Resume switch â used to retrieve the last speed of the vehicle or increase the .... resulted in ACC takes the traffic in front of the car into account; support the.
ADAPTIVE CRUISE CONTROL SYSTEM BY MAHLALELA JANUARY MALIBONGWE Durban University of Technology Department of Electronic Engineering February 2017
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ABSTRACT The cruise control system in a vehicle is studied in details. First, control concepts in cruise control system are investigated. Second, simplified cruise control models are developed and simulated. Third, an introduction to adaptive cruise control system is presented. Fourth, modeling of adaptive cruise control system in a traffic simulation is carried. Finally, the future development of the advanced adaptive cruise control system is presented.
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TABLE OF CONTENTS ABSTRACT ....................................................................................................................................................... ii LIST OF FIGURES ............................................................................................................................................. v 1. INTRODUCTION ................................................................................................................................. 1 PART 1 2. CONCEPTUAL DESIGN OF SYSTEM .................................................................................................... 2 2.1 Main Components ....................................................................................................................... 2 2.2 Control Philosophy ...................................................................................................................... 3 2.2.1 Cruise Control Operation ......................................................................................................... 3 2.2.2 Adaptive Cruise Control Operation .......................................................................................... 6 2.2.3 Safety Considerations ............................................................................................................... 7 PART 2 3. DYNAMIC MODELING ........................................................................................................................ 9 3.1 Cruise Control .............................................................................................................................. 9 3.2 Adaptive Cruise Control ............................................................................................................ 11 PART 3 4. CONTROLLER DESIGN ...................................................................................................................... 14 4.1 PID Design ................................................................................................................................. 14 4.2 Integrator Windup ..................................................................................................................... 15 5. RECOMMENDATIONS AND FUTURE RESEACH ................................................................................ 18 6. CONCLUSION ................................................................................................................................... 18 7. REFERENCES .................................................................................................................................... 19
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LIST OF FIGURES AND TABLES 1. Figure 1: Block Diagram of a Typical Fuel Injection System .............................................................. 2 2. Figure 2: Overview of a Typical Cruise Control.................................................................................. 5 3. Figure 3: A Typical Adaptive Cruise Control System ......................................................................... 7 4. Figure 4: Block Diagram of a Cruise Control for an Automobile ....................................................... 9 5. Figure 5: Braking distance of a car travelling at 100 km/h ............................................................. 13 6. Figure 6: Closed Loop of the Cruise Control .................................................................................... 14 7. Figure 7: Response of the System Due to a Step Input ................................................................... 15 8. Figure 8: Controller with Anti – Windup ......................................................................................... 16 9. Figure 9: (a) Shows the Multisim Simulation of the Cruise Control with an Anti – Windup PID Controller (b) Shows the Response of the Cruise Control to a Step Input. .................................... 17 10. Table 1: Measured Stopping Distance of Four Different Types of Cars .......................................... 12
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1. INTRODUCTION In modern automobile systems the use of cruise control has grown rapidly. This system has major advantages in speed control, safety and driver’s comfort. The system presented will operate in two modes. The modes are cruise control and adaptive cruise control (ACC) mode. The cruise control system attempts to keep the speed of the car constant in spite of disturbances caused by changes in the slope of a road and variations in the wind and road surface. The controller compensates for these unknowns by measuring the speed of the car and adjusting the throttle appropriately [1]. This paper consists of three parts, In PART 1; the conceptual design of the cruise control will be presented. The operation of the system in cruise control and adaptive cruise control mode will be explained. The fail - safe operation of the system will be presented. In PART 2; the dynamic model of the car will be presented. Calculation of safe – following distance by the ACC will be presented. In PART 3; the design of a suitable PID controller for the system will be explained. Issues and solutions associated with the use of PID controller in this application will be presented.
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PART 1 2. CONCEPTUAL DESIGN OF SYSTEM This part of the paper presents the conceptual design of the aforementioned system. As mentioned earlier the system maintains the set speed by adjusting the throttle appropriately. The throttle controls the amount of air to the engine, thus regulating the speed of the engine. Figure 1 below shows a block diagram of a typical fuel injection system to show the position of the throttle.
Figure 1: Block Diagram of a Typical Fuel Injection System
2.1 Main Components The main components of a typical cruise control system are as follows [2]. 1. Actuator – regulates the position of the throttle i.e. motor, vacuum-operated diaphragm; 2. Main switch – used to switch the cruise control on/off; 3. Set switch – used to select desired speed and decrease speed to a desired value; 4. Resume switch – used to retrieve the last speed of the vehicle or increase the speed; 5. Brake switch – it deactivates cruise control when brakes are applied; 6. Clutch and Automatic gearbox switch - It deactivates the cruise system to prevent the engine speed increasing if the clutch is pressed. The automatic gearbox switch will only allow the cruise to be engaged when it is in the ‘drive’ position; 7. Speed sensor – it measures the speed of the vehicle.
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2.2
Control Philosophy
2.2.1
Cruise Control Operation Figure 2 shows an overview of a typical cruise control system configured to achieve the operation discussed below. 1.
Main switch - When the switch is pushed once the cruise control system turns on and becomes ready to set the cruise control. When the switch is pushed again the cruise control turns off; 2. Set switch - When the Set switch/Coast is pressed while the vehicle is running at a speed greater than 40 km and the Main switch is on, the cruise control is set at the current vehicle speed (this speed becomes the “memorized speed”) and the vehicle maintains this speed thereafter; 3. Resume switch - When the Resume/Accelerate switch is turned on after the cruise control is temporarily cancelled, the vehicle speed returns to the memorized speed, which was stored just before the cruise control was cancelled. This occurs only when the vehicle is running at a speed greater than 32 km/h. In the following cases, however, the memorized speed is cleared. 3.1 Ignition switch is turned off; 3.2 Main switch is turned off; 3.3 Abnormality in the system is detected. 4. Deceleration control/Coast - When the Set/Coast switch is pressed for a prolonged time while the vehicle is governed by the cruise control, the memorized vehicle speed of the cruise control is changed to the vehicle speed value reached at the moment the switch is released after slowing down. However, the cruise control is cancelled when the vehicle speed becomes lower than the lower limit of the speed setting range; 5. Acceleration control/Resume- When the Resume/Acceleration switch is pressed for a prolonged time while the vehicle is governed by the cruise control, the memorized speed of the cruise control is changed to the vehicle speed value reached at the moment the switch is released after accelerating. However, when the vehicle speed is higher than the upper limit of the speed setting range, the upper limit becomes the memorized speed of the cruise control; 6. Cruise control cancel - When any of the following conditions is met, the cruise control is cancelled. 6.1 Stop light switch on - brake pedal depressed; 6.2 Brake switch off - brake pedal depressed; 6.3 Neutral switch on - shift lever moved to neutral; 6.4 Cancel switch is on; 6.5 Ignition switch is off; 6.6 Main switch off; 6.7 Transmission gear in 1st or reverse; 1.8 Actual vehicle speed drops below 32 km/h; 6.9 Abnormality in the system is detected.
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7.
Vehicle speed signals are sent from the ABS control module or vehicle dynamic control (VDC) control module to the engine control module (ECM), which uses the signals in controlling the cruise control function. 8. Engine Control Module - Based on signals from the related switches and sensors, the engine control module (ECM) controls all the following control functions: 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8
Constant speed control; Speed setting control; Deceleration control; Acceleration control; Resume control; Manual cancel control; Low speed limit control; Electronic control throttle.
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Figure 2: Overview of a Typical Cruise Control
(1) Battery (2) Ignition switch (3) Cruise indicator light (4) Cruise set indicator light (5) Main relay 5
Cancel switch signal Set/Coast switch signal (6) Starter (7) Stop light and brake switch (8) Brake pedal (9) Combination meter microprocessor (10) Body integrated unit (11) Low speed CAN communication (12) High speed CAN communication (13) Electronic control throttle (14) Vehicle speed signal (15) ABS control module/vehicle dynamic control (VDC) control module (16) Engine control module (ECM) (17) Main switch signal (18) Resume/Acceleration switch signal (19) Cruise control command switch (20) Ground (21) AT control module (22) Neutral signal (23) Inhibitor switch (24) Neutral position switch (25) Clutch switch (26) Clutch pedal 2.2.2
Adaptive Cruise Control Operation The operation of the adaptive cruise control is the same the one discussed above, with an exception that it maintains a safe following distance between the host car and the car ahead. (ACC) can automatically adjust the vehicle speed to the current traffic situation. The system has three main aims [2]. 1. Maintain a speed as set by the driver; 2. Adapt this speed and maintain a safe distance from the vehicles in front; 3. Provide a warning if there is a risk of collision. This paper does not emphasize ACC as a safety feature; the emphasis is rather on the driver’s comfort. Figure 3 shows a typical adaptive cruise control system. The system uses a radar/lidar headway sensor to measure the distance between the car and an obstacle. The measurement is then used to adjust the speed of the car to maintain a safe following distance or give a warning to the driver if a risk of collision is detected. A beam divergence of about 2.5 ° vertically and horizontally has been found to be the most suitable whatever headway sensor is used [2]. When an obstacle is detected the system will automatically switch the cruise control into adaptive mode, decrease the speed of the car until 6
a safe distance is achieved. If the optimum stopping distance cannot be achieved by just backing off the throttle, a warning is supplied to the driver.
Figure 3: A Typical Adaptive Cruise Control System
2.2.3
Safety Considerations In every complex system there is a possibility that something might go wrong. In such a system a fail-safe function for the system is essential. Discussed below are the cases considered for safe operation. 1. Conflict between signals - The cruise control system is deactivated if any of the cruise control switches (Set/Coast, Resume/ Acceleration, and Cancel switches) is turned on while any of the cancellation signal generating switches (brake, stop light, clutch, neutral position and inhibitor switches) is activated. When the ignition switch is turned on while any of the command switches is in the on position, the cruise control system is deactivated. The system deactivating function is retained until the ignition switch is turned off. 2. Abnormalities in electric circuits - The cruise control system is deactivated and the set speed is also canceled if any of the following abnormalities occurs in the system electric circuits. The system deactivation function is retained until the ignition switch is turned off. 2.1 Abnormality of the command switch is detected; 2.2 Abnormality of the stop light switch and brake switch is detected; 2.3 Abnormality of the inhibitor switch is detected; 2.4 Abnormality of the neutral position switch is detected; 2.5 Abnormality of the ignition switch is detected; 2.6 Change in vehicle speed signal is detected; 2.7 Abnormality in any of the engine related sensors is detected; 2.8 Abnormality of the brake switch input circuit in the engine control module (ECM) is detected; 7
2.9 The Main switch and command switch were already on when the ignition switch is turned on. 3. Cruise Control Cancel Function - When any of the following conditions is met, the cruise control is cancelled. 3.1 Abnormal engine speed acceleration is detected; 3.2 The vehicle speed has dropped below the lower control limit during cruise control driving; 3.3 The vehicle has been running at speed higher than the set speed for an abnormally long time during cruise controlled driving; 3.4 The set speed became impossible to be maintained for some reason (steep upgrade, hand brake operation, abnormal engine power drop, etc.); 3.4 Flat tire. 4. Traffic Condition – When there is traffic ahead the cruise control system must adapt to the traffic and maintain a safe following distance, if possible. The system must warn the driver if there is a risk of collision.
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PART 2 3. DYNAMIC MODELING
This part of the paper presents the model of the vehicle and the calculation of safe – following distance between two vehicles.
3.1 Cruise Control To model the complete system let us consider Figure 4 as the block representation of the cruise control system without the adaptive operation. Let be the speed of the car and the desired (reference) speed. The controller receives the signals and and generates a control signal u that is sent to an actuator that controls throttle position. The throttle in turn controls the torque delivered by the engine, which is then transmitted through gears and the wheels, generating a force that moves the car. There are disturbance forces due to variations in the slope of the road, the effects of rolling resistance and aerodynamic forces [1].
Figure 4: Block Diagram of a Cruise Control for an Automobile Let be the speed measured in m/s, m the total mass of the car in kg (including passengers), the force generated by the contact of the wheels with the road, and the disturbance force due to gravity and friction. The equation of motion of the car is –
(1)
The force is generated by the engine, whose torque is proportional to the rate of fuel injection, which is itself proportional to the control signal 0 ≤ u ≤ 1 that controls throttle position. The torque also depends on engine speed ω. A simple representation of the torque at full throttle is given by
( )
(
( 9
) ),
(2)
Let n be the gear ratio and r the wheel radius. The engine speed is related to the velocity through the expression
And the driving force can be written as ( )
(
)
The disturbance force Fd has three major components: Fg, the forces due to gravity; Fr, the forces due to rolling friction; and Fa, the aerodynamic drag, Letting the slope of the road be , gravity gives the retarding force Fg = mg sin , where g = 9.8 m/sec2 is the gravitational constant. A simple model of rolling friction is ,
(3)
Where Cr is the coefficient of rolling friction, Finally, the aerodynamic drag is proportional to the square of the speed: ,
2
(4)
Where ρ is the density of air, Cd is the shape-dependent aerodynamic drag coefficient and A is the frontal area of the car. The complete model is given by (
1
)
(5)
Eq. (1) can also be written in the form ̇
(6)
When the grade of the road is zero the transfer function of the car from Eq. (6) can be written as
( )
The transfer function of the vehicle body is a first order, but since the torque delivered by the engine could produce a non-linear curve and the aerodynamic drag is proportional to the square of the velocity of the car, makes the transfer function non-linear. Estimated parameters are as follows. 2 Then ( ) 10
kg Ns/m
3.2 Adaptive Cruise Control Cruise Control (CC) is a common and well known automotive Driver Assistance System (DAS). The driver sets a reference velocity and the throttle is controlled so that this reference velocity is maintained under influence of external loads such as wind, road slope or changing vehicle parameters. Further development resulted in ACC takes the traffic in front of the car into account; support the driver in its driving process and the goal is to increase driving comfort and traffic safety. Such systems are generally known as Advanced Driver Assistance Systems (ADAS). An ADAS is defined as a vehicle control system that uses environment sensors to improve driving comfort and/or traffic safety by assisting the driver in recognizing and reacting to potentially dangerous traffic situations. Some examples of these ADAS include Navigation systems, Adaptive Cruise Control, Lane departure warning, Collision detection, Intelligent Speed Adaptation, Car-to-car/car-to-infrastructure communication and Adaptive lighting [3]. ACC is designed to maintain a safe distance between the car (host) that has the ACC and the car (target) or obstacle in front of it. A radar/lidar sensor is used to measure the distance between the two cars. The measurement is then used by a controller to calculate the error signal and produce the appropriate output in order to maintain the set point. In this paper the reference distance is calculated by applying the 2 seconds rule (for light vehicles) presented by K53. 2 seconds is considered as a safe distance for that could allow a car to stop without hitting the predecessor. The calculation for stopping distance and the required acceleration to achieve it can be determined using from equation of motions: 2
(18)
From Eq.18 If the car is initially travelling at u m/s, then the stopping distance x m travelled by the car is given by
2
(19)
Table 1 below shows the results obtained after measuring the stopping distance of four different types of Cars [4].
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Table 1: Measured Stopping Distance of Four Different Types of Cars Type A, B & C has a deceleration of 10, if taking the nearest whole number. Therefore Eq. (19) becomes
2
(20)
Example 1: Use the formula derived above to find the braking distance of a car travelling at 100 km/h. Solution When v = 0 m/s, 2 2 Now calculating the time taken by the car to stop we get (
) √(
) ( )
( 1 )(
)
2 The required deceleration is In order to avoid collision with an obstacle that is at 38.8 m away from the point where the driver begins to apply brakes, an extra distance of 2 seconds would have been essential. Subtracting two seconds from, , makes s. Figure 5 shows that the car would have stopped at about 4 m before the obstacle. Therefore 2 seconds gap when travelling at 100 km/h is equal to 42.58 m.
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Velocity (km/h)
Braking Distance (m)
Figure 5: Braking distance of a car travelling at 100 km/h. The ACC will continuously calculate the required safe following distance of the car at every speed when no obstacle has been detected. Once an obstacle is detected the ACC will decelerate the car till the required gap is reached. If the gap between the car and obstacle becomes greater than the safe following distance as the car decelerate, then the ACC will be switched off. The ACC will also calculate the required deceleration for the car to be able to stop without hitting the obstacle, if the deceleration required will no longer be reached by throttling, and then the ACC will alert the driver to apply brakes. As mentioned earlier, ACC is marketed as a comfort system and not as a safety system, since the braking capacity is usually limited to around . ACC can therefore not be regarded as a collision avoidance system. Collision avoidance systems need higher decelerations, in the order of . In emergency situations, the driver has to take over and remains fully responsible for the vehicle maneuvering [3].
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PART 3 4. CONTROLLER DESIGN This part of the report explains the design of the controller for the cruise control. PID controller is used to control the speed of the car at a desired value. There are complications in PID control if the process under control has non-linearity or huge disturbances. The common problem with the use of PID controllers is known as “integrator windup”.
4.1 PID Design PID controller is used in this project to improve the transient and steady-state response of the closed loop system (cruise control). Figure 6 shows the closed loop of the cruise control system with the model of the PID controller, servomotor and vehicle. The system should have a maximum overshoot of 0 % and a settling time of 0.1 seconds, due to a unit step input.
PID Controller +
Vehicle
𝐾( + )2
u
1 + 0.167
-
Figure 6: Closed Loop of the Cruise Control The parameters (𝐾 ) of the PID were calculated using the computational optimization approach in octave. In this approach 𝐾 are given different ranges, the parameters are varied throughout the range until a combination of the parameters yield the desired response [5]. The values are 𝐾
1 80
And therefore 𝐾𝑝
,𝐾
2 & 𝐾𝑖
2
It can be seen from Figure 7 that the controller is able to produce the required settling time, but there’s large overshoot, thus undesirable. This bad response is due to “integrator windup”. Integrator windup and one of its solutions is explained in 4.2.
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Y(t)
Time (s)
Figure 7: Response of the System Due to a Step Input
4.2 Integrator Windup Integrator windup is a condition by which a control variable governed by a PID or PI controller reaches the actuator limits, thus the feedback loop runs as an opened loop. If a controller with integral action is used, the error will continue to be integrated. This means that the integral term may become very large, colloquially, ‘’winds up’’ [6]. It is then required that the error has opposite sign for a long time before things can return to normal. As a result a controller with integral action may give large transients when the actuator saturates. Integrator windup can be caused large set point changes, huge disturbances or equipment malfunction. This phenomenon is being accounted for in this design. The method used here to solve integrator windup is called “back - calculation and tracking”. It can be seen from Figure 7 that the response should have settled at the set point in less than 0.05 seconds, instead it overshoot to 1.1. Back – calculation works as follows [6]: when the output saturates, the integral is recomputed so that its new value gives an output at the saturation limit. It is advantageous not to reset the integrator instantaneously but dynamically with a time constant . Figure 8 shows a block diagram of a PID controller with anti – windup based on back – calculation. The system has an extra feedback path formed by measuring the actual actuator output or the estimated mathematical model of the actuator and forming an error signal 𝑒𝑠 as the difference between the output of the controller and the actuator output . Signal 𝑒𝑠 is fed to the integrator through gain . The signal is zero when there is no saturation. When the actuator saturates, the signal 𝑒𝑠 is not zero. The normal feedback path around the process is broken because the process input remains constant. But the feedback path around the integrator will drive the output of the integrator towards a value such that the input to the integrator is zero. 15
Figure 8: Controller with Anti – Windup The integrator input is 1
𝑒𝑠
𝑒
(21)
Where 𝑒 is the control error. Hence, 𝑒 in steady-state; Since 𝑒𝑠
𝑒
(22)
, it follows that 𝑖
𝑒
(23)
Where 𝑖 is the saturating value of the control variable. Since 𝑒 and 𝑖 have the same signs, it follows that is always larger than 𝑖 in magnitude. This prevents the integrator from winding up. A rule of thumb that has been suggested is to choose
√
𝑖
.
Figure 9 (a) shows multisim simulation of the implementation of back – calculation in this project. From Figure 9 (b) it can be seen that the response has 0 % overshoot and a settling time of 0.1 seconds as per design specifications.
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a V1
A12
A10
1V Key = A
OUT IN
+ + -
d dt
-160*0.00625
-
XSC1
1V/V 0V Tektronix
C A
C
P(s) Q(s)
1V/V 0V
A7 160/0.025
0V 1V/V A5 A
A9 C
A8
A
+ -
-
C
IN OUT
1V/V 0V
T
+ B
160V/V
1 2 3 4
A3
A
IN OUT B
P G
A4
A2
B
A11
+
∫
B
1V/V 0V
+ -
-
1V/V 0V
A6
1V/V 0V
OUT IN
1/(0.025*0.00625)^0.5
b
Figure 9: (a) Shows the Multisim Simulation of the Cruise Control with an Anti – Windup PID Controller (b) Shows the Response of the Cruise Control to a Step Input.
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5. RECOMMENDATIONS AND FUTURE RESEACH The dynamics of the modeled vehicle presented in this paper are easy to control, whereas other models would require the use of feed – forward control. In feed – forward control the grade of the road is measured, the measurement is fed to a feed – forward controller in order to assist the PID controller for better performance. The system presented in this paper does not work in velocities less than 32 km/h, therefore improvements needs to be done to allow the cruise control in ‘’ stop-and-go’’ condition. A research in the use of GPRS for predictive control will be conducted. This could help in bringing a smooth speed control, thus smooth and stable traffic flow. Research in Corporative Adaptive Cruise Control (CACC) will be done. CACC is an advanced version of ACC system. CACC system allows wireless communication about the speed and the acceleration of the vehicles between two or more vehicles equipped with CACC system. Therefore, CACC system can detect another CACC vehicle merges in sooner through the communication between the two vehicles than ACC system could.
6. CONCLUSION In PART 1; the conceptual design of the cruise control has been presented. The operation of the system in cruise control and adaptive cruise control mode has been explained. The fail - safe operation of the system will be presented. In PART 2; the dynamic model of the car has been be presented. Calculation of safe – following distance by the ACC has been presented. In PART 3; the design of a suitable PID controller for the system has been explained. Integrator windup and one of its solutions has been explained.
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7. REFERENCES [1] Feedback Systems: An Introduction for Scientists and Engineers (16 September 2006) [2] Automobile Electrical and Electronic Systems, third edition, by Tom Denton (2004) [3] Design of a Hybrid Adaptive Cruise Control Stop - & - Go System by R.A.P.M van den Bleek (October 2006 - 2007) [4] http://www.amsi.org.au/teacher_modules/pdfs/Maths_delivers/Braking5.pdf was accessed on [22/02/2017] [5] Modern Control Engineering, Firth Edition, by Katsuhiko Ogata [6] PID Controllers: Theory, Design, and Tuning; Second Edition by K. Aström and T. Haglund
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