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Ball and beam system is highly dynamic system which is categorised as a variant of highly nonlinear inverted pendulum system. It acts as a standard benchmark for testing and comparing various control algorithms (Eaton et., 2000; Rana et al., 2011; Qian et al., 2012). Its configuration makes it a highly unsteady, intricate and underactuated system. It resembles dynamics of many real-time convoluted systems (Kundu and Nigam, 2012; Kocak, 2008). Plenty of work has been carried out by researchers for control of ball and beam systems. Jiang et al. (1995) examined neural networks and pole placement technique for control of an open loop ball and beam system. Real-time experiments were performed which showed better performance of neural controller. Wang et al. (2004) presented a neural controller optimised using genetic algorithm for ball and beam system. The proposed controller successfully stabilises ball and beam system in various initial positions. A fuzzy cascade controller based on hierarchical fair-competition genetic algorithm for control of ball and beam system was developed by Oh et al. (2009). The proposed controller comprises of outer and inner cascaded architecture and used for tuning of fuzzy controller.
Colon and Diniz (2009) compared different control techniques namely PID, linear quadratic regulator (LQG) and feedback linearization for controlling ball and beam system. The authors applied Matlab simulink environment for comparing proposed techniques. A control based on feedback linearization and fuzzy logic for stabilising AMIRA's ball and beam system was proposed by Chien et al. (2010). The controller was able to handle any initial condition and tracking signal. An outer loop fuzzy control and inner loop PD control for ball and beam system was suggested by Amjad et al. (2010). Authors also considered a PID controller based on integral time absolute error for controlling beam position. Results showed better performance of outer loop fuzzy control compared to other controllers. In a study by Chang et al. (2011), an adaptive fuzzy technique has been successfully applied for control of ball and beam system. The adaptive approach was used for optimising parameters of fuzzy controllers. The Lyapunov theorem was further used for analysing close loop stability of proposed system.
A particle swarm optimisation algorithm for tuning parameters of fuzzy neural controller of ball and plate system was proposed by Dong et al. (2011). Naredo and Castillo (2011) applied ant colony optimisation (ACO) for tuning fuzzy controller of ball and beam system. The authors considered four inputs with two membership functions for designing of proposed fuzzy controller. The results showed that ACO with three parameter coding optimally tunes fuzzy controller. Ali and Kumar (2013) presented a fuzzy PID approach for real-time control of Googol's GBB1004 ball and beam system. The simulation responses further validated applicability of proposed technique. In a study by Andrej and Marcin (2013), a neuro dynamic programming algorithm for control of ball and beam system has been discussed. The weights of proposed neural controller were adjusted using reinforcement learning technique. The results were further confirmed through real-time experiments. Farooq et al. (2013) compared interval type-2 fuzzy PD controller with type-1 fuzzy PD controller to control ball and beam system. The results showed better performance of former controller even when subjected to noise and errors. A fuzzy-PID and Proportional-derivative (PD)-fuzzy controller for ball and beam system has been developed by Azman et al. (2014). Simulation results showed better performance of PD-fuzzy controller compared to other controllers. According to Choudhary (2014), a fractional order PID controller can be applied for control of ball and beam system. Simulation were performed which showed better performance of proposed controller compared to traditional PID controller. Lin et al. (2014) applied fuzzy neural network for developing position controller of ball and beam. The authors suggested a cascaded inner-loop technique and gradient descent method for tuning parameters of proposed controller. Hui and Sharma (2015) proposed a fuzzy-PID control of ball and beam system. The analytical model of the system was derived using state space representation. The proposed control approach was further validated in Matlab.