Robust optimal motion cueing algorithm based on the linear quadratic regulator method and a genetic algorithm

The aim of this paper is to design and develop an optimal motion cueing algorithm (MCA) based on the genetic algorithm (GA) that can generate high-fidelity motions within the motion simulator's physical limitations. Both, angular velocity and linear acceleration are adopted as the inputs to the MCA for producing the higher order optimal washout filter. The linear quadratic regulator (LQR) method is used to constrain the human perception error between the real and simulated driving tasks. To develop the optimal MCA, the latest mathematical models of the vestibular system and simulator motion are taken into account. A reference frame with the center of rotation at the driver's head to eliminate false motion cues caused by rotation of the simulator to the translational motion of the driver's head as well as to reduce the workspace displacement is employed. To improve the developed LQR-based optimal MCA, a new strategy based on optimal control theory and the GA is devised. The objective is to reproduce a signal that can follow closely the reference signal and avoid false motion cues by adjusting the parameters from the obtained LQR-based optimal washout filter. This is achieved by taking a series of factors into account, which include the vestibular sensation error between the real and simulated cases, the main dynamic limitations, the human threshold limiter in tilt coordination, the cross correlation coefficient, and the human sensation error fluctuation. It is worth pointing out that other related investigations in the literature normally do not consider the effects of these factors. The proposed optimized MCA based on the GA is implemented using the MATLAB/Simulink software. The results show the effectiveness of the proposed GA-based method in enhancing human sensation, maximizing the reference shape tracking, and reducing the workspace usage.

Alternative Formulation of the Discrete Linear Quadratic Regulator (DLQR)

In this paper, an alternative apriori and aposteriori formulation has been derived for the discrete linear quadratic regulator (DLQR) in a manner analogous to that used in the discrete Kalman filter. It has been shown that the formulation seamlessly fits into the available formulation of the DLQR and the equivalent terms in the existing formulation and the proposed formulation have been identified. Thereafter, the significance of this alternative formulation has been interpreted in terms of the sensitivity of the controller performances to any changes in the states or to changes in the control inputs. The implications of this alternative formulation to adaptive controller tuning have also been discussed.

Primary voltage control of a single-phase inverter using linear quadratic regulator with integrator

This paper proposes a linear quadratic regulator with integral action, ensuring fast dynamic response and resisting capability of voltage deviation from instantaneous reference grid voltage, to control the inverter voltage that can also be used in a microgrid. The proposed control strategy is based on a linear quadratic regulator, minimizing the cost function of the system, with integral action used to impede voltage degradation from a reference voltage for outside disturbances of the system, such as abrupt load change. The combined integral term assists to recover the voltage difference between grid and reference grid voltage. The validity of the proposed controller has been tested with linear and non-linear loads under various conditions. In both cases, the effectiveness of the controller has been proved. The result of the proposed controller is good to track the instantaneous reference grid voltage.

基于主动建模的无人直升机增强LQR控制

为了解决无人直升机控制问题,通过把主动建模与LQR(Linear Quadratic Regulator)控制相结合,提出一种能补偿模型差的控制方法。该方法在悬停状态下,采用简化模型设计LQR控制器,并通过UKF(Un-scented-Kalman-Filter)在线估计简化模型与全状态模型的模型差,使用模型差作为补偿项对LQR控制增强。针对实际直升机动力学模型进行仿真,验证了基于UKF的估计和增强LQR控制的有效性。仿真实验结果证明,基于UKF的主动建模技术能够快速估计状态和参数变化,并且增强LQR控制能够使系统适应模型不确定性。

Active control in flexible plates with piezoelectric actuators using linear matrix inequalities

The study of algorithms for active vibrations control in flexible structures became an area of enormous interest, mainly due to the countless demands of an optimal performance of mechanical systems as aircraft, aerospace and automotive structures. Smart structures, formed by a structure base, coupled with piezoelectric actuators and sensor are capable to guarantee the conditions demanded through the application of several types of controllers. The actuator/sensor materials are composed by piezoelectric ceramic (PZT - Lead Zirconate Titanate), commonly used as distributed actuators, and piezoelectric plastic films (PVDF-PolyVinyliDeno Floride), highly indicated for distributed sensors. The design process of such system encompasses three main phases: structural design; optimal placement of sensor/actuator (PVDF and PZT); and controller design. Consequently, for optimal design purposes, the structure, the sensor/actuator placement and the controller have to be considered simultaneously. This article addresses the optimal placement of actuators and sensors for design of controller for vibration attenuation in a flexible plate. Techniques involving linear matrix inequalities (LMI) to solve the Riccati's equation are used. The controller's gain is calculated using the linear quadratic regulator (LQR). The major advantage of LMI design is to enable specifications such as stability degree requirements, decay rate, input force limitation in the actuators and output peak bounder. It is also possible to assume that the model parameters involve uncertainties. LMI is a very useful tool for problems with constraints, where the parameters vary in a range of values. Once formulated in terms of LMI a problem can be solved efficiently by convex optimization algorithms.

Non-linear Control of an Autonomous Ground Vehicle

In this paper, in order to select a speed controller for a specific non-linear autonomous ground vehicle, proportional-integral-derivative (PID), Fuzzy, and linear quadratic regulator (LQR) controllers were designed. Here, in order to carry out the tuning of the above controllers, a multicomputer genetic algorithm (MGA) was designed. Then, the results of the MGA were used to parameterize the PID, Fuzzy and LQR controllers and to test them under laboratory conditions. Finally, a comparative analysis of the performance of the three controllers was conducted.

An alternative LQR-based excitation controller design for power systems to enhance small-signal stability

This paper presents a new approach to design excitation controller for power systems to enhance small-signal stability. Partial feedback linearization scheme is used to design the controller for a linearized power system model which transforms a part of this model into a new system through linear coordinate transformation. In this paper, the excitation control law as a function of state variables is determined from the dynamics of the partly transformed new system provided that the controller stabilizes the remaining dynamics of the system which are not transformed through feedback linearization. The stability of the remaining dynamics is also discussed in this paper. Since the proposed control scheme uses state variables as feedback, it is analogous to a linear quadratic regulator (LQR) based excitation controller. Therefore, the performance of the proposed scheme is evaluated on a single machine infinite bus (SMIB) system and compared to that of an LQR controller.

Stability enhancement of DFIG wind turbine using LQR pitch control over rated wind speed

A novel pitch control design method is proposed for the doubly fed induction generator (DFIG) wind turbine (WT) using linear quadratic regulator (LQR). A seven-order model represents the DFIG WT which is linearized by truncated Taylor series expansion. A systematic approach is adopted to determine the weighting matrices in LQR design for the optimal solution. Simulations have been carried out to compare the performance of the proposed LQR pitch control method against a PI pitch control for small and large disturbances. It is shown that the proposed control method enhances low-voltage ride-through capability and improves system damping under large disturbances.

Nonlinear Model Predictive Control for a multi-rotor with heavy slung load

In this paper a novel controller for stable and precise operation of multi-rotors with heavy slung loads is introduced. First, simplified equations of motions for the multi-rotor and slung load are derived. The model is then used to design a Nonlinear Model Predictive Controller (NMPC) that can manage the highly nonlinear dynamics whilst accounting for system constraints. The controller is shown to simultaneously track specified waypoints whilst actively damping large slung load oscillations. A Linear-quadratic regulator (LQR) controller is also derived, and control performance is compared in simulation. Results show the improved performance of the Nonlinear Model Predictive Control (NMPC) controller over a larger flight envelope, including aggressive maneuvers and large slung load displacements. Computational cost remains relatively small, amenable to practical implementation. Such systems for small Unmanned Aerial Vehicles (UAVs) may provide significant benefit to several applications in agriculture, law enforcement and construction.

Multi-rotor with suspended load: System dynamics and control toolbox

There is an increasing demand for Unmanned Aerial Systems (UAS) to carry suspended loads as this can provide significant benefits to several applications in agriculture, law enforcement and construction. The load impact on the underlying system dynamics should not be neglected as significant feedback forces may be induced on the vehicle during certain flight manoeuvres. The constant variation in operating point induced by the slung load also causes conventional controllers to demand increased control effort. Much research has focused on standard multi-rotor position and attitude control with and without a slung load. However, predictive control schemes, such as Nonlinear Model Predictive Control (NMPC), have not yet been fully explored. To this end, we present a novel controller for safe and precise operation of multi-rotors with heavy slung load in three dimensions. The paper describes a System Dynamics and Control Simulation Toolbox for use with MATLAB/SIMULINK which includes a detailed simulation of the multi-rotor and slung load as well as a predictive controller to manage the nonlinear dynamics whilst accounting for system constraints. It is demonstrated that the controller simultaneously tracks specified waypoints and actively damps large slung load oscillations. A linear-quadratic regulator (LQR) is derived and control performance is compared. Results show the improved performance of the predictive controller for a larger flight envelope, including aggressive manoeuvres and large slung load displacements. The computational cost remains relatively small, amenable to practical implementations.

Optimal blood glucose regulation of diabetic patients using single network adaptive critics

Diabetes is a long-term disease during which the body's production and use of insulin are impaired, causing glucose concentration level to increase in the bloodstream. Regulating blood glucose levels as close to normal as possible leads to a substantial decrease in long-term complications of diabetes. In this paper, an intelligent online feedback-treatment strategy is presented for the control of blood glucose levels in diabetic patients using single network adaptive critic (SNAC) neural networks (which is based on nonlinear optimal control theory). A recently developed mathematical model of the nonlinear dynamics of glucose and insulin interaction in the blood system has been revised and considered for synthesizing the neural network for feedback control. The idea is to replicate the function of pancreatic insulin, i.e. to have a fairly continuous measurement of blood glucose and a situation-dependent insulin injection to the body using an external device. Detailed studies are carried out to analyze the effectiveness of this adaptive critic-based feedback medication strategy. A comparison study with linear quadratic regulator (LQR) theory shows that the proposed nonlinear approach offers some important advantages such as quicker response, avoidance of hypoglycemia problems, etc. Robustness of the proposed approach is also demonstrated from a large number of simulations considering random initial conditions and parametric uncertainties. Copyright (C) 2009 John Wiley & Sons, Ltd.

Formation flying of small satellites using suboptimal MPSP guidance

Using the recently developed model predictive static programming (MPSP), a suboptimal guidance logic is presented in this paper for formation flying of small satellites. Due to the inherent nature of the problem formulation, MPSP does not require the system dynamics to be linearized. The proposed guidance scheme is valid both for high eccentricity chief satellite orbits as well as large separation distance between chief and deputy satellites. Moreover, since MPSP poses the desired conditions as a set of `hard constraints', the final accuracy level achieved is very high. The proposed guidance scheme has been tested successfully for a variety of initial conditions and for a variety of formation commands as well. Comparison with standard Linear Quadratic Regulator (LQR) solution (which serves as a guess solution for MPSP) and another nonlinear controller, State Dependent Riccati Equation (SDRE) reveals that MPSP guidance achieves the objective with higher accuracy and with lesser amount of control usage as well.

轮式移动机器人轨迹跟踪的最优控制

深入分析了轮式移动机器人的运动状态,建立了WMR路径偏差系统的非线性数学模型。应用小偏差线性化理论,将该多输入多输出非线性系统简化成一个单输入单输出线性系统。然后基于线性二次型调节器理论进行了系统最优控制器的设计,并针对该理论中加权矩阵Q与R难以确定的问题,从控制效果出发,采用自适应遗传算法对其进行了优化。实现了移动机器人对预定轨迹的满意鲁棒跟踪,同时满足了实时性要求。实验结果证明了该方法的正确性与实用性。