In this report a number of algorithms for optimal control of a double inverted pendulum on a cart (DIPC) are investigated and compared. Modeling is based on Euler-Lagrange equations derived by specifying a Lagrangian, difference between kinetic and potential energy of the DIPC system. This results in a system of nonlinear differential equations consisting of three 2-nd order equations. This sys...

A new multibody dynamics model, that is referred to as a chain pendulum on a cart, is presented. It is composed of an arbitrarily number of rigid links that are serially connected by spherical joints, and a cart that is moving in a horizontal plane. This yields rich dynamic structures on the nonlinear configuration manifold that is comprised of the copies of the unit-sphere and the two dimensio...

The paper adresses the problem of stabilization of a speci"c target position of underactuated Lagrangian or Hamiltonian systems. We propose to solve the problem in two steps: "rst to stabilize a set with the target position being a limit point for all trajectories originating in this set and then to switch to a locally stabilizing controller. We illustrate this approach by the well-known exampl...

When considering the issue of synthesis an automatic control system by a modular method using polynomial decomposition transfer functions object and controller, algorithms for fully controlled systems are proposed. However, question arises about possibilities this algorithm if condition is not met. The consideration is-sue turned out to be especially relevant multichannel models objects with no...

The paper presents two different ways of mathematical modeling of Inverted Pendulum. A Proportional-Integral-Derative (PID) controller is designed for its stabilization. Some reference stable system is selected after designing of PID controller to optimize different types of error using Genetic Algorithms. The proposed system extends classical inverted pendulum by incorporating two moving masse...

The Cart-Inverted Pendulum System (CIPS) is a classical benchmark control problem. Its dynamics resembles with that of many real world systems of interest like missile launchers, pendubots, human walking and segways and many more. The control of this system is challenging as it is highly unstable, highly non-linear, non-minimum phase system and underactuated. Further, the physical constraints o...

A controlled Lagrangian approach is presented for the stabilization of an inverted pendulum mounted on a cart. The stabilization strategy consists in forcing the closed-loop system to behave as an Euler-Lagrange system, with a fixed inertia matrix. For carrying it out, it is necessary to adequately shape the potential and kinetic energies of the closed-loop system. The idea behind this procedur...

In the classical control theory literature, the inverted pendulum stabilization problem has been addressed in two ways: as an application of the vibrational control principle, or by imagining that the pivot is on a cart moved according to a suitable feedback law. Several other stabilization methods have been recently proposed. In this paper we propose a new approach: the pendulum is assembled o...

In this paper, a method for the tuning the membership functions of a Mamdani type Fuzzy Logic Controller (FLC) using the Clonal Selection Algorithm(CSA) a model of the Artificial Immune System(AIS) paradigm is examined. FLC’s are designed for two problems, firstly the linear cart centering problem and secondly the highly nonlinear inverted pendulum problem. The FLC tuned by AIS is compared with...