Control of the Side Brush Street Sweeper for Various Road Surfaces Using PID and Sliding Mode Controllers

This paper examines the side brush control technologies for a novelty semi-autonomous road sweeper design. This study proposes a side brush structure and offers a brush control solution to improve working efficiency and reduce abrasive brush. For the mechanical system using a parallelogram mechanism, the direction of movement when raising and lowering the brush is always parallel to the road surface. The modeling of the side brush mechanism shows that this is a nonlinear system. Therefore, the Sliding Mode Control(SMC) was proposed and established from the dynamics equation. The Lyapunov theorem demonstrates its stability. Besides, we also consider the proportional-integral-derivative (PID) controller to evaluate the responsiveness of the linear controller for a nonlinear system. Finally, the parameters of the controllers are optimized by a genetic algorithm to consider the response of the sliding mode control compared to the PID controller to control the road sweeper side brush with different references.


INTRODUCTION
Nowadays, street sweepers are widely used to clean highways and industrial areas, etc. Most road sweepers use a device called a broom to sweep waste and use a unit to clean the dust suction or a conveyor to pick up the garbage. Usually, two rotating brooms are mounted on either side of the road sweeper to get rid of the debris near the side of the road. A long roller brush is placed at the rear of the vehicle or chassis to remove debris from the center of the road. A side brush sweeper consists of various crucial parts, which include load cell sensors to measure the force of the brush on the street, mechanical systems, a hydraulic cylinder, direction valves, etc.
The main components of the road sweeper, such as the side brush, main broom, cylinders, etc., must be included. The devices will be connected to a control panel in the cabin, and the driver must regularly observe the scan results to adjust accordingly, requiring the driver to have experience but also potentially dangerous when unable to concentrate on driving [1].
Previous studies have shown that side brush sweep about 80% of road debris in the region of the curb. Under the street sweeper, a roller brush removes the remaining 20% of the debris. Therefore, The design and automatic control of the road sweeper side brush are very important. It helps the street sweeper operate efficiently and reduces the complexity of the work for the driver [2], [3].
In previous studies, the influence of road surface roughness on the brush system was not considered when designing the control system. Moreover, The mathematical model of these studies is a linear model with vertically mounted components that increase the height of the mechanism, which is difficult to install on an actual road sweeper. Some other studies use the linearization method of the side brush system, thus only considering the relatively small working area of the brush system.
We develop an automatic brush control system that is adapted to different road surface conditions through the control method of brush penetration or brush pressure. So as to control the sweeping force, the appropriate downward pressure can be used. As necessary for the sweeping conditions, the pressure should be changed. In order to achieve the above objectives, this study has proposed a mathematical model of the side brush based on the previous studies on the finite element model of the brush. Based on the mathematical model, the study uses the sliding mode controller and PID controller to examine the responsiveness of the controllers to different road profiles. Road profiles are generated using the C class of road profiles defined by ISO 8608 standard, sinusoidal road profile, harversian road profile, and sine half-wave road profile [4], [5].

RELATED WORKS
In [2], research by Peel (2002) developed a design for a vehicle that sweeps roads semi-autonomously. However, the waste identification and control system still needs to be created. Two brush types flicking brush and cutting brush have been given in his study. Besides, theoretical steady-state modeling can determine the axial load, torque, and tine deflection geometry of these two brushes. In 2005, Wang [6] developed a Finite Element (FE) to study how debris interacts with brush tines through theoretical and experimental methods. The side brush parameters mentioned in his research as brushing force, tilt angle, and rotational speed. A proportional-derivative (PD) controller was used to improve the sweeping efficiency. Wang et al. [7] studied a mathematical regression model to summarize the FE model's results. The method could be used to predict features of different brushes under various operational variables. Useche et al. [8] evaluated the effectiveness of two-type tine brush, cutting and flicking (F128), under different operating conditions. Moreover, proper brush penetration, sweeper speed, and brush angle values for debris types were studied. Determine coefficients of friction for cutting and F128 brushes studied by Useche et al. [9]. This study investigated the effects of the brush force in the cutting brush and the F128 brush. Useche et al. [10] presented an experimental method to determine suitable values of Rayleigh damping coefficients of tine brush and clusters brush. The effectiveness of the side brushes in removing different types of debris is studied by Useche et al. [11]. The experiment using a brushing test rig considered two different brush types, cutting and F128.Useche et al. [12]evaluated the dynamics of a novel free-rotating oscillating brush based on the authors' analytical model. Useche et al. [13] investigated the dynamics of the flicking brush of a mathematical model when the brush was rotated freely. The dynamics and modeling of brushes are considered in research by Useche et al. [14], including the removal of fouling, post-CMP (Chemical Mechanical Polishing), street sweeping, etc. The FE model defines values of the normal contact stiffness, K n , and Integration Time Step (ITS) [15]. In research [16], the dynamic FE model was developed to investigate how a cup-shaped brush's dynamics and performance are affected by brush oscillations. In research [17], The performance of two types of side brushes: a cutting brush and an F128 brush, was studied. Besides, their work developed the nonlinear FE brush model. In another study [18], a dynamic model of cutting brush was considered with the tine brush modeling as cantilever beams. The research by experimental tests [19] investigated the ability of the brush to remove the different debris kinds and various sweeping parameters. Wahab et al. [20] presented modeling a bristle of a brush for street sweeping by two FE models. In the first one, the bristle ends following a specific circular path under a specific time function. In the others, inertia loads are applied when the same bristle end is completely restricted. Peel et al. [21] developed a technical identification of different street surfaces and debris by vision processing. Yang et al. [22] conducted experimental research on the cleaning performance of the street sweeper. Moreover, the mathematical models were established with three main parameters driving speed, disc brush speed, and roller brush speed.

The side brush road sweeper operation description
For most street sweepers, two rotary side brushes are mounted on both sides of a sweeper to remove the debris near the curb, as shown in Figure 1. At the same time, a roller brush is mounted beneath the chassis to clear the street center of debris. This paper presented a design for the control system of the side brush mechanism. A hydraulic motor powers the rotating brush. In this research, the brushing force or brush penetration of the automatic side brush is controlled by a hydraulic cylinder and load cell. The basic components of a side brush are given in Figure 2. The arm joints are parallelograms that help keep the brush direction parallel to the road surface. The measurement of the brush penetration is shown in Figure 3. The vertical height difference between a theoretically undeformed brush's lowest point and the road surface upon which the brush is deformed can be describe 0   d as the result when the brush is stationary and only touching the road surface.

Figure 3. Definition of brush penetration [2]
It z c is defined as the vertical distance between the road surface and the brush origin, then Figure 3 may be used to construct an expression that connects the plane of the road to the point origin of the brush [2]: .sin .cos( ) where L is the length of the tine, R rj is the largest mount radius, β is the assault angle for the brush,  is the tine mount's angle, Δ and is the brush penetration.

The kinematics of side brush
The side brush is considered to be a simple massdamping spring [6]. Since only the brush mechanism is evaluated at the operating position in Figure 2, it is not necessary to consider the side brush's mounting column and rotating cylinder. Therefore, the stitching and joint diagram of the side brush mechanism can be presented in Figure 4. The kinematics schematic in Figure 4 shows that: where θ 1 is the angle of link 1 (OB) from the Ox axis θ 2 is the angle of link 2 (BC) from link 1. Link 1 (A 1 ) is the coordinates of the centers of mass (x 1 ,z 1 ) can be given as follows: where β 0 is the initial angle of the angle MON.
The distance (MN) can be written by the formula:

The dynamic of the side brush
The system's kinetic and potential energies of link 1 can be written by the following equations: From equations (7), (8), the speed of the point A 2 can be determined as a function of the generalized coordinates θ 1 , θ 2 : From equations (6), (7), the system's kinetic and potential energies of link 2 can be written: It is easy to see that VA 2 = VA 3 , θ 3 = 0, from equations (8), (9), (12), the kinetic energy, the potential energy, and energy dissipation due to viscous friction of link 3 can be written: where K s , D b are the stiffness and damping coefficient, and y is the position disturbances of road profiles. They are representative of the brush's dynamic characteristics.
In research [6], the FE modeling results indicate that K s may vary from 1 kN/m to 50 kN/m when the side brush operates under different conditions. Let's formulate the mechanism dynamics equation based on the second type of General Lagrange equation [24,25]: where K and P are the system's kinetic and potential energies, respectively; q is the generalized coordinate, Ris energy dissipation because of viscous friction Q i is the corresponding loading in each coordinate. The kinetic energy function: The first derivative of the kinetic energy function with respect to the variable 1   : The second derivative of the kinetic energy function with respect to the variable 1   : The first derivative of the kinetic energy function with respect to the variable θ 1 : The first derivative of the potential energy function with respect to the variable θ 1 : The total dynamics load can be written by the following equations: From equations (10), (11), the moment generated by the hydraulic cylinder can be written by the following equations: where F is the force generated by the hydraulic cylinder.

ROAD PROFILE
In order to simulate the side brush system that has been described, a sufficient model of the variation in the road surface, y(t), is required. The sinusoidal road profile can be given using the following fundamental formulation [5,26]: where v is the vehicle's speed, H is the bump height, L is the bump length T = L/v and is the time to cross the bump. Moreover, the bump can be modeled using the halfsine function [5] [26]. The half-sine bump shape can be given by (29).
The half-sine model is somewhat harsh because, at time t = 0, its slope rapidly shifts from 0 to 2πH/T and thus, it needs a suitable model for a speed bump. Therefore the harversian function is a less severe bump model [5,26]: When performing more complex simulations, random variations that are based on statistical analyses of common road construction methods are sometimes used.
According to ISO 8608, the power spectral density (PSD) of profile elevations is given by the equation: where 2 / L    in rad/m denotes the spatial angular velocity, Φ 0 = Φ(Ω 0 ) in rad/m is the PSD values at the reference spatial angular velocity Ω 0 =1 rad/m, w is the amplitude reduction and w=2.
Besides, the road surface roughness (C class) in the time domain is as follows [4]: where the amplitude B n is defined as below:

Control System Analysis
A sliding mode controller that achieves robust control for uncertain systems combines the backstepping approach and sliding mode control. Let us assume the plant is a nonlinear system, as shown below [27]: where f(x,t), b(x,t) and d(x,t) are the nonlinear functions.
Besides setting x x   The following equation gives the output signal:

PID control law design
The traditional PID controller's simplicity provides benefits for use in both linear and nonlinear systems. [28,29] The PID controller's mathematical formulation is as follows: Tracking error: where u(t) is the input signal and the error signal e(t).
The PID controller's goal is still to reduce error by gradually fine-tuning the control variable u(t). The resulting error value, however, is calculated continuously, and the PID controller makes adjustments based on the proportional gain (k p ), integral gain (k i ), and derivative gain (k d ).
However, because k p , k i , and k d are frequently fixed, the PID controller struggles to deal with system uncertainties, including parameter fluctuations and outside disturbances. Therefore, a more reliable controller design has been necessary in recent years in order to enhance system performance by removing parametric uncertainties and outside disturbances.

Sliding mode control law design
The dynamics of a nonlinear system are changed via sliding mode control. This nonlinear control technique uses numerous control structures to ensure that trajectories always move in the direction of a switching condition [27,30].
Select Lyapunov function: The derivative Lyapunov function: Select the sliding mode function: For σ → 0, it is necessary to select the control signal u(t) so that V 0   : The control signal u(t) using saturation function: From the above control law, there is the equation: where K represents a constant rate. Saturation function: where γ is the boundary layer. The control signal u(t) using relay function: Relay function: where δ is a very small positive constant.

Controller parameters optimization by GA
The original goal of the GA, which was to create autonomous learning and decision-making systems, was to simulate the biological processes of natural selection and population genetics. GA is often used to create high-quality solutions to global optimization and find issues by utilizing operators inspired by biology, such as mutation, crossover, and selection [31]. The four fitness functions commonly used to evalu-ate trajectory trackings such as Integral Absolute Error (IAE), Integral Square Error (ISE), Integral Time Abso-lute Error (ITAE), and Integral Time Square Error (ITSE). These are defined by the following equation [32,33] ISE integrates the square of the error over time; control systems designed to minimize ISE have a tendency to eradicate major errors swiftly but will tolerate minor bugs that last for a long time.
IAE integrates the absolute error over time, though typically with less persistent oscillation, it tends to yield slower responses than ISE optimum systems.
ITAE integrates the absolute error multiplied by the time over time. It considers weight errors that exist at the beginning of the response far more significantly over time [34] [35].
Thoroughly reflect the operating state of the system and consider accumulated errors. Therefore, this paper selected the ITSE as the consideration function [36]. ITSE integrates time the square error over time, allowing for a faster control speed than ITAE. It is the only objective function for optimization by GA. One of the research about PID parameters optimi-zation using GA was studied by Aly [37]. Besides, sliding mode control based on GA was also studied by Kheshti et al. [38] and Ma et al [39]. Table 1 shows the evaluated values of GA parameters so that the GA tunes the PID and SMC gains.

RESULTS AND DISCUSSIONS
The side brush model of the street sweeper is designed by Solid Works software ( Figure 5). The parts of the model are the mounting column, rotating cylinder of the side brush, arm joint, hydraulic motor, and rotating brush. The rotating cylinder of the side brush is controlled ON/OFF. When the road sweep system operates, it takes the side brush in the working position and brings the side brush inward in the vehicle moving on the road. Research results focus only on controlling brush penetration through PID and sliding mode control. GA optimizes the parameters of the controller.
The side brush's kinematic measurements are as below:  The parameters for PID [k p , k i , k d ] in Table 1 and the parameters for SMC [K, c 1 ] in Table 2 were tuned by the ITSE fitness function. Moreover, the various road profiles were considered to evaluate the responsiveness of the controller. The GA-SMC uses functions such as a sign, sat, and relay to consider the nonlinear controller. The parameters were tuned and presented in Table 2. The penetration of the side brush (see Figure 6) is forced to track the nominal road profiles. The genetic artificial-based proportional-integral-derivative (GAPID) and the genetic artificial-based sliding mode control (GASMC) are designed to consider the responsiveness of linear (PID) and nonlinear (SMC) controllers. Besides, the GASMC uses sign function (GASMC-sign) in prac-tical engineering systems; the chattering of SMC can cause damage to system parts such as the actuator. One way to reduce the chattering is to use the saturation function (GASMC-sat) and relay function (GASMCrelay) instead of the sign function.
It can be seen that the real and reference trajectory curves both almost match after about 0,1s in road profiles: sinusoidal, half-sine, and harversian. The random profile also tracks quite well on trajectory curves. Figure 6 and Figure 7 shows the response and tracking error levels of control laws and road profiles. The GAPID has a short settling time, but it fluctuates widely in the initial period. The GASMC-sat and GASMCrelay show a good response and reduced chattering. The error of position tracking and phase trajectory for the side brush is presented in Figure 7 and Figure 8. The tracking error of the side brush position after settling time ( t s =0,4s) is less than 0.025 m. Finally, Figure 8 shows the phase trajectory of the side position of control rules for different road profiles.

CONCLUSION
This paper suggests a technique to automatically control the road sweeper's side brush to improve working efficiency and reduce brush wear. The paper uses different control laws and various road profiles to consider the level of response. GA optimizes the parameters of the controller.
Simulations have been performed for four different types of road surfaces, and the results show that the side brush system controllers are designed to track different types of road surfaces. The simulation results show that the GAPID controller fluctuates with large amplitude ( tracking error 0,075-0,187m) in a very short period of time (0.005-0.008s) at the initial time, which can cause damage to the mechanical systems of the side brushes.
The GASMC-sat and the GASMC-relay have a pretty good response in road profiles and reach a steady state after about 0.3s. With the road profiles such as sinusoidal, half-sine, and harversian, the controllers respond quite well. However, the random road profile is only the GASMC-sat and the GASMC-relay having a relatively good response. Besides, this study is given a novel method to control the side brush of the road sweeper. This method can be easily applied on road sweepers due to the automatic control of the brush by the hydraulic cylinder.

Δ
The brush penetration L The length of the tine R rj The largest mount radius Β The assault angle for the brush The tine mount's angle θ 1 The angle of link 1 from the Ox θ 2 The angle of link 2 from link 1 λ 1,2 The coordinates of mass centers y The position disturbances J A The moments of inertia of links relative to their centers of mass. β 0 The initial angle of the angle 

MON V A
The speed of the center of mass Ks The stiffness of the side brush D b Damping coefficient K The system's kinetic energy P The system's potential energy q The generalized coordinate R The energy dissipation

Q i
The corresponding loading in each coordinate τ The total dynamics load F The force generated by the hydraulic cylinder H The bump height L the bump length T The time to cross the bump Ω The spatial angular velocity Φ The power spectral density w The amplitude reduction

B n
The amplitude of the road surface roughness (C class) ψ n The phase angles V The vehicle velocity γ The boundary layer δ The very small positive constant