This paper describes some important classes of two degrees of freedom of underactuated mechanical system and also surveys review of the recent state-of-the-art concerning the mathematical modeling of these systems, their classification, and all the control strategies (linear, nonlinear, and intelligent) that have been made so far (i.e., from the year 2000 to date) to control these systems. Future research and challenges concerning the improvement, the effectiveness, and robustness of the proposed controllers for underactuated mechanical systems are presented.

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The rider plays an important role in the stability and control of two-wheeled vehicles. The rider model must be designed carefully according to the physical and geometric features of the target two-wheeled vehicle. This paper aims to disclose how the rider affects the control and stability of two-wheeled vehicles. First, the two-wheeled vehicle-rider system was modelled and subjected to dynamic analysis. Next, the motion equations of a two-wheeled vehicle were linearized with forwarding velocity and small disturbances in displacement. Further, the genetic algorithm (GA) was introduced to optimize the parameters of the proportional-integralderivative (PID) controller, taking the steering torque and lean torque from the rider as the inputs. Finally, the PID controller was compared with the PI and PD controllers through simulation of a two-wheeled vehicle-rider system. The results show that the rider plays the role of derivation action; the motion of the upper body of the rider has a secondary impact on vehicle stability; the rider can stabilize the vehicle through both lean and steering torques generated by his/her upper body movements.

The Modelling and control design of Two Wheel Vehicle represents an open and a challenging problem in terms of the complexity in these kind of vehicles. This article aims to represent a comparative analysis of two strategies of control which are modern controller LQR and Conventional Controller PID for the two wheeled vehicle. The main goal is to compare their performances in terms of the time specification and to determine the best control strategy. We begin our development with the implementation of the dynamic model of the two wheeled vehicle using Lagrange modeling with holonomic constraints. Further, the article deals with analyzing the eigenvalues of the linearized dynamic system at which the two wheeled vehicle lean and steer are stable. This research targets the development of the two controllers: PID and LQR. Those controllers are used to control both steer angle, and lean rate angle of two wheeled vehicle. The study includes as well a comparative assessment of those control strategies in terms of performance.

This paper presents a Backstepping controller for five degrees of freedom Spherical Inverted Pendulum. Since the system is nonlinear, unstable, underactuated and MIMO and has a nonsquare form, the classic control design cannot be applied to control it. In order to remedy this problem, we propose in this paper a new method based on hierarchical steps of the Backstepping controller taking into a count the nonlinearities that cannot be neglected. Furthermore, a Linear Quadratic Regulator controller and LQR + PID based on the linearized system model are also designed for performance comparison. Finally, a simulation study is carried out to prove the effectiveness of proposed control scheme and is validated using the virtual reality environment that proves the performance of the Backstepping controller over the linear ones where it brings the pendulum from any initial condition in the upper hemisphere while the base is brought to the origin of the coordinates.