We extend the method of controlled Lagrangians to include potential shaping for complete state-space stabilization of mechanical systems. The method of controlled Lagrangians deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complement...

Abstract — This paper describes the design and implementation of a self-balancing two-wheeled robot, the Equilibrist Robot. The system is similar to the classical unstable, non-linear mechanical control problem of an inverted pendulum on a cart. Using the Linear Quadratic Regulator method and PID for state feedback, this paper shows a control algorithm that solves this problem. This control is ...

In this paper, we study the tracking control problem for a nonlinear system in which the zero dynamics may be unstable. The objective here is to approximate the nonlinear system by another singularly perturbed system by using a small singular perturbation parameter  . The proposed approach is based on the methodology of exact input output linearization control, the integrator backstepping appr...

Sliding mode control is quickly becoming a popular research ...eld due to the several favorable qualities, including robustness. Linear quadratic control has been one of the more popular and more traditional control techniques, partially due to the ease of implementation and its optimality quality. In this paper, we provide an introduction to sliding mode control. A technique is suggested to al...

In the last decade, energy based control theory has undergone a significant breakthrough in dealing with underactated mechanical systems with two successful and similar tools, controlled Lagrangians and controlled Hamiltanians (IDA-PBC). However, because of the complexity of these tools, successful case studies are lacking, in particular, MIMO cases. The seminal theoretical paper of controlled ...

We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping compl...

This paper deals with system identification of a nonlinear, dynamic SIMO system of an inverted pendulum on a cart. Using the approach of compressed sensing the Ordinary Differential Equations (ODEs) describing the dynamics of this system are obtained from a time series data of the inputs and outputs. A library of functions is created and the correct coefficients of these functions are identifie...

In Wireless Networked Control Systems (WNCS), time-varying and unknown delays can significantly degrade the closed-loop performance and even lead to instability. This paper proposes using Dynamic Matrix Control for WNCS, where, a set of predicted control signals corresponding to possible delays are sent to the plant. Here the most appropriate control signal is selected based on the round-trip d...

Properties of simple strategies for swinging up an inverted pendulum are discussed. It is shown that the behavior critically depends on the ratio of the maximum acceleration of the pivot to the acceleration of gravity. A comparison of energy based strategies with minimum time strategy gives interesting insights into the robustness of minimum time solutions.

This paper illustrates a Comparative study of highly non-linear, complex and multivariable Inverted Pendulum (IP) system on Cart using different soft computing techniques. Firstly, a Fuzzy logic controller was designed using triangular and trapezoidal shape Membership functions (MF's). The trapezoidal fuzzy controller shows better results in comparison to triangular fuzzy controller. Secondly, ...