Katsuhisa Furuta

Swinging up a Pendulum by Energy Control

This paper presents the concept of energy control and shows how robust strategies for swinging up an inverted pendulum are obtained using this idea. The behavior obtained with the strategy depends critically on the ratio of the maximum acceleration of the pivot to the acceleration of gravity. A comparison with with minimum time strategies gives interesting insights into the robustness issues.

Variable structure control with sliding sector

A sliding sector, inside which a norm of the state decreases with zero input, is defined for both continuous- and discrete-time systems. Based on the sliding sector, continuous- and discrete-time variable structure (VS) controllers are proposed. Simulation results are given to show that the VS controllers proposed in the paper are quadratically stable and chatter free.

Swing up control of inverted pendulum

A bang-bang-type state feedback control algorithm which can swing up a pendulum from a pendant position to an upright position is proposed. In the control system a conventional LQ control method is also employed around the upright position to maintain the pendulum in the upright position after the pendulum has been swung up to this position by the bang-bang control. The control system was constructed and the validity of the control method was examined experimentally. Since the pendulum is attached by a hinge to a rotating arm fixed to a direct drive motorshaft, it contains fewer uncertainties introduced by transmission mechanisms, e.g., a belt and gears in a linear-type inverted pendulum. The advantages of the designed pendulum are that it is small and saves experimental space, and that the robustness of control algorithms can be easily tested with it since known parasitics can be added as uncertainties in the control loops, e.g., a flexible arm can be used instead of a rigid arm.<<ETX>>

Control of pendulum: from Super Mechano-System to Human Adaptive Mechatronics

The Super Mechano-System was the research project at the Tokyo Institute of Technology from 1997 to 2002 and the Human Adaptive Mechatronics (HAM) Project is the newly selected COE research project at Tokyo Denki University from 2003 to 2008. Both projects are sponsored by the Ministry of Education, Culture, Sports, Science and Technology in Japan. The author was the SMS project leader until 2000 and Prof. S. Hirose succeeded. Many mechanical systems with functions adapting to varying environment and the relating basic theory have been developed. The concurrent design method of the mechanism and controller has been developed by the control research group in the project. Human adaptive mechatronics is a system, which includes the human in the control loop and changes the functions and structure of the man-machine interface according to the improvement of the human operation skill. In this plenary lecture, the control of the multiple pendulums from the pendant to the upright position is discussed from the viewpoint of varying constraint systems. The swing-up control of pendulums is discussed by considering reachability of an unstable nonlinear system by nonlinear control. A new approach to analyse and to design a nonlinear control based on the fractal is presented. The results show that the map of the control parameters and the initial conditions give interesting results.

Discrete-time Variable Structure Control

This chapter presents some discrete-time variable structure (VS) control design algorithms with sliding sectors and then proposes a discrete-time VS controller with an invariant sliding sector. The invariant sliding sector is an invariant subset of the state space determined by a linear and a quadratic functions on the state variable. To ensure the invariance, a VS control law is implemented. Inside the sector with the VS control law, a Lyapunov function keeps decreasing. If the state is inside the subset in some time instance, then the VS control input will let the state remain inside. A discrete-time VS controller with the invariant sliding sector for discrete-time systems is designed such that the state is moved into the sector in finite steps and stays there from then on. The resultant VS control system is quadratically stable as there exists a Lyapunov function which decreases in the state space. Simulation results are given to show the efficiency of the proposed design algorithm of the discrete-time VS controller.

Self-tuning control based on generalized minimum variance criterion for auto-regressive models

Theoretical problems on self-tuning control include stability, performance and convergence of the recursive algorithm involved. In this paper, the problem of controlling minimum or non-minimum phase auto-regressive models with constant but unknown parameters is considered. The stability of an algorithm obtained by combining a recursive estimator for the controller parameters and a generalized minimum variance criterion is proved. The main result is the theorem which assures the overall stability for the closed-loop system in presence of white noise in the input-output relation, where the estimated parameters do not necessarily converge to the true values. The algorithm is proved by the Lyapunov theory.

VSS controller design for discrete-time systems

This paper presents an optimal and robust VSS controller for discrete-time systems. Firstly, a VSS control law is designed, which enables the system state to move into a sliding sector where the closed-loop system is stable. Then optimal control theory is used to design an optimal sliding sector. Finally, the bounded parameter uncertainty is taken into consideration, the robustness of the VSS control system is shown. The simulation of the pendulum control system shows that the VSS controller proposed in this paper is stable and robust to bounded parameter uncertainty.<<ETX>>

Internal model and saturating actuation in human operation from view of human-adaptive mechatronics

Human-adaptive mechatronics (HAM) is the area of mechatronics which adapts to the operator skill and assists its improvement. The analysis of human control action is one of the fundamental problems in the study of HAM. A special feature of human control action is the action being saturated with respect to the amplitude and velocity. At the same time, the human does not pay attention continuously to the response but intermittently scans and gets the information. In this paper, the continuous control action based on the scanned information is studied, and the desired trajectory of the human control action is considered to be generated by the closed-loop system including the internal model in the feedback path. Since the visual information is scanned intermittently, the closed-loop reference generator is considered as a sampled-hold system. The feedforward function of the cerebellum can be interpreted as the reference generator with a long scanning interval for the skilled operation. The saturating control action causing the pilot-induced oscillation is studied by taking the swing-up control of a single pendulum from the pendant to the upright position as an example. The two swing-up control laws are studied for reachability of the unstable nonlinear pendulum. One is the linear combination of sine function of the position and angular velocity, and the other is the variable-structure control for the sliding-mode function similar to the linear combination control law. The reachability is analyzed successfully by the color map.

Human adaptive mechatronics (HAM) for haptic system

Based on a new concept of a human-in-the-loop system called human adaptive mechatronics (HAM), a system structure and its design method are shown for a haptic system. HAM is a novel intelligent machine exerting high performance by enhancing human skill and by making machine functions adapt to skill level. In this report, we deal with a point-to-point task by human manipulation. An estimation method of a human controller is proposed under an assumption such that a human controller consists of a PD and a delay-time element. An assist control that adjusts support ratio from a machine side according to the human skill is proposed. From results of experiments to beginners, it was confirmed that parameters of the operators controller could be estimated sufficient and the human performance of manipulation was enhanced by the assistant method using estimated parameters.

Enhancement of stabilization for passive walking by chaos control approach

Abstract Passive walking is an attractive walking style which emerges autonomously on shallow slope without external input. It is known that the walking motion varies to chaotic in the vicinity of the limit of the stable walking. This phenomenon had been analyzed well, but had not been utilized directly for control. Usually only period-1 walking gait has been dealt with as an active usage of passive walking. In this paper, a strategy to enlarge the walkable range of passive walking by chaos control technique is presented. It is demonstrated by simulation that the walker can walk on more inclined slope and the levitation of legs is induced.