Linear Quadratic Control Research Articles

Study of Permanent Magnet Synchronous Motor With LQG Controller and Observer On The Hydraulic Pump System

In today's aircraft industry, the flight control system and landing gear system cannot be separated from the role of the hydraulic technology system. As the prime mover of the hydraulic pump or actuator hydraulic system, a permanent magnet synchronous motor (PMSM) is used. This PMSM is a substitute for the role of conventional combustion engines, and PMSM is considered to have several advantages in increasing performance and efficiency. This research will develop a system to find parameter values for Linear Quadratic Gaussian (LQG) controllers in a hydraulic pump system that is installed as a load from PMSM and then observe and analyze the performance of the response of the synchronous motor system, namely in the form of changes in rotor rotation speed, torque electric power, and stator current on the q-axis. The results of the research on the characteristics of the PMSM implemented in the hydraulic pump system show that the LQG controller is more optimal when compared to the observer controller. The LQG controller is known to have a faster transient response, which is indicated by the value of the settling time improvement at no load, namely 116.67% for the observer controller and 364.705% without the controller. Then when the synchronous motor serves the nominal load, the rotational speed of the rotor produced in the steady state becomes 8.29% faster than the observer controller and 74.49% without the controller. This rotor's rotational speed affects the time the actuator needs to extend and retract motion.

Toward an optimal twisting-sliding mode control of a three-phase PMSM for electric vehicles

This paper deals with an optimal twisting sliding mode controller (OT-SMC) for the operation of a three phase permanent magnet synchronous machine (PMSM) in an electric vehicle (EV). In order to drive these vehicles, optimal performance is needed with robust control against real-time disturbances such as the variable load torque, uncertainties such as the parameters variation and speed variations between medium, low, and high speed as well as good performance characteristics for enhanced drive quality and longer battery time. Several conventional techniques have been applied to PMSM but they suffer from the problem of uncertainties and disturbances due to the PI regulator. A hybrid approach comprising of a robust nonlinear and optimal controller to achieve these objectives is attempted for driving electrical vehicles. This advanced hybrid controller obtained after the merger of sliding mode control (SMC) and a linear quadratic controller (LQR) is found to outperform existing controllers due to their superb performance characteristics. Furthermore, SMC is designed based on the exponential reaching law for the twisting sliding mode control (T-SMC) in order to ensure stability of the system while reducing the chattering, accelerating the rate of convergence with higher accuracy of the control performance, and the LQR is developed using the steady-state error method (N-LQR) in order to obtaining better performance characteristics. In addition, the hybridization between a twisting SMC and an optimal LQR is characterized by stabilizing and minimizing the oscillations in the permanent regime thus optimizing the system’s performance. Extensive simulation results illustrate the effectiveness and validity of the proposed control for achieving the highest performance of the PMSM.

Intelligent Power Control of Inverter Air Conditioners in Power Systems: A Brain Emotional Learning-Based Approach

Inverter air-conditioning (IAC) units have been proved to be effective in frequency regulation by providing flexible capacities. This paper proposes a brain emotional learning (BEL)-based controller to provide the IACs with control signals to be efficiently involved in the frequency regulation in power systems. The BEL-based controller can learn quick-auto, making it appropriate in systems facing uncertainty. To assess the BEL controller performance in realistic conditions, the uncertainties as a consequence of variations in system parameters and load level are considered. The goal is to use the BEL controller to increase the IAC units' ability to track regulation signals accurately in uncertain circumstances. The controller is compared to a fuzzy-PI control, a proportional control scheme, a model predictive control and a linear quadratic regulator control. A delay-dependent stability criterion is used to calculate the highest time delay in the IACs response under which the system maintains stability. In addition, this paper presents an BEL-based coordinator to coordinate the IACs and traditional generation units for compensating considerable frequency variations caused by the time delays. Case studies are accomplished on a multi-area power system in MATLAB/Simulink environment. Eventually, real-time verifications by OPAL-RT real-time digital simulator on the simulated power system are executed to assess the control method.

Adaptive Linear Quadratic Gaussian Speed Control of Induction Motor Using Fuzzy Logic

Adaptive Linear Quadratic Gaussian Speed Control of Induction Motor Using Fuzzy Logic

Indefinite LQ optimal control for stochastic Takagi–Sugeno fuzzy system under sensor data scheduling: Finite‐horizon case

AbstractThe present paper considers the finite‐horizon indefinite linear quadratic (LQ) control problem for stochastic Takagi–Sugeno (T‐S) fuzzy systems with input delay. In this paper, we consider the presence of sensor data scheduling, which imposes a communication energy constraint and necessitates optimal state estimation for measurements. Then, by utilizing dynamic programming principles, the stochastic LQ problem under consideration can be solved, while the optimal control policy is developed in terms of the unique solutions to a set of coupled difference Riccati equations (CDREs). Specifically, for simple delay‐free case, the linear matrix inequalities based conditions are also proposed, whose feasibility is shown to be equivalent to the well‐posedness of the indefinite LQ control under consideration. As an application, our theoretic analysis is extended to study the intermittent observation model caused by random denial‐of‐service attack.

A fuzzy based intelligent scheme for enhancing the performance of the optimal controllers by online weighting matrix selection in seismically excited nonlinear buildings

In the present work, an effective strategy is proposed to improve the efficiency of the optimal controllers that are based on minimizing a performance index by using a fuzzy controller. In the used fuzzy system, the weighting matrices of the optimal controller are tuned online according to the response of the structural system. In order to assess the effectiveness of the proposed control scheme, its function is investigated in two phases on a 3-story nonlinear benchmark building equipped with MR dampers. In the first phase, a linear quadratic Gaussian (LQG) controller is combined with a fuzzy logic system (Fuzzy-LQG) and the efficiency of the used technique is compared with three different cases of the conventional LQG controllers. The results show that the Fuzzy-LQG, in addition to using an optimal level of demand energy, has a better performance than the conventional LQG methods in controlling the maximum responses of the structure. In the second phase, the performance of a polynomial optimal controller that is a summation of polynomials in nonlinear states in combination with the fuzzy system is investigated. At this stage, the effectiveness of the designed control system (Fuzzy Polynomial) in terms of seismic performance criteria with the results of a conventional LQG active control system, an optimal adaptive neuro-fuzzy inference system (ANFIS) and a neural network predictive control (NNPC) system is evaluated. The results show that this method is successful in improving the structural performance of a nonlinear building subjected to earthquakes.

The mean‐field linear quadratic optimal control problem for stochastic systems controlled by impulses

AbstractIn the present note, we state and solve the linear quadratic (LQ) control problem for a class of McKean–Vlasov stochastic differential equations for which the control actions are of impulsive nature. After reformulating the original optimization problem using an orthogonal decomposition of the state variables, we introduce an adequately defined system of two coupled matrix Lyapunov‐type differential equations with jumps. Such equations are central for the definition of the optimal feedback gains corresponding to the closed‐loop representation of the optimal LQ control.

The modeling and cascade sliding mode control of a moving mass-actuated coaxial dual-rotor UAV

In this study, an attitude control scheme based on a three-track moving mass control mechanism is proposed to address the problems of the overcomplicated rotor components, low service life, and low reliability of coaxial dual-rotor unmanned air vehicles (UAV). The motion and aerodynamic models of a moving mass-actuated ducted coaxial dual-rotor UAV are derived. The rotational dynamic characteristics of a moving mass-actuated UAV (MAUAV) with different slider positions and mass ratios are analyzed. An attitude controller based on backstepping sliding mode control is designed to address the nonlinearity and uncertainty of the MAUAV rotation. Based on this, we developed a position controller using cascade sliding mode control. The simulation results demonstrate that the designed attitude controller can achieve a settling time of 1.438 s in the unit-step response and a steady-state error of less than 5% in the sinusoidal attitude-tracking experiment. Additionally, the designed position controller exhibited a better trajectory-tracking effect under different levels of gust disturbance than that of a linear quadratic regulator control-based position controller.

L1 Adaptive Control for Marine Structures

Nowadays, many maritime structures require precise dynamic positioning (DP) of the constructive elements that compose them. In addition, the use of preconstructed elements that are later moved to the final location has become widespread. These operations have not been automated with the risks involved in carrying out the complex operations required. To minimize these operational risks and to perform a correct DP of floating structures, a new approach based on the L1 adaptive control technique is proposed. As an example of application, a proposed L1 adaptive controller was implemented in the dynamic positioning of a floating caisson. Several simulations of the system with wave disturbances were carried out, and the results were compared with those obtained by applying other classical and advanced control techniques, such as linear quadratic Gaussian control (LQG) and model predictive control (MPC). It was concluded that the proposed L1 adaptive controller performs correct dynamic positioning and reduces the tension generated on the lines concerning the other advanced control techniques with which it was compared. This reduction in line tension leads to an important improvement due to the possibility of reducing the size of the actuators or reducing their number, with the important economic and safety repercussions that these actions entail.

On the Sample Complexity of Decentralized Linear Quadratic Regulator With Partially Nested Information Structure

We study the problem of control policy design for decentralized state-feedback linear quadratic control with a partially nested information structure, when the system model is unknown. We propose a model-based learning solution, which consists of two steps. First, we estimate the unknown system model from a single system trajectory of finite length, using least squares estimation. Next, based on the estimated system model, we design a decentralized control policy that satisfies the desired information structure. We show that the suboptimality gap between our control policy and the optimal decentralized control policy (designed using accurate knowledge of the system model) scales linearly with the estimation error of the system model. Using this result, we provide an end-to-end sample complexity result for learning decentralized controllers for a linear quadratic control problem with a partially nested information structure.

Joint Watermarking-Based Replay Attack Detection for Industrial Process Operation Optimization Cyber-Physical Systems

This paper addresses the replay attack detection issue for a class of industrial process operation optimization (IPOO) cyber-physical systems (CPSs). In contrast to conventional CPSs with a single loop structure, the IPOO CPSs employ a dual-layer network environment consisting of a wireless network for the setpoint optimization loop and a CAN bus for the device control loop. Consequently, the issue of attack detection is more complicated for the IPOO CPSs, and this motivates our current research. First, a unified model of the IPOO CPS is built, with PI controller controlling the physical plants and LQG controller managing setpoint optimization. Then, a novel joint watermarking detection mechanism is established with the PI controller watermarking, LQG controller watermarking, and a watermarking compensator. The proposed watermarking compensator with an augmented Kalman filter is utilized to efficiently eliminate false alarms brought on by information interactions of the coupled cyber-layers, enabling the accurate detection and location of replay attacks. Furthermore, a linear relationship is established between watermarking parameters and system performance loss. Finally, simulations with a quadruple water tank system are conducted to verify the effectiveness of the proposed algorithm.

A study on PMSM drive systems fed by multi-level inverter using linear quadratic regulator control for electric vehicle applications

This paper presents research on a permanent magnet synchronous motor (PMSM) by a 5-level T-type inverter using linear quadratic regulator (LQR) control for speed control. The space vector modulation (SVM) structure for the 5-level T-type inverter to improve the control quality of the PMSM drive system is presented. This paper aims to successfully design a state feedback controller to control motor speed in a permanent magnet synchronous motor drive system. Simulink results are performed with different speed ranges and the same torque load. These results will focus on evaluating quality when the PMSM drive operates at all speeds. MATLAB/Simulink proves the results.

LQG Differential Stackelberg Game Under Nested Observation Information Patterns

We investigate the linear quadratic Gaussian Stackelberg game under a class of nested observation information patterns. The follower uses its observation data to design its strategy, whereas the leader implements its strategy using global observation data. We show that the solution requires solving a new type of forward-backward stochastic differential equation, whose drift components contain two conditional expectation terms associated to the adjoint variables. We then propose a method to find the functional relations between each adjoint pair, i.e., each pair formed by an adjoint variable and the conditional expectation of its associated state. The proposed method follows a layered pattern. More precisely, in the inner layer, we seek the functional relation for the adjoint pair under the sigma-sub-algebra generated by follower's observation information; and in the outer layer, we look for the functional relation for the adjoint pair under the sigma-sub-algebra generated by leader's observation information. Our result shows that the optimal open-loop solution admits an explicit feedback type representation.

Canal Controllability Identification Based on Automation Theory to Improve Water Delivery Efficiency in Irrigation Canal Systems

Canal controllability is an open and significant topic that addresses the unreliability/uncertainty in water delivery, efficiency, and modernization in the irrigation system. The study developed an analysis tool for canal controllability to estimate controllable performance and reduce the uncertainty of water delivery under steady and unsteady flow. We designed a linear quadratic control algorithm and applied it to the Nongchang test canal to verify the tool reliability and improve efficiency of water utilization. Finally, the effects of hydraulic variables on canal controllability were quantified. The numerical model of unsteady flow showed satisfactory predictions of water level (correlation coefficient, root mean square error, and mean absolute percentage error were 0.929%, 0.293%, and 12.86%, respectively). The Nongchang test canal was rather controllable (controllability indicator 0.265 to 0.279), implying that linear quadratic control algorithm was appropriate. The algorithm performed well under all conditions tested; the maximum absolute error was 3.66%–8.65%. The water level remained stable (deviation usually less than 0.05 m) and water delivery met user demands in terms of flow rate (the measure of performance relative to adequacy was 92.51%–98.94%) with relatively small gate movements. The bottom slope and roughness were the principal contributors to controllable performance, explaining approximately 46% of the variance. Specifically, controllability was highest when the bottom slope was low, and the roughness and side slope were high. We offer a reliable and flexible tool for assessment of canal controllability. Study results demonstrated that stakeholders benefit when conventional canal operation is modernized. The work will guide automation and upgrading of canal hardware as irrigation becomes optimized.

Error Analysis of the Feedback Controls Arising in the Stochastic Linear Quadratic Control Problems

Error Analysis of the Feedback Controls Arising in the Stochastic Linear Quadratic Control Problems

Zero-Order Asymptotics for the Solution of One Type of Singularly Perturbed Linear–Quadratic Control Problems in the Critical Case

Zero-Order Asymptotics for the Solution of One Type of Singularly Perturbed Linear–Quadratic Control Problems in the Critical Case

Control of Quarter-Car Active Suspension System Based on Optimized Fuzzy Linear Quadratic Regulator Control Method

Vehicle suspension systems, which affect driving performance and passenger comfort, are actively researched with the development of technology and the insufficient quality of passive suspension systems. This paper establishes the suspension model of a quarter of the car and active control is realized. The suspension model was created using the Lagrange–Euler method. LQR, fuzzy logic control (FLC), and fuzzy-LQR control algorithms were developed and applied to the suspension system for active control. The purpose of these controllers is to improve car handling and passenger comfort. Undesirable vibrations occur in passive suspension systems. These vibrations should be reduced using the proposed control methods and a robust system should be developed. To enhance the performance of the fuzzy logic control (FLC) and fuzzy-LQR control methods, the optimal values of the coefficients of the points where the feet of the member functions touch are calculated using the particle swarm optimization (PSO) algorithm. Then, the designed controllers were simulated in the computer environment. The success of the control performance of the applied methods concerning the passive suspension system was compared in percentages. The results are presented and evaluated graphically and numerically. Using the integral time-weighted absolute error (ITAE) criterion, the methods were compared with each other and with the studies in the literature. As a result, it was found that the proposed control method (fuzzy-LQR) is about 84.2% more successful in body motion, 90% in car acceleration, 84.5% in suspension deflection, and 86.7% in tire deflection compared to the studies in the literature. All these results show that the car’s ride comfort has been significantly improved.

A novel PID type iterative learning controller optimized by two‐dimensional infinite horizon linear quadratic iterative learning control for batch processes

AbstractAlthough a proportional integral derivative type iterative learning control (PIDILC) scheme can achieve good performance, its application is limited by open‐loop structure, parameter tuning, and initial state. In this paper, a novel PIDILC optimized by two‐dimensional infinite horizon linear quadratic regulator (PIDILC‐2D‐IHLQR) is proposed. First, by synthesizing the advantage of the conventional PIDILC method and proportional integral derivative (PID) strategy, a novel closed‐loop PIDILC scheme is obtained. Then, a novel two‐dimensional infinite horizon linear quadratic regulator (2D‐IHLQR) is developed to optimize the parameters of the PIDILC strategy. The limitations of parameter tuning and initial state are solved by this PIDILC‐2D‐IHLQR method. Therefore, the proposed method not only solves the aforementioned limitations but also inherits the advantages of PIDILC algorithm, PID method, and the novel 2D‐IHLQR scheme. Moreover, a stability condition is given based on Lyapunov theory and it can help judge whether the selection of control parameters meets the stability condition. The effectiveness of the proposed method is demonstrated by the case study on an injection modelling process.

Optimal Control of Semi-Active Suspension for Agricultural Tractors Using Linear Quadratic Gaussian Control.

In this study, a semi-active suspension based on a hydro-pneumatic mechanism was designed to minimize the ride vibration using a suspension control algorithm. The performance of the algorithm was critical for controlling the characteristics of the target tractor. A linear-quadratic-Gaussian (LQG) optimal control algorithm was designed as a semi-active suspension control algorithm. The plant model for developing this algorithm was based on the parameters of an actual tractor. The rear suspension deflection was represented by a Kalman-filter-based state observer feedback to estimate the state variables that were difficult to measure. The designed state observer of the LQG controller was validated in terms of an accuracy index. The estimated vertical velocity and acceleration accuracies of the cabin were 83% and 79%, respectively. The performance of the designed controller was validated in terms of a performance index by comparing the performance of a tractor equipped with a rear rubber mount with that of one equipped with a semi-active suspension. The peak and root-mean-square values of the vertical acceleration of the cabin were reduced by up to 48.97% and 47.06%, respectively. This study could serve as a basis for the application of the control algorithm to systems with similar characteristics, thereby reducing system costs.

Contemporary materials for semiconductor switches in an isolated bidirectional DC-DC converter using a closed loop system with linear quadratic regulator control

This research seeks to create a novel bidirectional DC-DC converter capable of high step-up/down power transfer for diverse applications, such as grid systems, energy backup systems, fuel cell vehicles and hybrid electric vehicles. The converter features an inductor linked to an electric power grid to facilitate multi-layer energy conversion with galvanic isolation for improved voltage ratio and galvanic isolation. Notable among its features is this converter's capacity to recycle energy from a leaky inductor without needing additional snubber mechanisms or clamped circuits. To facilitate efficient operation, the converter employs power switches capable of soft switching both step-up and step-down modes. This option permits using MOSFETs with low on-state resistance, which is advantageous due to reduced voltage endurance at the primary side. This research explores the application of a linear quadratic regulator (LQR) for use with a constant frequency bidirectional DC-DC converter. Leveraging the high-order nature of converters, LQR controllers make full use of their potential by offering rapid dynamic response time, reliability and minimal changes in settling time for an array of operating conditions. Thorough analyses were carried out into the availability and stability conditions of an LQR controller in step-up mode using MATLAB/Simulink simulation results as evidence. This study also emphasizes the significance of performance and effectiveness in electronic power-switching devices, which rely heavily on material properties for operation. While silicon has traditionally been employed for these switches, advances in material science have seen wider band-gap semiconductors adopted to improve switching device performance. Therefore, this research encompasses selecting and implementing appropriate semiconductor materials into power electronic switches used by DC-DC converters.