Vol.:(0123456789) 1 3 Journal of Ambient Intelligence and Humanized Computing https://doi.org/10.1007/s12652-020-02566-y ORIGINAL RESEARCH Improved ant colony optimization for achieving self‑balancing and position control for balancer systems Rupam Singh 1  · Bharat Bhushan 1 Received: 11 April 2020 / Accepted: 18 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract The balancer systems represent feedback in loop-based underactuated system which is electromechanical, multivariate, and nonlinear. This paper develops a self-balancing controller using an improved ant colony optimization (ACO) to optimize the proportional integral derivative controller (PID) controller. The proposed controller achieves self-balancing control for a ball on the plate by controlling the plate inclination angle. Initially, the modelling of the ball balancer system is achieved with the help of a two degree of freedom (2DoF) ball balancer system controlled by a PID controller. Further, ACO is employed to autonomously evaluate the condition of a process and fnd the optimal tuning parameters for the PID controller. The transition probability of the ACO is revised to improve the response and convergence speed of the algorithm resulting in an improved ACO. The developed control schemes were applied with the 2DoF ball balancer model both in simulation as well as for the real-time operation. The results depicted the performance of the proposed control scheme by analysing the characteristics such as transient response and steady-state error. Further, stability analysis has been done for the developed control schemes using describing function method for multiple frequencies. The results depicted the superiority of the improved ACO based PID controller over the conventional PID controller. Keywords Self-balancing control · Ball balancer setup · Proportional integral derivative control · Ant colony optimization 1 Introduction The approximation of underactuated nonlinear systems through automatic decision development and intelligent con- trol methods (Murray et al. 2003) is an issue that appears in many problems (Nelles 2001) and can be tackled through various approaches. The diversity and complexity of these systems have led researchers in the feld to analyse the action of various linear, nonlinear, model-free, passivity, and intel- ligent controllers. These controllers are focussed at achiev- ing self-balancing control and steady-state operation for various systems like inverted pendulum (Boubaker 2012; Moness et al. 2020), the twin rotor multi input multi output system (TRMS) (Chalupa et al. 2015), the ball beam system (Andreev et al. 2002; Nowopolski 2013), hovercraft (Aranda et al. 2006), Furuta pendulum (Acosta 2010), and ball and plate system (Awtar et al. 2002). In general, linear control- lers ofer a simple way of designing closed-loop control for these systems. Various linear controllers were available in the literature to solve the problems in underactuated systems (de Jager 1998; Olivares and Albertos 2013; Aguilar-Avelar and Moreno-Valenzuela 2015). But the complicated nonlin- ear dynamics of underactuated systems afect the capability of providing a plausible solution and limits the generalized applications of control laws. Besides, the linearization of the nonlinear systems is also carried which heavily afect the speed of system response. This motivated the develop- ment of several nonlinear control techniques to deal with the problems in underactuated systems. Lots of nonlinear con- trollers like Lagrangian, lambda method, and backstepping controller (Chang 2008; Choukchou-Braham et al. 2014; Rudra et al. 2017), have been evolved in the last few years. These controllers faced some drawbacks during the early stage of their development with the limitations of lambda method in dealing with external load and back stepping con- trollers lagging due to additional feedback. Apart from the above controllers, the adaptive iterative learning methods * Rupam Singh singhrupam99@gmail.com Bharat Bhushan bharat@dce.ac.in 1 Department of Electrical Engineering, Delhi Technological University, Shahbad Daulatpur, Delhi 110042, India