A Problem With the LQ Control of Overhead Cranes

2004 ◽  
Vol 128 (2) ◽  
pp. 436-440 ◽  
Author(s):  
Zhonghua Wang ◽  
Brian W. Surgenor
Keyword(s):  
Relative Mass ◽  
Overhead Crane ◽  
Optimum Control ◽  
Linear Quadratic ◽  
Overhead Cranes ◽  
Simulation And Experiment ◽  
The Subject ◽  
Design Recommendation ◽  
Lq Control ◽  
Optimum Control Problem

The control of an overhead crane is a classic optimum control problem, and its solution can be found in most textbooks on the subject of automatic controls. However, there is a design issue with respect to the relative mass of the cart and the suspended payload. If this problem is ignored, then the results of an analysis can be misleading and the response can be unstable. Based on a stability analysis, a design recommendation for optimal asymptotic linear quadratic (LQ) controllers with fixed gains is presented to avoid this problem. The results are validated by both simulation and experiment.

scholarly journals Signature PSO: A novel inertia weight adjustment using fuzzy signature for LQR tuning

2021 ◽  
Vol 10 (1) ◽  
pp. 308-318
Author(s):  
Achmad Komarudin ◽  
Novendra Setyawan ◽  
Leonardo Kamajaya ◽  
Mas Nurul Achmadiah ◽  
Zulfatman Zulfatman
Keyword(s):  
Linear Quadratic Regulator ◽  
Absolute Error ◽  
Control Parameters ◽  
Optimum Control ◽  
Exploration And Exploitation ◽  
Linear Quadratic ◽  
Lqr Control ◽  
Inertia Weight ◽  
Adjustment Strategy ◽  
Complete Optimization

Particle swarm optimization (PSO) is an optimization algorithm that is simple and reliable to complete optimization. The balance between exploration and exploitation of PSO searching characteristics is maintained by inertia weight. Since this parameter has been introduced, there have been several different strategies to determine the inertia weight during a train of the run. This paper describes the method of adjusting the inertia weights using fuzzy signatures called signature PSO. Some parameters were used as a fuzzy signature variable to represent the particle situation in a run. The implementation to solve the tuning problem of linear quadratic regulator (LQR) control parameters is also presented in this paper. Another weight adjustment strategy is also used as a comparison in performance evaluation using an integral time absolute error (ITAE). Experimental results show that signature PSO was able to give a good approximation to the optimum control parameters of LQR in this case.

scholarly journals Takagi-Sugeno Fuzzy Modeling and PSO-Based Robust LQR Anti-Swing Control for Overhead Crane

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Xuejuan Shao ◽  
Jinggang Zhang ◽  
Xueliang Zhang
Keyword(s):  
Linear Quadratic Regulator ◽  
Pso Algorithm ◽  
Fuzzy Modeling ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Overhead Crane ◽  
Linear Quadratic ◽  
Highly Nonlinear ◽  
The Stability ◽  
Takagi Sugeno

The dynamic model of overhead crane is highly nonlinear and uncertain. In this paper, Takagi-Sugeno (T-S) fuzzy modeling and PSO-based robust linear quadratic regulator (LQR) are proposed for anti-swing and positioning control of the system. First, on the basis of sector nonlinear theory, the two T-S fuzzy models are established by using the virtual control variables and approximate method. Then, considering the uncertainty of the model, robust LQR controllers with parallel distributed compensation (PDC) structure are designed. The feedback gain matrices are obtained by transforming the stability and robustness of the system into linear matrix inequalities (LMIs) problem. In addition, particle swarm optimization (PSO) algorithm is used to overcome the blindness of LQR weight matrix selection in the design process. The proposed control methods are simple, feasible, and robust. Finally, the numeral simulations are carried out to prove the effectiveness of the methods.

Energy-Based Approach for Controller Design of Overhead Cranes: A Comparative Study

2013 ◽  
Vol 365-366 ◽  
pp. 784-787 ◽  
Author(s):  
Nguyen Quang Hoang ◽  
Soon Geul Lee
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Asymptotically Stable ◽  
Overhead Crane ◽  
Overhead Cranes ◽  
Swing Angle ◽  
Optimal Linear ◽  
Linear And Nonlinear ◽  
Invariance Theorem ◽  
Lyapunov Technique

In this paper, five controllers including linear and nonlinear ones for an underactuated overhead crane are derived based on the passivity of the system. The total energy of the system and its square are used in Lyapunov candidate function to design controllers. The equilibrium point of the closed loop is proven to be asymptotically stable by the Lyapunov technique and LaSalle invariance theorem. In addition, the optimal linear controller is also combined to force the swing angle to converge fast to zero by reaching destination of the trolley. Numerical simulations are carried out to evaluate the controllers.

Design and Analysis of Linear Quadratic Regulator for a Non-Linear Positioning System

2015 ◽  
Vol 761 ◽  
pp. 227-232 ◽  
Author(s):  
Tang Teng Fong ◽  
Zamberi Jamaludin ◽  
Ahmad Yusairi Bani Hashim ◽  
Muhamad Arfauz A. Rahman
Keyword(s):  
Physical System ◽  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Upright Position ◽  
System Model ◽  
Optimum Control ◽  
Control Vector ◽  
Linear Quadratic ◽  
Non Linear ◽  
Lqr Controller

The control of rotary inverted pendulum is a case of classical robust controller design of non-linear system applications. In the control system design, a precise system model is a pre-requisite for an enhanced and optimum control performance. This paper describes the dynamic system model of an inverted pendulum system. The mathematical model was derived, linearized at the upright equilibrium points and validated using non-linear least square frequency domain identification approach based on measured frequency response function of the physical system. Besides that, a linear quadratic regulator (LQR) controller was designed as the balancing controller for the pendulum. An extensive analysis was performed on the effect of the weighting parameter Q on the static time of arm, balance time of pendulum, oscillation, as well as, response of arm and pendulum, in order to determine the optimum state-feedback control vector, K. Furthermore, the optimum control vector was successfully applied and validated on the physical system to stabilize the pendulum in its upright position. In the experimental validation, the LQR controller was able to keep the pendulum in its upright position even in the presence of external disturbance forces.

scholarly journals The Time Delay Filtering Method for Cancelling Vibration on Overhead Transportation Systems Modelled as a Physical Pendulum

2007 ◽  
Vol 14 (1) ◽  
pp. 53-64 ◽  
Author(s):  
G. Peláez ◽  
J. Doval-Gandoy ◽  
N. Caparrini ◽  
J.C. García-Prada
Keyword(s):  
Time Delay ◽  
Dynamic Response ◽  
Transportation Systems ◽  
Overhead Crane ◽  
Physical Pendulum ◽  
Filtering Method ◽  
Overhead Cranes ◽  
Simple Pendulum ◽  
Pendulum Model

An investigation of the response of a physical pendulum to time delay filtered inputs was conducted. It was shown that the physical pendulum model is more accurate than the simple pendulum for modelling the dynamic response of overhead cranes with loads hanging from hooks. Based on the physical pendulum model a Specified Time Delay filter for an experimental mini overhead crane was synthesized. While somewhat limited in the scope by the hardware conditions placed in the system, the results provide basic insights into the successful application of the Time Delay Filtering method to overhead cranes.

Based on the State Feedback Optimal Controler Design

2012 ◽  
Vol 241-244 ◽  
pp. 1265-1268
Author(s):  
Wei Zhang
Keyword(s):  
State Feedback ◽  
Low Cost ◽  
State Equation ◽  
The State ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Control Scheme ◽  
Simulation And Experiment ◽  
Quadratic Optimal Control ◽  
Real State

The study on linear quadratic optimal control based on state feedback has been achieved fruitful results. This paper design a linear quadratic optimal controler based on the state feedback, and used it in a real state equation. The control scheme proposed has advantage of simple cotroller structure,low cost and easy to implement. Through simulation and compare with the performance target ,the Simulation and experiment show that the designed controller is effective, to the system dynamic response has good tracking performance and anti-interference ability.

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