fuzzy-Linear Quadratic Gaussian (FLQG) and Fuzzy-Linear Quadratic Regulator (FLQR) controllers adapting to road disturbances are proposed to enhance vehicle comfort through the reduction of the driver's overall body acceleration. The simulation findings demonstrate that the FLQR and FLQG controllers are efficient in adjusting the automotive suspension configuration under varying road profiles compared to those of the conventional LQR and LQG controllers.