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The control method based on the time-state control form has been proposed to stabilize the chained system, which is a canonical-form nonlinear system. In this study, the control method is used for controlling a mobile robot in auto-parking situations. The proposed controller includes a parameter that is allowed to switch at arbitrary times without...
Citations
... Therefore, many controllers developed for chained systems include time-varying functions or non-smooth functions such as a sign function [15]. The control design method based on the time-state control form requires the discontinuous switches of controllers for stabilizing the chained systems [16,17]. However, if one state of the system is not required to become 0, the other states can be stabilized by the controller designed based on a strict linearization model. ...
... 3.3. According to the method written in Ref. [17], a strict linearization model is derived by paying attention to the motion in the x-y plane. Namely, from Eqs. (1)-(3), the second derivative of y with respect to x is obtained as ...
... where κ P and κ I are the proportional and integral gains [17]. ...
The knowledge of control engineering for mechanical engineers seems to become more important with the continuous development of automated technologies. To cultivate this knowledge, many experimental devices have been proposed and used. Devices with direct current (DC) motors are widely used because the DC motors can be controlled with sufficient accuracy based on the classical linear control theory. Mobile robots are used as educational platforms attracting the attention of students in various problem-based learning subjects. However, they have been hardly used to teach linear control theory because of the nonlinearity. This paper shows an experimental curriculum to learn control theory using a mobile robot instead of a motor. Although the model of the mobile robot is nonlinear, a strict linearization method makes it possible to adjust the control gains using the linear control theory. By applying the method, the characteristics of linear control systems are explicitly observed in the traveling paths of the mobile robot, so an experimental curriculum to learn the basic linear control theory can be realized using an inexpensive mobile robot. The proposed experimental curriculum was carried out in a class of a mechanical engineering course, and its results are discussed in this paper.
Many experimental devices employing DC motors have been used to study control engineering. The model of them can be approximated as a linear system and we can control the angle or the angular velocity of a DC motor sufficiently by using classical control theory, like PID control. However, just rotating a motor does not seem to attract the attention of students in mechanical engineering classes. Thus, an experimental curriculum employing a mobile robot is proposed to learn control theory. The kinematic model of the mobile robot includes non-linearity. In this paper, two representations are used to analyze and design a controller for the nonlinear mobile robot: a linear approximated model and a linear model obtained by a strict linearization method. The responses when a PID controller is applied are analyzed based on the linear approximated model, and the limits for controlling the mobile robot using a PID controller are shown. When the nonlinear controller designed based on a strict linearization method is used, the control gains can be adjusted based on linear control theory, that is, the pole assignment method. Students can recognize the relationship between the poles and responses of the controlled system as the traveling path of a mobile robot. The proposed experiments were actually performed in some classes and attracted the attention of the students.
