Application of Genetic Algorithm Optimization LQR Weighting Matrices Control Inverted Pendulum

2014 ◽  
Vol 543-547 ◽  
pp. 1274-1277 ◽  
Author(s):  
Peng Shen
Keyword(s):  
Genetic Algorithms ◽  
Inverted Pendulum ◽  
Control Method ◽  
Algorithm Optimization ◽  
Control Effect ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Optimal Control Method ◽  
Weighted Matrix ◽  
Triple Inverted Pendulum

In practice, the key problem to apply LQR optimal control method is how to correctly choose the weighted matrix of performance index. At present, there is no formulaic approach for this problem. To obtain the satisfying results, people must repeat to test many times. This kind of LQR control method based on genetic algorithms, which can obtain satisfying control results at first hand, is presented for triple inverted pendulum system. The method optimizes the Q-matrix by using genetic algorithms, selects trace of the result of Riccati equation as the objective function. The control problem of triple inverted pendulum is resolved successfully. The simulation results prove that the control effect by this method is better than the other methods mentioned in the references.

An Optimized Design for Inverted Pendulum System of Active Disturbance Rejection Control Based on Generic Algorithm

2013 ◽  
Vol 313-314 ◽  
pp. 553-558 ◽  
Author(s):  
Jun Du ◽  
Jiu Long Jiang
Keyword(s):  
Inverted Pendulum ◽  
Control Method ◽  
System Control ◽  
Optimized Design ◽  
Control Effect ◽  
Generic Algorithm ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Disturbance Rejection Control ◽  
System Controller

The dissertation comes up with an optimized design for ADRC inverted pendulum system controller based on Generic Algorithm. This design making full use of ADRC method ,which can coordinate the ability to the response time and overshoot meanwhile it can also be provided with the characteristic of high anti-jamming ability, well Robustness ability ,designing ADRC inverted pendulum system controller for improving the performance of inverted pendulum system .At the same time ,aiming at more parameter of ADRC implement-designed ,more difficult to carry on designing problem ,it conducts more excellent design of excellent parameter with applying generic optimization algorithm ,and obtains the most excellent parameter of performance .At last simulate the control model with the help of MATLAB. Emulation result indicates ,the ADRC inverted pendulum system control method that the dissertation showing has provided with well evanescence and stabilization ,less responding time without overshoot ,with more control effect.

Nonlinear Optimal Control for the Wheeled Inverted Pendulum System

Robotica ◽  
2019 ◽  
Vol 38 (1) ◽  
pp. 29-47 ◽  
Author(s):  
G. Rigatos ◽  
K. Busawon ◽  
J. Pomares ◽  
M. Abbaszadeh
Keyword(s):  
Optimal Control ◽  
Inverted Pendulum ◽  
Control Method ◽  
Taylor Series Expansion ◽  
Nonlinear Optimal Control ◽  
Algebraic Riccati Equation ◽  
Time Step ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Wheeled Inverted Pendulum

SummaryThe article proposes a nonlinear optimal control method for the model of the wheeled inverted pendulum (WIP). This is a difficult control and robotics problem due to the system’s strong nonlinearities and due to its underactuation. First, the dynamic model of the WIP undergoes approximate linearization around a temporary operating point which is recomputed at each time step of the control method. The linearization procedure makes use of Taylor series expansion and of the computation of the associated Jacobian matrices. For the linearized model of the wheeled pendulum, an optimal (H-infinity) feedback controller is developed. The controller’s gain is computed through the repetitive solution of an algebraic Riccati equation at each iteration of the control algorithm. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, by using the H-infinity Kalman Filter as a robust state estimator, the implementation of a state estimation-based control scheme becomes also possible.

The Design of Output Feedback Controller for Inverted Pendulum System

2013 ◽  
Vol 336-338 ◽  
pp. 489-492
Author(s):  
Hong Xing Li ◽  
An Shan Lu
Keyword(s):  
Output Feedback ◽  
Attitude Control ◽  
Inverted Pendulum ◽  
Control Method ◽  
Paper Analysis ◽  
Order System ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Non Linear ◽  
Sufficiency Conditions

Inverted pendulum system is a complex, non-linear and uncertain high-order system. It is a simple model of the rockets vertical attitude control and two-legged walking robot control. It is used to study and validation of different control methods. The paper analysis the non-linear inverted pendulum system, then deduces sufficiency conditions of the existence of controller with output feedback and designs controller. It utilizes MATLAB software to get the answer. The feasibility of control method and robustness of controller are demonstrated by numerical examples.

Optimal Control Theory Research on Inverted Pendulum System

2014 ◽  
Vol 494-495 ◽  
pp. 1118-1121
Author(s):  
Shuo Mei Wu ◽  
Jian Wei Song ◽  
Wen Qing Zhang
Keyword(s):  
Optimal Control ◽  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Good Control ◽  
Control Effect ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Theory Research

The state space expression can be deduced by establishing the mathematical model of inverted pendulum system. In this paper, linear quadratic regulator (LQR) is used to control the inverted pendulum system, providing better balance between system robustness stability and rapidity. The simulation structure shows that the better the system anti-interference capability is, the shorter its recovery time is. Good control effect can be achieved by applying linear quadratic optimal control in the control of double inverted pendulum balancing system.

LQR Control of Single Inverted Pendulum Based on Square Root Filter

2012 ◽  
Vol 433-440 ◽  
pp. 6999-7003 ◽  
Author(s):  
Hong Mei Wang ◽  
Shi Jin Jiang
Keyword(s):  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Weight Coefficient ◽  
Feedback Gain ◽  
Square Root ◽  
Control Effect ◽  
Linear Quadratic ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Square Root Filter

Inverted pendulum system is a nonlinear, coupling, multi-variable and unstable system. In this paper, Linear Quadratic Regulator (LQR) is used to achieve optimal control of single inverted pendulum. First, the state-space model of the system is created. Then state feedback gain is calculated by selecting suitable weight coefficient matrix. Because the inverted pendulum system exists all kinds of disturbs inevitably, the states have errors and the accuracy of control drops. So square root filter is used to estimate states on line before LQR. The simulation results show control effect has obvious improvement because of adopting square root filter.

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