Linear Quadratic Regulator Controller Research Articles

A novel quadrotor carrying payload concept via PID with Feedforward terms

PurposeThis paper introduces control strategy to enhance the performance of a novel quadrotor unmanned aerial vehicle designed for medical payload delivery. The aim is to achieve precise control and stability when carrying and releasing payloads, which alter the quadrotor’s mass and inertia characteristics.Design/methodology/approachThe equations of motion specific to the payload-carrying quadrotor are derived. A feedforward-proportional-integral-derivative (FF-PID) control strategy is then proposed to address the dynamic changes during payload release. The PID components use propeller speed/orientation information for stability. FF terms based on derivatives of desired position/orientation variables enable adaptation to real-time mass fluctuations.FindingsExtensive simulations, encompassing various fault scenarios, substantiate the effectiveness of the FF-PID approach. Notably, our findings demonstrate superior performance in maintaining altitude precision and stability during critical phases such as takeoff, payload release and landing. Graphical representations of thrust and mass dynamics distinctly illustrate the payload release event. In contrast to the linear quadratic regulator (LQR) and conventional PID control, which encountered difficulties during the payload release process, our approach proves its robustness and reliability.Research limitations/implicationsThis study, primarily based on simulations, demands validation through real-world testing in diverse conditions. Uncertainties in dynamic parameters, external factors and the applicability of the proposed approach to other quadrotor configurations require further investigation. Additionally, this research focuses on controlled payload release, leaving unexplored the challenges posed by unforeseen scenarios or disturbances. Hence, adaptability and fault tolerance necessitate further exploration. While our work presents a promising approach, practical implementation, adaptability and resilience to unexpected events are vital considerations for future research in the field of autonomous aerial medical deliveries.Practical implicationsThe proposed control strategy promises enhanced efficiency, reliability and adaptability for autonomous aerial medical deliveries in critical scenarios.Social implicationsThe innovative control strategy introduced in this study holds the potential to significantly impact society by enhancing the reliability and adaptability of autonomous aerial medical deliveries. This could lead to faster and more efficient delivery of life-saving supplies to remote or disaster-affected areas, ultimately saving lives and reducing suffering. Moreover, the technology’s adaptability may have broader applications in fields like disaster relief, search and rescue missions, and industrial cargo transport. However, its successful integration into society will require careful regulation, privacy safeguards and ethical considerations to ensure responsible and safe deployment while addressing potential concerns related to noise pollution and privacy intrusion.Originality/valueWhile PID control of quadrotors is extensively studied, payload release dynamics have been overlooked. This research studies integration of FF control to enable PID adaptation for a novel payload delivery application.

Linear Quadratic Regulation Control for Falling Liquid Films

Linear Quadratic Regulation Control for Falling Liquid Films

Learning model predictive controller for wheeled mobile robot with less time delay

The weak spots have been examined, a solution has been suggested, the solution has been applied, and a comparison between the simulation and experimental test results has been given in this work. In order to do this, a nonlinear model predictive controller and a linear quadratic regulator controller have been utilized to control a four-wheel mobile robot during modeling and implementation. But the combination of these classic and modern controllers with machine learning can greatly help to make these controllers work more accurately; As a result, in order to increase the accuracy of the performance of these controllers, by training neural networks of multilayer perceptrons, the controllers have been made intelligent. Controllers with cost function have coefficients as weighting to the matrix of system state variables and control input, which are greatly affected by changing these two weighting matrices of problem solving and optimization. For this reason, it is necessary to extract these two matrices for each separate path in order to improve the performance of the controller by trial and error. But by applying the proposed network which is trained with a new algorithm, not only the performance accuracy has increased, but the network extracts these two matrices without the need to spend human energy. Additionally, by training additional neural networks to optimally extract the benefit of the forecast horizon, fewer calculations and faster solution times have been achieved, helping to reduce the current time delays, particularly in the implementation of the nonlinear controller on the robot in the experimental mode. In the hardware section, the solution time has been shortened by looking at and utilizing operators like the U2D2 interface and the pixy camera, which are quicker than the standard procedure. The information indicates that the proposed intelligence technology reacts 40%–50% quicker than the NMPC standard procedure. The suggested algorithm has also minimized the path tracking error since it extracts the optimal gain at each stage. Moreover, a hardware mode solving speed comparison between the recommended and conventional methods is given. In this domain, a 33% increase in solving speed has been noted.

Intelligent vehicle trajectory tracking control based on physics-informed neural network dynamics model

In order to solve the accuracy problem of trajectory tracking control method based on data-driven model, an intelligent vehicle trajectory tracking control method based on physics-informed neural network (PINN) vehicle dynamics model is proposed. Aiming at the problem of poor interpretability of data-driven model, a vehicle dynamics model based on the PINN is established, and the physics-driven deep learning method is used instead of the data-driven deep learning method to obtain the dynamic characteristics of the intelligent vehicle, to benefit from both the physical-based method and the data-driven method. A sequential training method is also proposed to solve the coupling problem when training multiple PINNs simultaneously. The model takes the nonlinearity of the neural network model and physical interpretability into consideration compared to the standard neural network model. Then, based on the PINN vehicle dynamics model, a trajectory tracking controller based on the iterative linear quadratic regulator (ILQR) control algorithm is developed. The optimal control law is derived by optimizing the ILQR control algorithm to implement the intelligent vehicle’s precise and stable tracking for the desired trajectory. The Levenberg-Marquardt (LM) algorithm and line search technology are used and damping factor adjustment rules are set up to enhance the convergence performance of the ILQR control algorithm. In order to verify the effectiveness of the proposed method, the simulation is conducted under the condition of double lane change. The simulation results demonstrate that the proposed method can track the reference trajectory accurately under the limited conditions. Its control performance is much better than other algorithms.

Automatic design of interpretable control laws through parametrized Genetic Programming with adjoint state method gradient evaluation

This work investigates the application of a Local Search (LS) enhanced Genetic Programming (GP) algorithm to the control scheme’s design task. The combination of LS and GP aims to produce an interpretable control law as similar as possible to the optimal control scheme reference. Inclusive Genetic Programming (IGP), a GP heuristic capable of promoting and maintaining the population diversity, is chosen as the GP algorithm since it proved successful on the considered task. IGP is enhanced with the Operators Gradient Descent (OPGD) approach, which consists of embedding learnable parameters into the GP individuals. These parameters are optimized during and after the evolutionary process. Moreover, the OPGD approach is combined with the adjoint state method to evaluate the gradient of the objective function. The original OPGD was formulated by relying on the backpropagation technique for the gradient’s evaluation, which is impractical in an optimization problem involving a dynamical system because of scalability and numerical errors. On the other hand, the adjoint method allows for overcoming this issue. Two experiments are formulated to test the proposed approach, named Operator Gradient Descent - Inclusive Genetic Programming (OPGD-IGP): the design of a Proportional–Derivative (PD) control law for a harmonic oscillator and the design of a Linear Quadratic Regulator (LQR) control law for an inverted pendulum on a cart. OPGD-IGP proved successful in both experiments, being capable of autonomously designing an interpretable control law similar to the optimal ones, both in terms of shape and control gains.

A deep learning optimized LQR method for enhanced formation control with embedded systems

To achieve higher accuracy throughout the formation control processes and enhance precision in dynamic environments, particularly for the formation control of follower vehicles with embedded systems, this paper proposes a method and framework for vehicle formation control. An Ackermann-model based Linear Quadratic Regulator (LQR) controller is developed for lateral distance control and a Proportional-Derivative (PD) controller for longitudinal distance control. To enhance the efficacy of the LQR controller, the Deep Deterministic Policy Gradient Derivative (DDPG) method is introduced into the control system. The DDPG networks are trained in a simulation environment and can subsequently predict LQR parameters in real-time experiments. The practical application of the method is showcased, and the concluding remarks emphasize the potential and superior performance of our proposed formation control approach by experimental comparison with other controllers. This method can be implemented in small vehicles that possess limited computational resources and is also suitable for scenarios requiring dynamic motion control with higher tracking accuracy and stability.

Enhancing Mechanical Safety in Suspension Systems: Harnessing Control Lyapunov and Barrier Functions for Nonlinear Quarter Car Model via Quadratic Programs

Limiting the suspension stroke in vehicles holds critical and conceivable benefits. It is crucial for the safety, stability, ride comfort, and overall performance of the vehicle. Furthermore, it improves the reliability of suspension components and maintains consistent handling during regular and rough driving conditions. Hence, the design of a safety-critical controller to limit the suspension stroke for active suspension systems is of high importance. In this study, we employed a quarter-car model that incorporates a suspension spring with cubic nonlinearity. The proposed safety-critical controller is the control Lyapunov function–control barrier function–quadratic programming (CLF-CBF-QP). Initially, we designed the reference controller as a linear quadratic regulator (LQR) controller based on the linearized quarter-car model. The reference state-feedback LQR controller simplified the design of the control Lyapunov function. Consequently, from the nonlinear model, we construct a simple control Lyapunov function that relies only on the sprung mass velocity to have a relative degree of one. The CLF intends to improve the performance by considering the nonlinearity and via online optimization. We then formulate the control barrier function to restrict the suspension stroke from breaching its limits. To assess the effectiveness of the proposed controller, we present two challenging road inputs for the nonlinear quarter-car model when employing CLF-CBF-QP and LQR controllers. The CLF-CBF-QP findings surpassed the LQR controller in terms of safety and performance. This study highlights the immense potential of CLF-CBF-QP for suspension systems, improving the time-domain performance, limiting the suspension stroke, and guaranteeing safety.

Control of linear instabilities in two-dimensional airfoil boundary layers

The present study deals with the control of linear, modal and non-modal growth of perturbations in a trapezoidal wing boundary layer. The asymmetric NACA 2515 airfoil is chosen for the analysis. The boundary layer velocity profiles, at different locations on the airfoil, are obtained using the Falkner–Skan equations. The non-modal linear stability theory is used to obtain the amplification of the initial perturbations, for which the state-space approach is adopted. The control is brought about using a Linear Quadratic Regulator (LQR) controller by the means of addition of fluid momentum in the wall-normal direction from the wing surface. Maximum transient energy growth is calculated across a range of wavenumber pairs, and control is applied to the pair with the highest energy growth. In this numerical analysis, we show that the transient growth is higher towards the trailing edge because of the adverse pressure gradient of the flow. Upon control actuation, the reduction in the transient energy growth of perturbations is achieved up to a maximum of 54.6%.

Towards High-Precision Quadrotor Trajectory Following Capabilities: Modelling, Parameter Estimation, and LQR Control

Abstract Quadrotor unmanned aerial vehicles (UAVs) are small, agile four-rotor systems suitable for various applications, from surveillance to disaster support missions. Hence, achieving high-precision trajectory tracking is crucial for their successful deployment. This research focuses on modelling, parameter identification, and Linear Quadratic Regulator (LQR) control design for quadrotors, aiming to enhance their trajectory following capabilities. The quadrotor dynamics are a sixth degree-of-freedom (6DOF) equation of motion derived from Newton’s second law, encompassing moment of inertia, centre of gravity, weight, and thrust of propeller parameters. Experimental measurements are conducted to accurately determine these parameters, ensuring a realistic representation of the quadrotor system. Subsequently, a linearized model is constructed to provide a suitable plant for control system development. The LQR control design is intended to improve the trajectory tracking performance. This control strategy is validated through simulation and practical experiments, demonstrating its effectiveness in achieving high-precision trajectory following capabilites. The proposed approach demonstrates that LQR control effectively guides the quadrotor to resemble a predefined trajectory, experiencing only 3 % overshoot observed during the initial phase of flight.

Design of intelligent control for flexible linear double inverted pendulum based on particle swarm optimization algorithm

For the problem of control of flexible linear double inverted pendulum (FLDIP), considering that the method of obtaining LQR parameters through traditional manual trial-and-error is too cumbersome, and the basic particle swarm optimization algorithm has a slower convergence speed and is prone to a local optimal solution, in this paper, a control method is proposed that it can achieve autonomous optimization based on improved the particle swarm optimization (PSO) algorithm. Firstly, the mathematical model of the FLDIPs is given to analyse the stability of the system. Then, the PSO algorithm is improved from the perspective of dynamically adjusting inertia weights to optimize linear quadratic regulator (LQR) parameters. Finally, through simulation comparison with the LQR control effect obtained by the manual trial and error method, the feasibility of the improved PSO algorithm is verified. This method can not only improve the control performance of the system but also effectively overcome the problem of blindness in selecting Q for traditional LQR optimal control.

Tracking and Disturbance Suppression of the Radio Telescope Servo System Based on the Equivalent-Input-Disturbance Approach

This paper presents a composite control algorithm for the radio telescope servo control system to address the target tracking and matched/mismatched disturbance suppression problems. The algorithm consists of the equivalent-input-disturbance (EID) approach and the optimal control method. An EID estimator is developed using the difference between the estimated output of the state observer and the measurement output and then the estimate of the EID is fed forward into the control input to reject the disturbance. A cost function with clear physical meaning is selected and the weighting parameters are adjusted for the optimal controller to improve tracking performance. Considering the nonminimum phase characteristics of the radio telescope system, the state observer gain is computed using the linear matrix inequality (LMI) method. The system stability is analyzed using the small gain theorem, and the linear quadratic regulator (LQR) control method is utilized to determine the state feedback gain. Finally, the composite controller is designed for an identified telescope model. Simulation results show that for the tracking performance, the settling time of proposed method is 1.13 s and reduces by about 0.32 s and 0.87 s than that of the ADRC controller and PI controller, respectively. For the antidisturbance performance, the RMS value and the maximum error of the proposed method are 0.0039 and 0.0128, which are 42.86% and 40.38% of the ADRC controller and 30.71% and 27.77% of the PI controller, respectively, which indicates that the proposed method has better control performance. In addition, the proposed controller has certain robustness to systematic parameter perturbations.

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.

Distributed Minmax Strategy for Multiplayer Games: Stability, Robustness, and Algorithms.

This article studies a distributed minmax strategy for multiplayer games and develops reinforcement learning (RL) algorithms to solve it. The proposed minmax strategy is distributed, in the sense that it finds each player's optimal control policy without knowing all the other players' policies. Each player obtains its distributed control policy by solving a distributed algebraic Riccati equation in a multiplayer noncooperative game. This policy is found against the worst policies of all the other players. We guarantee the existence of distributed minmax solutions and study their L2 and asymptotic stabilities. Under mild conditions, the resulting minmax control policies are shown to improve robust gain and phase margins of multiplayer systems compared to the standard linear-quadratic regulator controller. Distributed minmax solutions are found using both model-based policy iteration and data-driven off-policy RL algorithms. Simulation examples verify the proposed formulation and its computational efficiency over the nondistributed Nash solutions.

Modular Open Source Solar Photovoltaic-Powered DC Nanogrids with Efficient Energy Management System

Initially the concept of a DC nanogrid was focused on supplying power to individual homes. Techno-economic advances in photovoltaic (PV) technology have enabled solar PV stand-alone nanogrids to power individual devices using device-specific architectures. To reduce costs and increase accessibility for a wider range of people, a modular open-source system is needed to cover all applications at once. This article introduces a modular PV-powered nanogrid system, consisting of a do it yourself (DIY) PV system with batteries to allow for off-grid power. The resultant open-source modular DC nanogrid can deliver DC power to loads of different voltage levels, which is possible because of the efficient and parametric energy management system (EMS) that selects modes of operation for the grid based on DC bus voltage and state of charge of batteries. Simulation results verify the coordination between the EMS and the PV-battery system under varying PV power generation and load conditions. This EMS has potential to enable easy personalization of a vast area of applications and expand appropriate technology for isolated communities. A thorough stability analysis has been conducted, leading to the development of an LQR (Linear Quadratic Regulator) controller as a replacement for the conventional PI (Proportional - Integral) controllers for better transient stability of the system.

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.

Vibration control enhancement in a full vehicle dynamic model by optimization of the controller’s gain parameters

Purpose In this paper, improvements in reducing transmitted accelerations in a full vehicle are obtained by optimizing the gain parameters of an active control in a roughness road profile.Design/methodology/approach For a classically designed linear quadratic regulator (LQR) control, the vibration attenuation performance will depend on weighting matrices Q and R. A methodology is proposed in this work to determine the optimal elements of these matrices by using a genetic algorithm method to get enhanced controller performance. The active control is implemented in an eight degrees of freedom (8-DOF) vehicle suspension model, subjected to a standard ISO road profile. The control performance is compared against a controlled system with few Q and R parameters, an active system without optimized gain matrices, and an optimized passive system.Findings The control with 12 optimized parameters for Q and R provided the best vibration attenuation, reducing significantly the Root Mean Square (RMS) accelerations at the driver’s seat and car body.Research limitations/implications The research has positive implications in a wide class of active control systems, especially those based on a LQR, which was verified by the multibody dynamic systems tested in the paper.Practical implications Better active control gains can be devised to improve performance in vibration attenuation.Originality/value The main contribution proposed in this work is the improvement of the Q and R parameters simultaneously, in a full 8-DOF vehicle model, which minimizes the driver’s seat acceleration and, at the same time, guarantees vehicle safety.

Gyroscopic precession control for maneuvering two‐wheeled robot recoil stabilization

AbstractA two‐wheeled robot has high maneuverability and can spin around with a high velocity but is prone to roll over under a recoil force. Because the wheels are only used to control the maneuver speed of the robot. However, a two‐wheeled robot using a gyroscope does not need the control of the wheels and can maintain the stability of the robot under a recoil force during maneuvers even if the gimbal of the gyroscope is not controlled by a torque. In this study, the equations of motion of the gyroscopic robot are derived via Lagrangian equations, and the balancing performance of the uncontrolled gyroscope is simulated via Matlab to determine a desired configuration for mechatronics system design. Then, a linear‐quadratic regulator (LQR) is implemented to the chosen control moment gyroscope (CMG) configuration and compared in simulations of RecurDyn. LQR controller was used to prevent oscillating motions of double CMGs under the recoil force of a weapon. The simulation results showed that the gyroscopic two‐wheeled robot is improved using an LQR controller and powerfully balanced in static with excellent performance.

Active vibration control of fluid-conveying pipelines: Theoretical and experimental studies

For the fluid-conveying pipeline with macro-fiber composites (MFC), relevant dynamic modeling and experimental testing studies are rarely found in previous papers. Therefore, this paper has carried out related research work. Firstly, considering the fluid-structure interaction and piezoelectric effects, a semi-analytical modeling method for the fluid-conveying pipeline with MFC attaching to any position is proposed. A new Runge-Kutta-Gear (RKG) time-domain solution method is presented for solving state-space equations with the characteristics of rigid equations, and the design methods of Linear-Quadratic Regulator (LQR) controller and Proportional-Integral-Derivative (PID) controller are introduced, respectively. Secondly, an experimental system for active control and vibration test is built, and the dynamic model and control method are verified by experiments and simulations. Finally, the influence of relevant control parameters in the controller on the active control effect is discussed, and the influence law of fluid parameters such as fluid velocity and fluid pressure on the active control is also clarified. The novelty of this work is that the active vibration control and solution methods for the fluid-conveying pipeline with MFC are proposed, and the feasibility of MFC for pipeline vibration suppression is verified by experiments, which provides a new technical idea for the vibration reduction design of the fluid-conveying pipeline.

Optimal Control Strategy of Electro-hydraulic Position Servo System Using Genetic Algorithm

Background: The optimal control strategy has been widely used in electro-hydraulic position servo systems to achieve high-precision position tracking. However, the difficulty of selecting the weighted matrices in optimal control often leads to poor tracking accuracy. Objective: This patent proposes an optimal control strategy using a genetic algorithm to improve the tracking accuracy of the electro-hydraulic servo system. Methods: The patent first established the system state equation of the valve-controlled asymmetric cylinder. Secondly, based on linear quadratic optimal control theory and genetic algorithm, an optimal control strategy using a genetic algorithm was proposed. Finally, the simulation and experimental results showed that the designed controller has high position tracking accuracy . Results: The optimal controller using a genetic algorithm was designed using Matlab/Simulink, and the effectiveness of the controller was verified through simulation. Additionally, experimental results showed that the proposed optimal control controller using a genetic algorithm had higher tracking accuracy than the proportional-integral-derivative controller and traditional backstepping controller for a given reference signal. Conclusion: The control technology of the optimal controller using a genetic algorithm was found to be superior to proportional-integral-derivative and traditional backstepping controllers, and the tracking error of the linear quadratic regulator controller was reported to be relatively small. This demonstrated the effectiveness of the optimal control strategy using a genetic algorithm in this patent.

Genetically Tuned Linear Quadratic Regulator for Trajectory Tracking of a Quadrotor

In this paper, a linear quadratic regulator (LQR) controller operating according to the genetically tuned inner-outer loop structure is proposed for trajectory tracking of a quadrotor. Setting the parameters of a linear controller operating according to the inner-outer loop structure is a matter that requires profound expertise. Optimization algorithms are used to cope with the solution of this problem. First, the dynamic equations of motion of the quadrotor are obtained and modelled in state-space form. The LQR controller, which will operate according to the inner-outer loop structure in the MATLAB/Simulink environment, has been developed separately for 6 degrees of freedom (DOF) of the quadrotor. Since adjusting these parameters will take a long time, a genetic algorithm has been used at this point. The LQR controller with optimized coefficients and a proposed LQR controller-based study in the literature are evaluated according to their success in following the reference trajectory and their responses to specific control inputs. According to the results obtained, it was observed that the genetically adjusted LQR controller produced more successful outcomes.