Underactuated mechanical systems are those possessing fewer actuators than degrees of freedom. Examples of such systems abound, including flexible joint and flexible link robots, space robots, mobile robots, and robot models that include actuator dynamics and rigid body dynamics together. Complex internal dynamics, nonholonomic behavior, and lack of feedback linearizability are often exhibited by such systems, making the class a rich one from a control standpoint. In this article the author studies a particular underactuated system known as the Acrobot: a two-degree-of-freedom planar robot with a single actuator. The author considers the so-called swing up control problem using the method of partial feedback linearization. The author gives conditions under which the response of either degree of freedom may be globally decoupled from the response of the other and linearized. This result can be used as a starting point to design swing up control algorithms. Analysis of the resulting zero dynamics as well as analysis of the energy of the system provides an understanding of the swing up algorithms. Simulation results are presented showing the swing up motion resulting from partial feedback linearization designs. >

The swing up control problem for the Acrobot

Brief Swinging up a pendulum by energy control

Robust Control Design with MATLAB (second edition) helps the student to learn how to use well-developed advanced robust control design methods in practical cases. To this end, several realistic control design examples from teaching-laboratory experiments, such as a two-wheeled, self-balancing robot, to complex systems like a flexible-link manipulator are given detailed presentation. All of these exercises are conducted using MATLAB Robust Control Toolbox 3, Control System Toolbox and Simulink. By sharing their experiences in industrial cases with minimum recourse to complicated theories and formulae, the authors convey essential ideas and useful insights into robust industrial control systems design using major H-infinity optimization and related methods allowing readers quickly to move on with their own challenges. The hands-on tutorial style of this text rests on an abundance of examples and features for the second edition: rewritten and simplified presentation of theoretical and methodological material including original coverage of linear matrix inequalities; new Part II forming a tutorial on Robust Control Toolbox 3; fresh design problems including the control of a two-rotor dynamic system; and end-of-chapter exercises. Electronic supplements to the written text that can be downloaded from extras.springer.com/isbn include: M-files developed with MATLAB help in understanding the essence of robust control system design portrayed in text-based examples; MDL-files for simulation of open- and closed-loop systems in Simulink; and a solutions manual available free of charge to those adopting Robust Control Design with MATLAB as a textbook for courses. Robust Control Design with MATLAB is for graduate students and practising engineers who want to learn how to deal with robust control design problems without spending a lot of time in researching complex theoretical developments.

Robust control design with MATLAB

https://www.control.utoronto.ca/~broucke/ece1653s/Intro/ast_fur96.pdf

Swinging up a Pendulum by Energy Control

Swing-up control, that is the transfer of a pendulum from a pendant state to the inverted one, is a good laboratory experiment of optimal control theory for non-linear control systems. The optimal control can be determined by the maximum principle and obtained as a function of time. Since the control is, however, determined in a feedforward fashion, the control is not robust to disturbances and uncertainties of the system, and the transfer of the state of the pendulum is not assured. In the paper, a robust swing-up control using a subspace projected from the whole state space is proposed. Based on the projected state space or pseudo-state, the control input is determined depending on the partitioning of the state as a bang-bang type control. The control algorithm is applied for a new type of pendulum (TI Tech pendulum), and the effectiveness and robustness of the proposed control are examined by experiments.

Swing-up Control of Inverted Pendulum Using Pseudo-State Feedback:

This paper relates to the design of a control system for a mechanical system which contains an unstable mode and to an experiment for demonstrating that the control theory may be applied to practical real systems. In this paper the object treated is the control of the pendulum-cart system, which has been studied by many control theorists and engineers as an inverted pendulum problem, and a composite control system is designed not only to stabilize the inverted pendulum but to swing the pendulum from the natural pendent position up to the inverted position, which is actually made. The experimental results are presented.

Control of unstable mechanical system Control of pendulum

Hybrid Controller for Inverted Pendulum

Compatibility of Observer and Zero Sensitivity Observer

This note revisits the theoretical foundation of the Daum–Huang particle filter concepts for solving Bayesian updating problems. We reexamine the defining necessary and sufficient condition, in the form of an operator equation, for a flow to generate a particular homotopy between the a priori and the a posteriori probability density functions. We show that two well-known flows indeed satisfy this sufficient condition in the linear-Gaussian case, restating some of the significant results in a recent series of papers coauthored by Fred Daum with our alternative proof, which we hope will provide a useful perspective for future flow-based filter developments.

Shozo Mori

Papers

Control of unstable mechanical system Control of pendulum

Hybrid Controller for Inverted Pendulum

Compatibility of Observer and Zero Sensitivity Observer

A Note on Particle Flow Methods for Solving Bayesian Updates

The compatibility of regulator to the variation of plant dynamics