The approximation of humanoid robot by an inverted pendulum is one of the most used models to generate a stable walking patterns using a planned Zero Moment Point (ZMP) trajectory. However, on account of the difference between the multi-body model of the humanoid robot and the simple inverted pendulum model, the ZMP error might be bigger than the polygon of support and the robot falls down. To ...

To use numerical investigation of functional differential equations it is very important to know if difference analogues of the considered differential equations have the reliability to preserve some general properties of these equations, in particular, property of stability. This problem is considered here by investigation of a difference analogue of the linear mathematical inverted pendulum. ...

1 Purpose The purpose of this experiment is to apply controller and observer design techniques to a physical “difficult-to-control” system, namely, the inverted pendulum on a cart system. The controller will mainly be designed via optimal control techniques. The control objective is for the cart to track a square wave while the pendulum remains upright. Also, the controller must be improve the ...

A nonlinear sliding mode control method is presented for single inverted pendulum position tracking control. Sliding mode control (SMC) is a special nonlinear control method which have quick response, insensitive to parameters variation and disturbance, online identification for plants are not needed, its very suitable for nonlinear system control, but in reality usage, the chattering reduction...

The approximation of a humanoid robot by an inverted pendulum is one of the most frequently used models to generate a stable walking pattern using a planned zero moment point (ZMP) trajectory. However, on account of the difference between the multibody model of the humanoid robot and the simple inverted pendulum model, the ZMP error might be bigger than the polygon of support and the robot fall...

In this paper, the solution expansion for an inverted pendulum system with time delay is studied. The linearized model of this nonlinear system near its equilibrium is derived on the assumption that a unique equilibrium exists in it. Then the asymptotic expressions of its eigenvalues and the eigenvalues’ corresponding eigenvectors are obtained. Moreover, although the set of these eigenvectors d...

The proposed method called terminal sliding Fuzzy Sliding Parallel Distributed Compensation (TSF-PDC) control is developed in this paper to deal with the nonlinear systems subjected to bounded disturbances. The TSF-PDC controller is combined with Fuzzy Parallel Distributed Compensation (F-PDC) control and terminal sliding mode (TS) control to deal with nonlinear systems. In the design of TSF-PD...

We study the stabilizability, via the method of energy shaping, of a given Lagrangian system with two degrees of underactuation and with n ≥ 4 degrees of freedom. By making use of the formal theory of PDEs, we derive an involutive system of PDEs which governs energy shapability, and thus deduce, for the first time, easily verifiable conditions under which energy shaping is guaranteed. We illust...

 The paper presents a hybrid system controller, incorporating a neural and an LQG controller. The neural controller has been optimized by genetic algorithms directly on the inverted pendulum system. The failure-free optimization process stipulated a relatively small region of the asymptotic stability of the neural controller, which is concentrated around the regulation point. The presented hyb...

In this paper, taking the inverted pendulum as an example of nonlinear systems which are not exactly linearizable, we give a controller design method for the system based on the approximate linearization. In the method, we try to suppress the e ect of the higher order residual terms in choosing the new coordinate for the approximate linearization. Furthermore, we show its e ectiveness by experi...