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.     

基于二阶矩阵微分方程的机械振动系统线性二次型调节器设计

本文讨论机械振动系统线性二次型状态调节器（LQR）问题，直接针对系统二阶运动微分方程，性能指标为一个依赖于二阶导数的泛函。由欧拉-拉格朗日方程得出一个系统矩阵增广的二阶线性微分方程，指出该方程稳定的特征对就是最优控制振动系统闭环特征对，并给出求解最优控制状态反馈矩阵的方法，另外，由本文方法还可得出基于速度和加速度反馈的最优控制反馈矩阵。这里不涉及求解代数矩阵Riccati方程。     

改进型负输入整形与最优控制结合的振动抑制方法

针对诸如柔性机械臂这类柔性系统的主动振动控制问题,提出了基于改进型负输入整形和最优控制结合的振动抑制方法。以柔性机械臂为研究对象,设计最优状态反馈控制实现其旋转机动任务及柔性振动抑制。为增强柔性振动抑制效果和改善系统的运动时间,根据引入线性二次型调节器(LQR)反馈后整个闭环系统的振动频率和阻尼比设计改进型负输入整形器作为前馈控制器。将前馈控制与反馈控制相结合能发挥其各自的优点,提高系统的性能。仿真分析结果表明,所设计的混合控制策略可以有效地抑制柔性振动,且可以减少系统响应时间的延迟和加快系统响应速度。     

Optimal placement of piezoelectric actuators on plate structures for active vibration control via modified control matrix and singular value decomposition approach using modified heuristic genetic algorithm

The present work deals with the optimal placement of piezoelectric actuators on a thin plate using modified control matrix and singular value decomposition (MCSVD) approach. The MCSVD is considered as the fitness function and optimal positions of the actuators are obtained by maximizing it with MHGA (modified heuristic genetic algorithm). Vibration suppression has been studied for simply supported plate with piezoelectric patches in optimal positions to suppress first specified modes using LQR (linear quadratic regulator) controller. It is observed that the positions of patches obtained with this approach give greater vibration suppression, reduced computational requirements, and provide global optimum solution only.     

LQR/RPS design of robust controllers for a one‐link robot

Abstract

In this paper, a design method for robust controllers for a one‐link robot is developed. Based on a linearized model of this nonlinear robot system, the linear quadratic regulator (LQR) design method is incorporated with a reduced parameter sensitivity (RPS) technique to design a robust proportional‐plus‐integral (PI) controller to achieve better performance in position control. This robust controller can tolerate real parameter variations resulting from the mechanical loads of applications. A direction method is further developed and used to evaluate the stability robustness of this controlled system. Combining the direction method with the LQR/RPS method, a robust PI controller can be generated to avoid improper over‐design. Both computer simulation and experimental results demonstrate the feasibility and effectiveness of the proposed approach.     

柔性耦合隔振系统主动控制方法的仿真研究

针对柔性耦合主动隔振系统,本文采用阻抗/导纳方法和矩阵传递法相结合的方法,建立了包括被隔离设备、电磁式主被动一体隔振器和柔性基础在内的柔性耦合系统的数学模型。并在此基础上,应用线性二次型高斯控制方法(linear quadratic Gaussian,LQG)对隔振系统进行了主动控制器的设计,最后通过仿真证明了控制方法的有效性。     

有约束复杂随动系统模型建立与控制研究

提出了一种有约束复杂随动系统--小碗摆球系统,并以小碗摆球系统为研究对象,针对有约束复杂随动系统的控制策略进行研究;利用拉格朗日动力学方法建立了小碗摆球系统的动力学模型。在讨论了系统能控和能观性的基础上分别采用鲁棒性双闭环PID控制和基于遗传算法的线性二次型最优控制进行了实际系统控制效果的实验对比,对比结果表明鲁棒性双闭环PID控制器具有更好的鲁棒性和瞬态特性,而遗传算法优化的线性二次型控制具有更好的动态特性。     

Optimal-control theory applied to ship maneuvering in restricted waters

Ship drivers have long understood that powerful interaction forces exist when ships operate in close proximity to rigid boundaries or other vessels. Controlling the effects of these forces has been traditionally handled by experienced helmsmen. The purpose of this study is to apply modern optimal-control theory to such maneuvering scenarios in order to show that helmsmen may some day be replaced by modern controllers. The maneuvering equations of motion are cast in a linear state-space framework, permitting the design of a linear quadratic (LQ) controller. The hydrodynamic effects are modeled using potential-flow theory in order to simulate the interaction forces and test the performance of the controller. This study demonstrates that the linear quadratic regulator effectively controls ship motions due to the presence of a boundary or other vessel over a broad range of speeds and separation distances. Viscous effects are modeled by equivalent linearization and, when compared to the effective damping introduced by the controller, are shown to be insignificant.     

不确定离散模糊系统的最优保性能控制

对一类具有范数有界,时变参数不确定性的离散模糊时间系统和一个二次型性能指标,研究其最优保性能状态控制律的设计问题.通过采用线性矩阵不等式的方法,导出了存在保性能控制律的一个充要条件,进而,证明了该条件等价于一组线性矩阵不等式的可解性问题,并用这组线性矩阵不等式的可行解给出了保性能控制律的一个参数化表示.在此基础上,通过建立并求解一个凸优化问题,给出了最优保性能控制律的设计方法.     

频域加权的LQG振动主动控制实验研究

针对实际工程领域中存在的伴有大量宽频干扰/噪声的复杂振动环境,直接影响了常规振动主动控制(AVC)的性能甚至稳定性。本文提出了频域加权的线性二次高斯型(LQG)控制方法,实现对特定振动主频重点衰减的同时,保证宽频域的干扰/噪声控制作用。最后利用压电陶瓷贴片的悬臂梁,振动主动控制试验验证了该方法的有效性。     

基于部分反馈线性化的三杆体操机器人控制策略

针对复杂的非线性欠驱动三杆体操机器人系统,提出了一种基于部分反馈线性化的控制策略.首先,将三杆体操机器人的运动空间分为两个区域:摇起区和平衡区,然后,在摇起区利用部分反馈线性化设计摇起控制器,对第二杆与第三杆进行联动控制,确保欠驱动三杆体操机器人迅速摆起,并且摆起后第二杆和第三杆自然伸展;进入平衡区后,采用基于线性二次型调节器(LQR)的平衡控制器,将系统稳定在竖直向上的位置,实现系统控制目标.仿真结果验证了该控制策略的有效性.     

不确定离散时滞系统的弹性保性能控制

针对一类不确定离散时滞系统,同时考虑对象和控制器本身的不确定性,利用线性矩阵不等式(LMI)方法,给出弹性保性能状态反馈控制器的设计方法。通过LMI的可行解构造控制器,数值算例显示该方法的可行性。     

MODELING AND NONLINEAR CONTROL OF A CONTINUOUS KCI-NaCI CRYSTALLIZER

A controller is developed by combining the extended linear quadratic matrix control (EQDMC) and neural network algorithms. The dynamic neural network scheme is used to identify the process and generate a nonlinear model. The control algorithm is applied to a multi-input multi-output (MIMO) evaporative cooling KCl-NaCl-H₂O crystallizer. Closed loop responses of the system using the proposed algorithm and those of PID controllers are compared. It is shown that in all cases, the response of the proposed controller to step changes in setpoints is faster than the PID controllers.     

Passive estimated state feedback fuzzy controller design for discrete perturbed fuzzy systems with multiplicative noises

This article presents an estimated state feedback fuzzy controller design method for uncertain passive discrete-time nonlinear stochastic systems with multiplicative noises. The nonlinear stochastic systems considered in this article are represented by Takagi–Sugeno (T–S) fuzzy models. For describing stochastic behaviors, stochastic differential equations are used to structure the stochastic T–S fuzzy model for representing nonlinear stochastic systems. Besides, the uncertainties of the controlled system are considered for dealing with molding errors and varying parameters. The concept of parallel distributed compensation is employed in this article to construct the estimated state feedback fuzzy controllers. Applying the Lyapunov and passivity theories, the sufficient stability conditions are derived in terms of linear matrix inequality. Finally, a numerical example is provided to show the effectiveness and applicability of the proposed fuzzy controller design approach.     

Stability analysis of a single-link flexible arm driven by a motor of speed reference type

Abstract

The stability analyses for motion and vibration control of a single-link flexible arm having a tip payload are investigated using a linear distributed parameter model. The controller design in this paper includes the joint angle proportional–integral–derivative (PID), the bending strain (S) and bending strain integration (SI) feedbacks, and their combinations. The paper presents a new method applying the properties of an irrational passive transfer function and root locus to study the effect of various feedbacks on the infinitely many open loop poles, necessary and sufficient conditions in terms of the dimensionless positive gain constants are reported such that the closed-loop is asymptotically stable. The exact solutions of the infinite-dimensional closed-loop system are obtained using the infinite product formulation. Since the controller design is based on the infinite-dimensional system and is independent of system parameters, the proposed system promises stability robustness to parameter uncertainties and is also free of spillover problems. The validity of the controllers is assessed and compared with the experimental results in the existing literature.     

MODELING AND NONLINEAR CONTROL OF A CONTINUOUS KCI-NaCI CRYSTALLIZER

ABSTRACT

A controller is developed by combining the extended linear quadratic matrix control (EQDMC) and neural network algorithms. The dynamic neural network scheme is used to identify the process and generate a nonlinear model. The control algorithm is applied to a multi-input multi-output (MIMO) evaporative cooling KCl-NaCl-H₂O crystallizer. Closed loop responses of the system using the proposed algorithm and those of PID controllers are compared. It is shown that in all cases, the response of the proposed controller to step changes in setpoints is faster than the PID controllers.     

含有非线性扰动的时滞随机微分系统的鲁棒均方稳定性

研究一类含有非线性扰动的多时变时滞随机微分系统在有记忆状态的反馈控制器下的鲁棒均方稳定性问题.通过构造Lyapunov-Krasovskii泛函,运用Ito公式,引入适当的自由权矩阵,利用积分不等式和分析技巧,基于线性不等式(LMI)方法和Schur补定理,获得含该系统的鲁棒均方渐近稳定和鲁棒均方指数稳定,并给出了相应反馈控制器设计.所得结果与时滞和随机干扰相关,丰富了已有的结果.     

一种新型不确定奇异时滞系统的时滞相关稳定性判据及鲁棒镇定

研究了含范数有界参数不确定性的奇异时滞系统的时滞相关状态反馈镇定控制器的设计问题。首先,利用Lyapunov技巧,以LMIs的形式给出了标称奇异时滞系统正则,无脉冲模且零解渐近稳定的一种新的时滞相关型判据。然后,基于广义二次稳定性的概念,以LMIs的形式给出了时滞相关状态反馈镇定控制器存在的一个充分条件。     

Fuzzy controllers for nonlinear interconnected tmd systems with external force

Abstract

This paper investigates the effectiveness of a passive tuned mass damper (TMD) and active fuzzy controllers in reducing structural responses under external forces. In general, TMD is good for linear systems. We propose here a fuzzy controller to deal with nonlinear systems. For the fuzzy controller, a stability criterion in terms of Lyapunov's direct method is derived to guarantee the stability of interconnected TMD systems. Based on decentralized control and this criterion, a set of model‐based fuzzy controllers are then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear interconnected TMD system. Finally, an example is given to illustrate the concepts discussed throughout this paper.     

Synthesis of fault-tolerant static output feedback controllers for networked control systems

This paper is concerned with the design of static output feedback control laws for stabilizing a networked control system under possible element failures. Multiple faults can occur on sensors, actuators, or other electrical or mechanical componentes. With considering consecutive packet loss and time-varying network-induced delay, the closed-loop system is modeled as an equivalent time-delay system with several possible modes. By constructing a Lyapunov–Krasovskii function, sufficient conditions for the existence of static output feedback fault-tolerant stabilizing controllers are derived. Moreover, by the simultaneous stabilization approach, it is shown that a static output feedback fault-tolerant controller can be obtained by solving linear matrix inequalities (with equality constraints). Simulation results are presented to validate the theoretical results.