Linear Quadratic Optimal Control Method Research Articles

Path tracking control strategy for the intelligent vehicle considering tire nonlinear cornering characteristics in the PWA form

To improve the path tracking control performance of the intelligent vehicle under critical maneuvers, a novel control strategy is introduced in this work. Considering that the tire cornering characteristics show high nonlinearities and uncertainties under those special driving conditions, a three-dimensional piecewise affine (PWA) identification method is proposed to realize the nonlinear modeling of the tire cornering characteristics for the first time. On this basis, the PWA model of the vehicle lateral dynamics is established. To obtain the vehicle target yaw rate for path tracking, a driver direction control model with adaptive preview time is put forward. Then, the linear quadratic optimal control method is further adopted to design multiple path tracking controllers for different working areas of the affine subsystems, thus the optimal steering angles of the front wheels can be generated to guarantee the path tracking performance for the intelligent vehicle under a wide range of driving conditions. Finally, to evaluate the performance of the proposed path tracking control strategy which considers the tire nonlinear cornering characteristics in the PWA form, the CarSim-Simulink co-simulation work is conducted. The co-simulation results show that the proposed control strategy presents significant performance advantages over the other two methodologies and demonstrates satisfactory path tracking control performance.

Research on control method of three-phase inverter based on LQR optimal tracking control

According to the linear quadratic optimal control principle, the idea of optimal tracking control is applied to the three-phase inverter control system, which can effectively improve the output characteristics of the system. Based on the establishment of mathematical model, the nonlinear load and load mutation are regarded as the uncertain factors affecting the performance of three-phase inverter, and the parameter optimization design of state feedback and input feedforward is carried out based on the linear quadratic optimal control method. The simulation results show that the LQR optimal tracking control can better adapt to the adverse effects of nonlinear load and load mutation than the traditional quasi-PR control, and the system has good harmonic performance, dynamic performance and the ability to resist load disturbance.

Active balancing control for time-delay rotor via linear-quadratic regulator

Many imaging platforms, e.g., robotic devices and autonomous systems, require timely reaction to external events. The active balancing control is important to suppress rotor vibration and hence acquire stable videos and imagery. However, there is an inevitable delay in active balancing control of the high-speed, time-delay rotor systems. Eliminating this delay is crucial in real-world applications. The integral transformation term is introduced to transform the dynamic model of the time-delay rotor system into a dynamic model of the rotor system without time delay. Based on the linear-quadratic optimal control method, the influence of weight matrix is discussed. Moreover, an active balancing control strategy of the time-delay rotor is designed. The simulation model of the time-delay rotor control system is implemented with MATLAB, and a real device is fabricated to conduct both simulations and real-world experiments. Our results demonstrate that our proposed online active balancing control method effectively suppresses the vibration of the time-delay rotor system under different time-delay. The convergence time is short, and the system is agile.

Predictive Position Control of Planar Motors Using Trajectory Gradient Soft Constraint With Attenuation Coefficients in the Weighting Matrix

This article proposes a predictive position control method of planar motors using trajectory gradient soft constraint with attenuation coefficients in the weighting matrix to achieve high-precision, time-varying, and long-stroke positioning. Based on a built dynamics model of a planar motor developed in the laboratory, a predictive model is established to predict the future positions of the motor. To improve the positioning precision, a soft constraint defined by a trajectory gradient difference between the gradients of the reference position and predictive position sequences is introduced to the cost function. Then, an explicitly analytical solution of the optimal control is obtained by minimizing the cost function. To highlight the stronger effects of the trajectory gradients closer to the current time, the attenuation coefficients are applied to the weighting matrix of the added soft constraint. The stability of the control system is proved employing the linear quadratic optimal control method and the Lyapunov stability theory. Moreover, the time complexity is discussed based on the analytical control action to show low computational burden of the proposed method. Finally, the given simulation and experimental results demonstrate the effectiveness of the proposed method to achieve high-precision time-varying positioning for planar motors.

Frequency Regulation Strategy for AC–DC System During Black Start

High-voltage direct current (HVDC) can speed up the recovery of a power system. However, both rectifier and inverter sides of HVDC are weak systems during a black start. To coordinate frequency characteristics of both sides within the frequency deviation constrain, a frequency regulation strategy for AC–DC system during a black start is proposed. First, the mathematical models of asynchronous interconnected AC–DC system are established, and the optimal HVDC transmission power leading to minimum frequency deviation of both sides is obtained based on the linear quadratic optimal control method. To adapt to the continuously changing parameters and configurations of the AC power system during a black start, a Narendra adaptive tracking control method is developed to obtain the control law of the target value of governor, which allows the actual system frequency follow the reference system frequency under the optimal HVDC transmission power. Finally, the simulation model is established using PSCAD/EMTDC software to verify the proposed strategy.

Event-triggered and self-triggered control for linear systems with actuator saturation

In this paper, both event-triggered and self-triggered transmission strategies are proposed for dynamical systems subject to actuator saturation. The designed triggering condition, which is expected to save more network resources, is closely related to the cases where either the actuator saturates or it does not. The linear quadratic optimal control method is utilized to guarantee the asymptotic stability of the closed-loop systems. Global and local stability results are considered, respectively. For local stability, two sufficient conditions are presented to derive the asymptotic stability region. The minimum inter-transmission time of the proposed triggering mechanism is explicitly formulated to eliminate the Zeno behaviour. Finally, an example is provided to demonstrate the effectiveness of the theoretical results.

Research on the Vibration Control Algorithms for Large Space Truss Structure Based on Precise Integration Method

In this paper, vibration control algorithms for a large space truss structure are investigated. First, a precise integration method is used to solve the differential equation such that the validity and efficiency of the algorithm are guaranteed. Second, on the basis of the discrete algebraic equation combined with the decentralized control theory, the solving method of the control force based on the linear quadratic (LQ) optimal control theory is improved. Third, a new control method, the eigenvalue control method, is proposed in this paper, and its relationship with the LQ optimal control method is discussed. Finally, these two control methods are applied to the structure to analyze the effectiveness of vibration suppression. The simulation results show that the proposed algorithms can quickly suppress the vibration of a large space truss structure.

Reducing the model-data misfit in a marine ecosystem model using periodic parameters and linear quadratic optimal control

Abstract. This paper presents the application of the Linear Quadratic Optimal Control (LQOC) method to a parameter optimization problem for a one-dimensional marine ecosystem model of NPZD (N for dissolved inorganic nitrogen, P for phytoplankton, Z for zooplankton and D for detritus) type. This ecosystem model, developed by Oschlies and Garcon, simulates the distribution of nitrogen, phytoplankton, zooplankton and detritus in a water column and is driven by ocean circulation data. The LQOC method is used to introduce annually periodic model parameters in a linearized version of the model. We show that the obtained version of the model gives a significant reduction of the model-data misfit, compared to the one obtained for the original model with optimized constant parameters. The found inner-annual variability of the optimized parameters provides hints for improvement of the original model. We use the obtained optimal periodic parameters also in validation and prediction experiments with the original non-linear version of the model. In both cases, the results are significantly better than those obtained with optimized constant parameters.

Universal Clutch Starting Control of AMT/DCT Automatic Transmission Based on Optimal Control

Starting and shifting states of clutch in automatic transmission are identified on the basis of the motion states of driven plates of the clutch.Unified dynamic model is set up for the starting control of clutches in both automatic mechanical transmission(AMT) and dual clutch transmission(DCT).The linear quadratic optimal control method is used to achieve the optimum starting control of the clutches,in which the jerk is converted to one of the restrain conditions,and the minimization of sliding friction work of the clutches is set as optimal target in control.Universal optimal starting control of AMT and DCT clutches is realized through selection of state variables,setting of parameters and modifying of restrain conditions in the unified model for clutch starting of AMT,single and dual clutch starting of DCT.Simulation is carried out and then verified by experiment.The research results lay the foundation for the construction of universal development platform of the AMT and DCT automatic transmissions.

Optimal Control for Thrust Vectoring Unmanned Aerial Vehicle

In this paper the application of linear quadratic (LQ) optimal control based techniques to a thrust vectoring unmanned aerial vehicle (TV-UAV) control problem is considered. A general nonlinear dynamic model of the TV-UAV is built, which is different from the common UAV. The longitudinal and lateral linearization models are derived in a benchmark flight state. Two thrust deflections are considered as control variables, associated with the rudder control variables. LQ optimal control method based multivariable control system is designed for the attitude stability control problem. Simulations of a nonlinear model described UAV is carried out, results of which show the superiority of the hybrid control strategy, and also show that the TV-UAV has better properties than the common UAV, in the aspects of anti-disturbance and control efficiency.

Optimal control of hydraulic position system employing high speed On/Off solenoid valve

A hydraulic position system was designed employing two high speed On/Off solenoid valves with PWM(Pulse-width-modulation) technique and using LQ(Linear-Quadratic) optimization principle. Based on the system, the parts of system can be formulated with equations. According to equations, the mathematical model of the system was established. By simulation, the corresponding LQ optimal controller was designed and the PWM signals were generated. The comparison of the simulation and experiment results show that LQ optimal control method with PWM technique employing high speed On/Off solenoid valve can provide better system performance and a high position precision is obtained.

QN control method for building vibration caused by periodic excitation acting on intermediate story

It has been proved in the authors' latest paper that the effective location of active control devices for building vibration caused by periodic excitation acting on intermediate story is the adjacent three floors to the vibration source. However, in terms of the Discrete-Optimizing control method, the control forces are on-line calculated step-by-step and time-delay must exist. The degradation of control effect caused by time-delay can not be avoided. In this paper, QN control method is proposed in order to resolve this practical problem. Since the external excitations which the building structure would experience are supposed to be periodic to some degree, Quasi-Newton method is applied into the close-loop Linear–Quadratic optimal control method and the new control method is called the ‘QN control method’. In this new control method, instead of solving the Riccati equation, the feedback gain matrix is determined by optimizing the quadratic performance index of the structure with the Quasi-Newton method, one of the most commonly used minimization of functions. The new control law can easily be implemented for time-delay problems, the degradation can be greatly improved with compensated feedback gain matrix. As a result, the QN control method is proved to be an efficient method to determine the feedback gain matrix. Copyright © 2000 John Wiley & Sons, Ltd.

Trade-Off Between Energy Capture and Dynamic Loads in Variable Speed Wind Turbines

This paper investigates the trade-off between the objectives of generating maximum power and minimizing the dynamic loads of a variable speed wind tumine operated below rated wind speed. Linear quadratic optimal control methods are used to investigate this balance. Four models of different complexity are compared, and established to have similar behaviour. The controllers have been simulated with a non-linear aerodynamic torque model, and the simulation confirmed the predicted characteristics. It is also shown that the systems are robust to parameter changes, even when the model used in the controller design is of lower order than the true system.