**1. Introduction**

The human being shows the difficulty in making decisions when there is imprecise information. Fuzzy logic, developed by Lofti Asker Zadeh in 1965, allows emulating of human reasoning and making correct decisions despite the information [1, 2]. It is considered a flexible tool that is based on linguistic rules dictated by experts, composed of a set of mathematical principles based on degrees of membership, whose function is to model information [3]. This modeling is done based on linguistic rules that approximate a function through the relationship between the inputs and outputs of the system. This logic presents membership ranges within an interval between zero and one, unlike conventional logic, in which the content is limited to two values: zero and one [4].

Control systems, on the other hand, are an arrangement of physical components linked or related in such a way that they command, direct or regulate the same system or another [5]; control systems are classified as open-loop control systems and [6] closed-loop control systems. Systems in which the output has no effect on the control action are called open-loop control systems. Systems that maintain a given relationship between the output and the reference input, comparing them and using the difference as a means of control, are called closed-loop control systems or feedback control systems [7, 8].

Fuzzy control is created from the combination of fuzzy logic and control systems techniques, which can be considered an expert closed-loop system in real time, implemented from the experience of an operator or process engineer unfamiliar with the process. It lends itself to being easily expressed in situation-action rules instead of differential equations [9].

Controllers based on fuzzy logic or fuzzy systems are represented by propositional rules *if-then* that can provide an understandable and easy-to-use knowledge representation [10]. This can be seen as a high-level programming language, where the program consists of conditional rules and the compiler or interpreter results in a nonlinear control algorithm, so programming through qualitative statements, represented by of *ifthen* statements, to obtain a program that works in quantitative domains, provided by signals from sensors and actuators is the basis of fuzzy control [11]. Intuitively, this implies a loss of information, because there is no single translation from a qualitative entity to a quantitative representation, except in some special cases.

Traction control systems (TCSs) have come to revolutionize the behavior of automobiles as we know them today; however, thanks to the performance shown in human-crewed vehicles, it is possible to open a branch of the study of the traction controllers for mobile robots. The implementation of traction controllers in mobile robots seeks to improve the performance of the robots either due to energy consumption or the accuracy of arrival at the desired point [12]. The energy consumption in mobile robots depends significantly on the adhesion between the tires and the ground; therefore, the greater the bonding, the better stability in autonomous driving produced. This can be translated into more excellent stability in the system. Traction, on the other hand, is considered a vehicular propulsive force produced by the friction present between the tire and the surface. The inherent friction characteristics are nonlinear and uncertain, making TCSs have a high degree of [13] design.

In robotics, these types of systems are not relatively new but have not been fully addressed due to the scarcity of processing tools; current advances in embedded systems have allowed techniques from different areas to be implemented in [14] robotics. TCSs applied to mobile robots are based on modern controllers and nonlinear sliding mode controllers based on state observers [13–15].

Being wholly linked to friction, traction exhibits nonlinear behavior over time, so modern controllers must append a matrix representing the approximate nonlinear coefficients of friction to act on the control signal. In combination with traction controllers, mobile robots allow the robot to move freely on spaces with smooth, wet, and slippery surfaces. Traction control lets the robot wheels turn at similar speeds on surfaces with near-zero coefficients of friction, and when an imbalance exists, the traction controller must be activated to prevent unnecessary plant slippage, which translates to not reaching the working path [16].

Some authors have worked on different strategies related to slip control and traction control for mobile robots. For instance, [17] introduces an adaptive control strategy for a tracked mobile robot that compensates for the longitudinal slip to reach

### *PID-like Fuzzy Controller Design for Anti-Slip System in Quarter-Car Robot DOI: http://dx.doi.org/10.5772/intechopen.110497*

a trajectory. Another controller based on the dynamic and kinematic model with slip is presented in [18]. [19] proposes an algorithm for optimal slip control of wheeled robots with the trade-off between traction and energy consumption based on observing a change in a robot's velocity on different soil surfaces. An optimal slip ratio control using a current sensing method is presented in [20]. The controller consisted of a fuzzy PID structure. In [21] shows a slip control for a nonholonomic wheeled robot where the kinematic model of a differential-driven wheeled mobile robot is used to solve the trajectory tracking problem using fuzzy and optimal fuzzy logic. The trajectory tracking problem of a wheeled mobile robot which is actuated by two independent electrical motors is attacked in [22]. A simple non-mode-based fuzzy logic controller is used to reduce the tracking error provoked by the slippage.

As the reader can see, there are many works with different perspectives to attack the slip control in other structures. Hence, this work proposes a new methodology to control the slippery of a Quarter-Car robot using an internal loop based on fuzzy logic inference to compute the gains of a Proportional-Integral (PI) structure. The slip is calculated, such as the difference between the linear velocity given by an S-curve velocity profile and the longitudinal speed calculated according to the rotational speed of the Quarter-Car tire. This difference is the input of the external control loop. Whether the slip is significant, the slave controller must do that both velocities go at the same speed controlling the current of the DC motor. The external loop controls the angular velocity so that the linear velocity has the same magnitude. The outer loop uses an adaptive PID-like fuzzy controller structure.

The chapter is divided into the following sections. Section 2 describes the dynamic model of the test bench. Section 3 presents the methodology for self-tuning PID-like fuzzy controller. In Section 4, the simulations and results of the experimentation are presented, and, finally, in Section 5, the conclusions are given.
