Swing up and stabilization control of rotary inverted pendulum based on energy balance, fuzzy logic, and LQR controllers

Rotary Inverted Pendulum (RIP) mimics the behavior of many practical control systems like crane mechanism, segway, unicycle robot, traction control in vehicles, rocket stabilization, and launching. RIP is a fourth-order nonlinear open-loop unstable dynamical system and is widely used for testing the effectiveness of the newly developed control algorithms. In this paper, a Hybrid Control Scheme (HCS) based on energy balance and fuzzy logic controllers is proposed to implement the swing up and stabilization control of RIP. In the proposed control scheme, the fuzzy logic-based state feedback gains are dynamically tuned in real-time by minimizing the absolute error between the desired and actual states to get robust control performance. The proposed HCS is also compared with the conventional Linear Quadratic Controller (LQR) for this application. The comparative results show that the proposed fuzzy logic-based hybrid control scheme gives the optimal control performance in terms of achieving satisfactory transient, steady-state, and robust responses from a given RIP system, as compared to the conventional LQR based control scheme. The proposed control scheme is also relatively less complex with a low computational cost and provides desired response characteristics as compared to the existing ones in the literature.

Robust Adaptive Super-twisting Sliding Mode Stability Control for Underactuated Rotary Inverted Pendulum with Experimental Validation

In this paper, an adaptive proportional-integral-derivative (PID) sliding mode control method combined with super-twisting algorithm is designed for the stabilization control of rotary inverted pendulum system in the appearance of exterior perturbation. The state-space model of rotary inverted pendulum in the presence of exterior disturbance is obtained. Then, the super-twisting PID sliding mode controller is designed for finite time stability control of this underactuated control system. The upper bounds of perturbation are presumed to be unknown; accordingly, the adaptive control procedure is taken to approximate the uncertain bound of the external disturbances. The stability control of rotary inverted pendulum system is proved by means of the Lyapunov stability theory. In order to validate accuracy and efficiency of the recommended control technique, some simulation outcomes are prepared and compared with other existing method. Moreover, experimental results are implemented to show the success of the proposed method.

Analytical and Experimental Analyses of Nonlinear Vibrations in a Rotary Inverted Pendulum

Gaining insight into possible vibratory responses of dynamical systems around their stable equilibria is an essential step, which must be taken before their design and application. The results of such a study can significantly help prevent instability in closed-loop stabilized systems through avoiding the excitation of the system in the neighborhood of its resonance. This paper investigates nonlinear oscillations of a Rotary Inverted Pendulum (RIP) with a full-state feedback controller. Lagrange’s equations are employed to derive an accurate 2-DoF mathematical model, whose parameter values are extracted by both the measurement and 3D modeling of the real system components. Although the governing equations of a 2-DoF nonlinear system are difficult to solve, performing an analytical solution is of great importance, mostly because, compared to the numerical solution, the analytical solution can function as an accurate pattern. Additionally, the analytical solution is generally more appealing to engineers because their computational costs are less than those of the numerical solution. In this study, the perturbative method of multiple scales is used to obtain an analytical solution to the coupled nonlinear motion equations of the closed-loop system. Moreover, the parameters of the controller are determined, using the results of this solution. The findings reveal the existence of hardening- and softening-type resonances at the first and second vibrational modes, respectively. This led to a wide frequency range with moderately large-amplitude vibrations, which must be avoided when adjusting a time-varying set-point for the system. The analytical results of the nonlinear vibration of the RIP are verified by experimental measurements, and a very good agreement is observed between the results of both approaches.

Difference-Based Mutation Operation for Neuroevolution of Augmented Topologies

In this paper, a novel search operation is proposed for the neuroevolution of augmented topologies, namely the difference-based mutation. This operator uses the differences between individuals in the population to perform more efficient search for optimal weights and structure of the model. The difference is determined according to the innovation numbers assigned to each node and connection, allowing tracking the changes. The implemented neuroevolution algorithm allows backward connections and loops in the topology, and uses a set of mutation operators, including connections merging and deletion. The algorithm is tested on a set of classification problems and the rotary inverted pendulum control problem. The comparison is performed between the basic approach and modified versions. The sensitivity to parameter values is examined. The experimental results prove that the newly developed operator delivers significant improvements to the classification quality in several cases, and allow finding better control algorithms.