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Control Design Technique
Abstract
In this chapter, the main features of the newly proposed control design methodology are presented. First, the class of systems to be considered is defined, and the key points in the design approach are drafted. Then, an introductory example allows the understanding of the main properties and to state the procedure to design the control. The Linear Algebra-Based Control Design (LAB CD) methodology is then outlined and the properties of the controlled plant are analyzed. Its applicability in DT is shown to be immediate, and the treatment of uncertainties and disturbances is introduced. Finally, a summary of the LAB CD approach, as a guideline for its application to a variety of processes in the following chapters, is given.
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This paper presents the design of four controllers for a mobile robot such that the system may follow a preestablished trajectory. To reach this aim, the kinematic model of a mobile robot is approximated using numerical methods. Then, from such approximation, the control actions to get a minimal tracking error are calculated. Both simulation and experimental results on a PIONEER 2DX mobile robot are presented, showing a good performance of the four proposed mobile robot controllers. Also, an application of the proposed controllers to a leader robot following problem is shown; in it, the relative position between robots is obtained through a laser.
A predictive functional control (PFC) technique is applied to the temperature control of a pilot-plant batch reactor equipped with a mono-fluid heating/cooling system. A cascade control structure has been implemented according to the process sub-units reactor and heating/cooling system. Hereby differences in the sub-units dynamics are taken into consideration. PFC technique is described and its main differences with a standard model predictive control (MPC) technique are discussed. To evaluate its robustness, PFC has been applied to the temperature control of an exothermic chemical reaction. Experimental results show that PFC enables a precise tracking of the set-point temperature and that the PFC performances are mainly determined by its internal dynamic process model. Finally, results show the performance of the cascade control structure to handle different dynamics of the heating/cooling system.
A stable tracking control rule is proposed for nonholonomic
vehicles. The stability of the rule is proved through the use of a
Liapunov function. Inputs to the vehicle are a reference posture ( x
<sub>r</sub>, y <sub>r</sub>, θ<sub>r</sub>)<sup>t
</sup> and reference velocities (ν<sub>r</sub>, ω<sub>r</sub>)
<sup>t</sup>. The major objective of this study is to propose a control
rule to find reasonable target linear and rotational velocities (ν,
ω)<sup>t</sup>. Linearizing the system's differential equation is
useful for deciding parameters for critical dumping for a small
disturbance. In order to avoid slippage, a velocity/acceleration
limitation scheme is introduced. Several simulation results are
presented with or without the velocity/acceleration limiter. The control
rule and limiting method proposed are robot independent and hence can be
applied to various kinds of mobile robots with a dead reckoning ability.
This method was implemented on the autonomous mobile robot Yamabico-11.
Experimental results obtained are close to the results with the
velocity/acceleration limiter
This brief proposes a sliding-mode control method for wheeled-mobile robots in polar coordinates. A new sliding-mode control method is proposed for mobile robots with kinematics in two-dimensional polar coordinates. In the proposed method, two controllers are designed to asymptotically stabilize the tracking errors in position and heading direction, respectively. By combining these controllers together, both asymptotic posture (position and heading direction) stabilization and trajectory tracking are achieved for reference trajectories at global regions except the arbitrary small region around the origin. In particular, constraints on the desired linear and angular velocities as well as the posture of the mobile robot are eliminated unlike the previous studies based on kinematics expressed in polar coordinates. Accordingly, arbitrary trajectories including a circle and a straight line in various forms can be followed even with large initial tracking errors and bounded disturbances. The stability and performance analyzes are performed and also simulations are included to confirm the effectiveness of the proposed scheme.
A mobile robot is one of the well-known nonholonomic systems. The
integration of a kinematic controller and a torque controller for the
dynamic model of a nonholonomic mobile robot has been presented (Fierro
and Lewis, 1995). In this paper, an adaptive extension of the controller
is proposed. If an adaptive tracking controller for the kinematic model
with unknown parameters exists, an adaptive tracking controller for the
dynamic model with unknown parameters can be designed by using an
adaptive backstepping approach. A design example for a mobile robot with
two actuated wheels is provided. In this design, a new kinematic
adaptive controller is proposed, then a torque adaptive controller is
derived by using the kinematic controller