Linear Quadratic Regulator Technique Research Articles

Concomitant Observer-Based Multi-Level Fault-Tolerant Control for Near-Space Vehicles with New Type Dissimilar Redundant Actuation System

This paper presents a concomitant observer-based multi-level fault-tolerant control (FTC) for near-space vehicles (NSVs) with a new type dissimilar redundant actuation system (NT-DRAS). When NSV flight control system faults occur in NT-DRAS and attitude-corresponding sensors, the NSV hybrid output states, including the concomitant observer usable states and the real system states, are applied to solve the FTC gain by using the linear quadratic regulator (LQR) technique. Furthermore, since NT-DRAS is used in NSVs, a multi-level (actuation system level and flight control level) FTC strategy integrating NT-DRAS channel switching and flight control LQR is proposed for complex and worsening fault cases. The most important finding is that though the proposed strategy is applicable for worsening fault cases in NSVs, systematic and accurate criteria for the process being performed are necessary and can improve the FTC efficiency with minimal FTC resources. Additionally, such criteria can improve the NSV’s responsiveness to comprehensive faults, provided that the real-time performance of the fault detection and diagnosis (FDD) scheme can be further optimized. The concomitant observer convergence and the multi-level FTC strategy have been verified by numerical simulations based on the Matlab/Simulink platform.

Decentralized Retrofit Model Predictive Control of Inverter-Interfaced Small-Scale Microgrids

In recent years, small-scale microgrids have become popular in the power system industry because they provide an efficient electrical power generation platform to guarantee autonomy and independence from the power grid, which is a critical feature in cases of catastrophic events or remote areas. On the other hand, due to the short distances among multiple distribution generation systems in small-scale microgrids, the interconnection couplings among them increase significantly, which jeopardizes the stability of the entire system. Therefore, this work proposes a novel method to design decentralized robust controllers based on a retrofit model predictive control scheme to tackle the issue of instability due to the short distances among generation systems. In this approach, the retrofit model predictive controller receives the measured feedback signal from the interconnection current and generates a control command signal to limit the interconnection current to prevent instability. To design a retrofit controller, only the model of a robust closed-loop system, as well as an interconnection line, is required. The model predictive control signal is added in parallel to the control signal from the existing robust voltage source inverter controller. Simulation results demonstrate the superior performance of the proposed technique as compared with the virtual impedance and retrofit linear quadratic regulator techniques (benchmarks) with respect to peak-load demand, plug-and-play capability, nonlinear load, and inverter efficiency.

Propelling precision of longitudinal vibration mitigation in ship propeller shafts through advanced nonlinear intelligent semi-active control leveraging adaptive neuro-fuzzy inference system with linear quadratic regulator

This study presents a pioneering method to address longitudinal vibrations in ship propeller shafts by integrating an intelligent semi-active control system. By leveraging Adaptive Neuro-Fuzzy Inference System (ANFIS) and Linear Quadratic Regulator (LQR) techniques, the proposed system offers a novel solution to a longstanding challenge in maritime engineering. The efficacy of the semi-active control system is assessed through two complementary analyses: frequency domain analyses and Percentage Reduction Index (PRI) values. The investigation reveals substantial PRI values, ranging from 24.68% to 46.87%, indicating notable enhancements in vibration control with the adoption of semi-active technology. Furthermore, frequency domain analyses demonstrate significant advantages, with a peak reduction of 68.21% observed at 750 r/min. To rigorously evaluate the statistical significance of these improvements, paired t-tests were conducted between the semi-active control system and passive strategies. The results confirm a statistically significant difference in vibration reduction ( p < .05) between the two systems. Specifically, for Percentage Reduction Index Values, the t test yielded a p-value of .023, while for Frequency Domain Analyses, the t-statistic significantly exceeded the critical value (t ≈ 8.09, tcritical ≈ 2.571). Both data sets provide compelling evidence to reject the null hypothesis, indicating a significant difference in vibration reduction between the semi-active control system and passive strategies. The PRI values consistently demonstrate superior performance for the semi-active control system, highlighting its effectiveness in mitigating vibrations. These findings validate the effective ness of the system. These results show the practical implications of implementing semi-active control systems in maritime engineering, offering enhanced safety, fuel efficiency, and operational reliability in ship propeller shaft applications.

Optimised output feedback PID controller for LQR inability

ABSTRACT Linear–quadratic regulator (LQR) is a control technique successfully implemented for several complex systems. However, LQR technique in certain cases fails due to disturbances mainly caused by the improper choice of weighting matrices Q and R. Methods using particle swarm optimisation (PSO) are used to find the weighting matrices of LQR and have been proven to be superior. The paper proposes an output feedback LQR proportional–integral–derivative (PID) controller, which is also compared with LQR and PSO-based LQR. The output feedback LQR–PID provides a better response, and the effectiveness of the proposed method is demonstrated through simulations, and experimental validations are conducted on various cases.

Coordinated control of path tracking and yaw stability for distributed drive electric vehicle based on AMPC and DYC

Maintaining both path-tracking accuracy and yaw stability of distributed drive electric vehicles (DDEVs) under various driving conditions presents a significant challenge in the field of vehicle control. To address this limitation, a coordinated control strategy that integrates adaptive model predictive control (AMPC) path-tracking control and direct yaw moment control (DYC) is proposed for DDEVs. The proposed strategy, inspired by a hierarchical framework, is coordinated by the upper layer of path-tracking control and the lower layer of direct yaw moment control. Based on the linear time-varying model predictive control (LTV MPC) algorithm, the effects of prediction horizon and weight coefficients on the path-tracking accuracy and yaw stability of the vehicle are compared and analyzed first. According to the aforementioned analysis, an AMPC path-tracking controller with variable prediction horizon and weight coefficients is designed considering the change of vehicle speed in the upper layer. The lower layer involves DYC based on the linear quadratic regulator (LQR) technique. Specifically, the intervention rule of DYC is determined by the threshold of the yaw rate error and the phase diagram of the sideslip angle. Extensive simulation experiments are conducted to evaluate the proposed coordinated control strategy under different driving conditions. The results show that, under variable speed and low adhesion conditions, the vehicle yaw stability and path-tracking accuracy have been improved by 21.58% and 14.43%, respectively, compared to AMPC. Similarly, under high speed and low adhesion conditions, the vehicle yaw stability and path-tracking accuracy have been improved by 44.30% and 14.25%, respectively, compared to the coordination of LTV MPC and DYC. The results indicate that the proposed adaptive path-tracking controller is effective across different speeds. Furthermore, the proposed coordinated control strategy successfully enhances the vehicle stability while maintaining good path-tracking accuracy even under extreme conditions.

State feedback control of four-phase interleaved boost converter combined with PEM fuel cell

In this paper, a state feedback controller is designed for a four-phase interleaved dc-dc boost converter connected to PEM fuel cell to regulate the output voltage and current around desired values. The proposed controller features two loops based on state feedback, transforming the system into a state representation. The synthesis of the controller gains is validated using the Linear Quadratic Regulator (LQR) technique. To demonstrate its effectiveness, a typical proportional-integral (PI) controller based on the same average modelling is designed for further comparison and discussion. The performance metrics, including output voltage, source current ripples, settling time, and overshoot showcase the high robustness and dynamic characteristics of the proposed controller.The simulations are conducted using Matlab Simulink with a 1kW fuel cell system.

Method of Autonomous Vehicle Control Using Simplified Reference Models and Regulators

This study contains a conceptual solution of the control method for an autonomous vehicle based on a simplified reference model and controllers. The whole issue is considered on the example of the execution phase of the lane change manoeuvre, in which the well-known 4WS (Four-Wheel-Steering) bicycle model and Kalman regulators based on the LQR (Linear-Quadratic Regulator) technique were used. The overall developed control mechatronic system was subjected to simulation studies in Matlab&Simulink. The simulation results showed correct functioning of the entire mechatronic control system and allowed us to determine further research directions. The developed control method can also find application in military vehicles.

Distributed Generation Based WADC for Inter-Area Oscillations Considering Unknown Inputs

Inter-area oscillations (IAOs) are one of the main problems for contemporary power systems because of their low-damping characteristics. Additionally, the damping behaviors of IAOs might be further deteriorated by the addition of low inertial distributed generation (DG) to the power system. Therefore, a novel wide-area damping controller (WADC) for DG-integrated power systems is developed utilizing a modal linear quadratic regulator (LQR) technique that only targets essential IAOs without degrading other local modes. The states participated in linear combination from modal LQR are generally unavailable and need to be estimated. Full order observers are frequently used in literature, although they may not function if some inputs are unavailable. Hence, an unknown input observer (UIO) is suggested in this paper to estimate the states despite certain inputs being unknown. The proposed methodology is then tested on a DG-integrated 4-machine, 11-bus system and 10-machine, 39-bus system to validate the overall proposed design process. Results show that the proposed WADC successfully dampens the crucial IAO modes by 10% and 15% while not degrading other modes of the system.

L1 Adaptive Control Based on Dynamic Inversion for Morphing Aircraft

Morphing aircraft are able to keep optimal performance in diverse flight conditions. However, the change in geometry always leads to challenges in the design of flight controllers. In this paper, a new method for designing a flight controller for variable-sweep morphing aircraft is presented—dynamic inversion combined with L1 adaptive control. Firstly, the dynamics of the vehicle is analyzed and a six degrees of freedom (6DOF) nonlinear dynamics model based on multibody dynamics theory is established. Secondly, nonlinear dynamic inversion (NDI) and incremental nonlinear dynamic inversion (INDI) are then employed to realize decoupling control. Thirdly, linear quadratic regulator (LQR) technique and L1 adaptive control are adopted to design the adaptive controller in order to improve robustness to uncertainties and ensure the control accuracy. Finally, extensive simulation experiments are performed, wherein the demonstrated results indicate that the proposed method overcomes the drawbacks of conventional methods and realizes an improvement in control performance.

Optimal tracking in two-degree-of-freedom control systems: Coupled tank system

This article presents an optimal design of a two-degree-of-freedom (2-DoF) controller that will lead to zero asymptotic steady-state tracking error. The reference inputs are chosen from the set of steps, ramps, and other persistent signals used currently. The main idea is to transform the tracking 2-DoF problem into an equivalent state-space feedback-control synthesis one. Where, an internal model of the reference input is introduced. Then, through the linear quadratic regulator (LQR) technique, the desired performance objectives are addressed by minimizing a quadratic cost function. Finally, the computed state-feedback optimal gains are linked to the polynomials used within the 2-DoF formalism. The fundamental aspect of the design is that it only utilizes the measurable information of the plant provided by its inputs and outputs and take advantage of efficient state-space numerical algorithms. The proposed method is applied to a coupled-tank system, the results achieved confirm the effectiveness of the approach.

SIMULATION OF OPTIMAL SPEED CONTROL FOR A DC MOTOR USING LINEAR QUADRATIC REGULATOR (LQR)

This paper describes DC motor speed control based on optimal Linear Quadratic Regulator (LQR) technique. Controller's objective is to maintain the speed of rotation of the motor shaft with a particular step response.The controller is modeled in MATLAB environment, the simulation results show that the proposed controller gives better performance and less settling time when compared with the traditional PID controller.

Optimization Techniques in the Control of Fluid Flow Dynamics

This paper explores the application of optimization techniques in fluid dynamics, focusing on mathematical modeling, numerical simulations, and practical case studies. We begin by providing a comprehensive overview of optimization methods in fluid dynamics, covering gradient-based optimization, adjoint methods, control theory approaches, and machine learning techniques. Subsequently, we delve into three key application areas: aerodynamic shape optimization, flow control in pipelines, and environmental fluid dynamics. Through detailed case studies, we demonstrate the effectiveness of optimization algorithms in improving system performance and efficiency. In aerodynamic shape optimization, we minimize drag while maintaining lift, showcasing the power of gradient-based optimization and adjoint methods. In flow control, we optimize inlet velocity profiles to minimize energy loss and ensure specified flow rates, employing linear quadratic regulator (LQR) techniques. Finally, in environmental fluid dynamics, we address pollutant dispersion in rivers by optimizing flow rates from upstream sources to minimize downstream pollution concentration, using model predictive control (MPC) methods. Our study contributes practical insights into the integration of optimization techniques with fluid dynamics, offering guidance for researchers and practitioners in tackling real-world engineering challenges.

Trajectory Tracking and Stabilization Control of Rotary Inverted Pendulum based on LQR and LQT Techniques: Simulation and Experiment

Rotary Inverted Pendulum (RIP) plays a vital role in control engineering. Rotary Inverted Pendulum is a complex, nonlinear, non-minimum-phase and under-actuated system which has various applications in the field of Robotics. The main contribution of this paper is to design and control RIP by using Linear Quadratic Regulator (LQR) controller for stabilization at vertically upright position - the unstable equilibrium point, and Linear Quadratic Tracker (LQT) controller for tracking the desired trajectory. Besides, stability of the closed-loop system is analyzed for ensuring the reliability of the developed controller. The simulation is carried out in MATLAB/Simulink environment, and the proposed controllers have been tested on Rotary Inverted Pendulum hardware that is designed by authors. The analysis and results conducted on the system demonstrate the performance of the control schemes, including stabilization of unstable equilibrium point, tracking the desired trajectory, and system response showing the robustness and effectiveness of methods.

Special issue on “Optimal design and operation of energy systems”

Special issue on “Optimal design and operation of energy systems”

Computing of LQR Technique for Nonlinear System Using Local Approximation

The main idea behind the present research is to design a state-feedback controller for an underactuated nonlinear rotary inverted pendulum module by employing the linear quadratic regulator (LQR) technique using local approximation. The LQR is an excellent method for developing a controller for nonlinear systems. It provides optimal feedback to make the closed-loop system robust and stable, rejecting external disturbances. Model-based optimal controller for a nonlinear system such as a rotatory inverted pendulum has not been designed and implemented using Newton-Euler, Lagrange method, and local approximation. Therefore, implementing LQR to an underactuated nonlinear system was vital to design a stable controller. A mathematical model has been developed for the controller design by utilizing the Newton-Euler, Lagrange method. The nonlinear model has been linearized around an equilibrium point. Linear and nonlinear models have been compared to find the range in which linear and nonlinear models’ behaviour is similar. MATLAB LQR function and system dynamics have been used to estimate the controller parameters. For the performance evaluation of the designed controller, Simulink has been used. Linear and nonlinear models have been simulated along with the designed controller. Simulations have been performed for the designed controller over the linear and nonlinear system under different conditions through varying system variables. The results show that the system is stable and robust enough to act against external disturbances. The controller maintains the rotary inverted pendulum in an upright position and rejects disruptions like falling under gravitational force or any external disturbance by adjusting the rotation of the horizontal link in both linear and nonlinear environments in a specific range. The controller has been practically designed and implemented. It is vivid from the results that the controller is robust enough to reject the disturbances in milliseconds and keeps the pendulum arm deflection angle to zero degrees.

On Vehicle Stabilization Under Saturation Constraints by Linear Quadratic Regulator

The stability of a four-wheel vehicle is an issue widely discussed. As an effort to reduce accidents involving four-wheel vehicles, many studies have been conducted to develop a vehicle stability control system. So far, all studies utilize vehicle lateral dynamics model as the reference to derive the desired states. However, defining the desired states using steady-state cornering values may yield instability due to changes in tire cornering stiffness. This paper proposes a simple vehicle stability control system that could stabilize the vehicle and allow tracking of a desired state under the case of vehicle instability due to reduced rear tire cornering stiffness. The controllers are designed using Linear Quadratic Regulator (LQR) technique and combined with the servo control system to track a reference state. Simulations are performed in MATLAB to validate the controller’s performance with and without controller constraint. Results show that the controller successfully stabilizes the vehicle and tracks the desired state.

Implementation of System Identification Techniques and Optimal Control for RC Model Selection by Means of TRNSYS Simulation Results and Experimental Data

Simulating the thermal model of a district requires simultaneously retaining accuracy and simplicity, in order to avoid cumbersome calculations and unrealistic predictions. Within this scope, introducing a simple structure for modeling the energy consumption of a building that can be expanded to the district level becomes essential. In this paper, a hierarchy of thermal models with increasing complexity is developed to identify the simplest structure that can effectively represent the thermal behavior of a building, using a simulated building in TRNSYS and the measurements of a real building as two datasets to estimate the model parameters. Each model is placed in a closed loop system to track the constant indoor temperature by means of the linear quadratic regulator (LQR) technique. To select the best structure, the model outputs are compared to TRNSYS simulations and measurements. The main features of the selected models include the use of only a few parameters to predict the indoor temperature, peak power, total heat demand, and transient behavior of a building. It is shown that the proposed models are able to determine the indoor temperature with less than 1 °C of error, and the total heat demand and peak power are also determined with an error lower than 25%.

Controller Design for the Pitch Control of an Autonomous Underwater Vehicle

In recent years, the Autonomous Underwater Vehicle (AUV) has found its application in a large number of areas, especially in the ocean environment. But due to its highly non-linear nature with six degrees of freedom and the presence of hydrodynamic forces, the equations for AUV control become complex and difficult to design. Hence, in order to overcome this complexity and non-linearity, a reduced-order subsystem is derived for controlling the pitch. Linear Quadratic Regulator (LQR) and Fractional Order PID (FOPID) techniques have been applied for determining the controller for better performance of pitch control in the presence of disturbance.

Linear Quadratic Regulator and Fuzzy Control for Grid-Connected Photovoltaic Systems

This work presents a control scheme to control a grid-connected single-phase photovoltaic (PV) system. The considered system has four 250 W solar panels, a non-inverting buck-boost DC-DC converter, and a DC-AC inverter with an inductor-capacitor-inductor (LCL) filter. The control system aims to track and operate at the maximum power point (MPP) of the PV panels, regulate the voltage of the DC link, and supply the grid with a unity power factor. To achieve these goals, the proposed control system consists of three parts: an MPP tracking controller module with a fuzzy-based modified incremental conductance (INC) algorithm, a DC-link voltage regulator with a hybrid fuzzy proportional-integral (PI) controller, and a current controller module using a linear quadratic regulator (LQR) for grid-connected power. Based on fuzzy control and an LQR, this work introduces a full control solution for grid-connected single-phase PV systems. The key novelty of this research is to analyze and prove that the newly proposed method is more successful in numerous aspects by comparing and evaluating previous and present control methods. The designed control system settles quickly, which is critical for output stability. In addition, as compared to the backstepping approach used in our past study, the LQR technique is more resistant to sudden changes and disturbances. Furthermore, the backstepping method produces a larger overshoot, which has a detrimental impact on efficiency. Simulation findings under various weather conditions were compared to theoretical ones to indicate that the system can deal with variations in weather parameters.

Design and Implementation of a State-feedback Controller Using LQR Technique

The main objective of this research is to design a state-feedback controller for the rotary inverted pendulum module utilizing the linear quadratic regulator (LQR) technique. The controller maintains the pendulum in the inverted (upright) position and is robust enough to reject external disturbance to maintain its stability. The research work involves three major contributions: mathematical modeling, simulation, and real-time implementation. To design a controller, mathematical modeling has been done by employing the Newton-Euler, Lagrange method. The resulting model was nonlinear so linearization was required, which has been done around a working point. For the estimation of the controller parameters, MATLAB LQR function has been utilized. Simulation has been performed for the designed controller and it also has been implemented and tested over the real inverted pendulum. From the results, it is vivid that the designed controller keeps the inverted pendulum in an upright position and rejects the disturbances and falling under gravitational force by adjusting the rotation of the horizontal link.