scholarly journals Optimal Control of Nonlinear Inverted Pendulum System Using PID Controller and LQR: Performance Analysis Without and With Disturbance Input

2014 ◽  
Vol 11 (6) ◽  
pp. 661-670 ◽  
Author(s):  
Lal Bahadur Prasad ◽  
Barjeev Tyagi ◽  
Hari Om Gupta
Keyword(s):  
Optimal Control ◽  
Performance Analysis ◽  
Pid Controller ◽  
Inverted Pendulum ◽  
Pendulum System ◽  
Inverted Pendulum System

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.

Optimisation of a PID Controller for an Inverted Pendulum Using the Bees Algorithm

2015 ◽  
Vol 789-790 ◽  
pp. 1039-1044 ◽  
Author(s):  
Muhammed Arif Sen ◽  
Mete Kalyoncu
Keyword(s):  
Pid Controller ◽  
Inverted Pendulum ◽  
Controller Design ◽  
Stable State ◽  
Bees Algorithm ◽  
Pid Controllers ◽  
Pendulum System ◽  
Tuning Method ◽  
Inverted Pendulum System ◽  
Optimal Gains

The inverted pendulum system is a challenging control problem in the control theory, which continually moves away from a stable state. The paper presents the design of a Proportional-Integral-Derivative (PID) controller for a single-input multi-output (SIMO) inverted pendulum system and using the Bees Algorithm (BA) to obtain optimal gains for PID controllers. The Bees Algorithm optimizes the gains so that the controller can move the cart to a desired position with the minimum amount of the change in the pendulum’s angle from the vertically upright position during the movement. The tuning aim is to minimize the control responses of the cart’s position and the pendulum’s angle in time domain. MATLAB/Simulink simulation has been performed to demonstrate that the effects on the system performance of PID controllers with optimal gains. The obtained results show that the tuning method by using the Bees Algorithm produced PID controllers successfully within the controller design criteria. Following a description of the inverted pendulum system and the Bees Algorithm, the paper gives the obtained simulation results for the system demonstrating the efficiency of the design.

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