Parameter Estimation of Damped Compound Pendulum Using Bat Algorithm

Abstract

Abstract. In this study, the parameter identification of the damped compound pendulum system is proposed using one of the most promising nature inspired algorithms which is Bat Algorithm (BA). The procedure used to achieve the parameter identification of the experimental system consists of input-output data collection, ARX model order selection and parameter estimation using bat algorithm (BA) method. PRBS signal is used as an input signal to regulate the motor speed. Whereas, the output signal is taken from position sensor. Both, input and output data is used to estimate the parameter of the autoregressive with exogenous input (ARX) model. The performance of the model is validated using mean squares error (MSE) between the actual and predicted output responses of the models. Finally, comparative study is conducted between BA and the conventional estimation method (i.e. Least Square). Based on the results obtained, MSE produce from Bat Algorithm (BA) is outperformed the Least Square (LS) method.

The experimental multi-arm pendulum on a cart: A benchmark system for chaos, learning, and control

“…Notable variants of the system include: the double pendulum on the cart [25] , the rotary double pendulum [26] , [27] , [28] , the “acrobot” [29] , which is a double pendulum with actuation torque on the second arm, and the “pendubot” [30] , [31] , which is a double pendulum with actuation torque on the first arm. The double pendulum remains relevant in the study of nonlinear dynamics and has emerged as an important benchmark problem in system identification [11] , [32] , [33] , [34] , [35] and machine learning [11] , [15] , [34] , [36] , [37] , [38] , [39] , [40] , [41] .…”

“…With such interest in understanding and controlling the dynamics of pendulums, a number of researchers have build physical models to visualize and test their theoretical calculations; these experimental demonstrations include the single [6] , [7] , [9] , [10] , [12] , [13] , [30] , [32] , [46] , [48] , [50] , [51] , [53] , [57] , [58] , [83] , [83] , [84] , [85] , double [19] , [21] , [25] , [29] , [30] , [31] , [58] , [67] , [86] , [87] , [88] , [89] , [90] , and triple pendulum [70] , [71] , [73] , [74] , [75] , [91] , [92] . Among these physically-realized pendulums, it is the pendulum on a moving cart that has received the most attention.…”

The Experimental Multi-Arm Pendulum on a Cart: A Benchmark System for Chaos, Learning, and Control

“…8. First, the bearing housing is assembled, which includes two steps: 1) a 3D printed spacer (32) is press-fitted into the bearing hole (33). 2) A thin layer of Loctite is applied to the outer ream of the bearing (31).…”

“…Notable variants of the system include: the double pendulum on the cart [25], the rotary double pendulum [26][27][28], the "acrobot" [29], which is a double pendulum with actuation torque on the second arm, and the "pendubot" [30,31], which is a double pendulum with actuation torque on the first arm. The double pendulum remains relevant in the study of nonlinear dynamics and has emerged as an important benchmark problem in system identification [11,[32][33][34][35] and machine learning [11,15,34,[36][37][38][39][40][41].…”

“…With such interest in understanding and controlling the dynamics of pendulums, a number of researchers have build physical models to visualize and test their theoretical calculations; these experimental demonstrations include the single [6,7,9,10,12,13,30,32,46,48,50,51,53,57,58,83,[83][84][85], double [19, 21, 25, 29-31, 58, 67, 86-90], and triple pendulum [70, 71, 73-75, 91, 92]. Among these physically-realized pendulums, it is the pendulum on a moving cart that has received the most attention.…”