1
Cruise Control System in Vehicle
Karen Lie, CalvinCollege
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.
Index Terms—Cruise Control, Control System, Vehicle, Modeling, Simulation
I. Introduction
C
ruise control system has become a common feature in automobiles nowadays.Instead of having the driver frequently checking the speedometer and adjusting pressure on the gas pedal or the brake, cruise control system control the speed of the car by maintaining the constant speed set by the driver. Therefore, cruise control system can help reduce driver’s fatigue in driving a long road trip.This paper presents the control system behind the cruise control.
II. Background
Before getting into to the control system concepts of cruise control, the components and the basic mechanism of the cruise control system in a vehicleare summarized.
A. Components of Cruise Control
Cruise control system can be divided in to three main parts, which are the input, the processor, and the output. The input of the system includes the setting buttons on the steering wheel, gas pedal, brake, clutch and the feedback signal of the cruise control. The processorof the system is to control the speed of the car by utilizing the control system theory. The output is the throttle position, which is corresponding to the actual speed of the car.
1) Input of Cruise Control
There are usually three to five setting buttons on the steering wheels for the input to the cruise control system. The buttons are on/off, set/accel, resume, and coast. The on button turns on the cruise control function. The off button turns off the cruise control function. The set/accel button is to set the speed of the car to the current speed that the car is driving at. Also, bytapping the set/accel button once can increase the speed of the car by 1mph and so forth. The resume button is to set the speed of the car back to the last maintained speed, which is the speed right before the cruise control is disengaged. The coast button is to decrease the speed of the car.
The brakeand the clutch arethe other inputs to the cruise control system. When the pedal is pressed, the cruise control system is disengaged, so the speed control of the car is taken over by the driver in adjusting the gas pedal and the brake.
Furthermore,the speed for the cruise control can be set by pressing the gas pedal to accelerate the car to the desired speed, and then hitting the set button. Also, when the cruise control is engaged, the gas pedal overrides the set speed from the cruise control, so the car accelerates as long as the gas pedal is pressed.
Finally, the feedback signal from the measured speed of the car is taken into account of the input of the curse control system. This input is closely related to the control system of the cruise control. The detailed of the feedback input is presented under the control system of cruise control later.
2) Processor of Cruise Control
The processor of a cruise control is a control system designed to obtain the speed set by the driver. It plays an important role in the cruise control system. The processor is integrated with electronic components to a system transfer function, which is discussed under the control system of cruise control in detail.
3) Output of Cruise Control
The output of the cruise control is the throttle position. The actual speed of the car varies corresponding to different throttle position, as the throttle valve limiting how much air the engines takes in. Adifferent air-to-fuel ratio in the combustion process affects the power and the speed of the engine, and this eventually leads to the change of the car speed.
B. Mechanism of Cruise Control
An overview of the relationship between different components of cruise control system is shown in Fig. 1. The processor of the cruise control system is shown as the Cruise Control Computer in the figure.
The process of the cruise control system in a vehicle is: First, the driver sets the desired speed of the car by turning on the cruise control at the desired speed that the car is traveling at and hit the set button. An alternate way to set the desired speed of the car is by tapping the set/accel button to increase the speed of the car or by tapping the coast button to decrease the speed of the car. Second, the processor of the system gets the input signal, and then sends the output signal to the actuator. Third, the actuator adjusts the throttle position. Finally, the changes in the throttle position would leads to the changes in the speed of the car traveling. Also, the actual speed of the car is measured by a sensor and sent to the processor.The process of sending the current speed of the car continues for the processor to maintain the desired speed, as long as the cruise control is engaged [1]. This process is explained in details in terms of control system concepts later.
Fig. 1. Relationship between different components in cruise control system
The throttle valve connects to the actuator and the gas pedal by cables, so the throttle position can be adjusted by the actuator and the gas pedal. Some actuators are powered by the engine vacuum to close and open the throttle. The pulse frequency corresponding to the speed of the car is sent to the vacuum controlled diaphragm conned to the accelerator, and it regulates the amount of the vacuum the diagram received [2].
III. Control system in Conventional cruise control
A. Design Consideration
A cruise control system needs to accelerate to the desired speed in a short time without overshooting the speed of the car. Also, it needs to maintain the speed with little deviation, when the car is driving up or down a steep hill.
B. Physical Model
First, the inertia of the wheels of the car is neglected. Second, the friction of the car is assumed to be the friction caused by the motion of the car. Then, aphysical model of the cruise control systemis illustrated as shown in Fig. 2 [3]. The mass, m, is indicated as the mass of a car.
Fig. 2. Free-body diagram of a car
By using Newton’s second law of motion, a differential equation of the cruise control model can be obtained, as in (1).
(1)
where v is the velocity of the car, b is the friction of the car and u is the force from the engine.Then, by applying Laplace Transform theorem, Eq. (1) becomes Eq. (2).
(2)
After rearranging Eq. (2), the transfer function of the open-looped cruise control system is obtained, as is (3).
(3)
where Y(s) is V(s) in Eq. (2).
Cruise Control System in a vehicle is a closed-loop control system. A simplified model of the cruise control system is developed, and its block diagram is shown in Fig. 3.
Fig 3. Block Diagram of Cruise Control System in a Car
C. Design Specification
Since it is critical for a cruise control system to obtain the desired speed in a short time without overshoot, the design specification is determined:
Rise time < 5 sec
Overshoot < 10%
Steady-state error < 2%
D. Assumption
For the simplified cruise control model, the mass, the friction constant and the force from the engine of the car is assumed:
m = 1000kg
b = 50 N*sec/m
u = 500 N
E. Modeling and Simulation
Models of cruise control system are developed from the open-loop system to the closed-loop system. Then, models with PI controller are further developed in terms of different control constants. Also, simulations of different models are presented and discussed.
1) Open-loop System
The cruise control system without controller and feedback is implemented on the Simulink, as shown in Fig. 4. In other words, the control system for the speed of the car takes no consideration of the actual speed of the car traveling.
Fig. 4 Cruise control System without feedback and controller
The response of the open-loop system to a step input is shown in Fig. 5.
Fig. 5. Response of the open-loop of cruise control
The steady state error is about 98%. A feedback loop is needed to add to the system to bring the response back to the desired speed.
2) Closed-loop System
The cruise control system with a unity feedback loop is implemented as shown in Fig. 6. The response of the system to a step input is shown in Fig. 7.
Fig. 6. Cruise control system with feedback
Fig. 7. Response of the closed-loop system
The steady state error of the closed-loop system is even slightly larger than that of the open-loop systemas in Fig. 5, because the feedback-loop reduces the accuracy of the response.
3) PIController
A PI controller is added to the cruise control system to achieve the desired response of the system. Therefore, a PI controller is added to the model of cruise control system, as shown in Fig. 8.
Fig. 8. Cruise control system with controller
First, only the proportional control (Kp) in the controller is considered. The closed-loop transfer function of the cruise control system with a proportional control is obtained, as in (5).
(5)
The proportional controlin the controller is turned on and is set to 100. The response of the system with Kp = 100 is shown in Fig. 9. The steady state error of the system with the proportional control is reduced from 98% to 34%. Also, the settling time of the system is decreased.
Fig. 9. Response of the system with Kp=100
Second, both the proportional control (Kp) and the integral control (Ki) in the controller are considered in the cruise control model. The closed-loop transfer function of the cruise control system with the PI controller is obtained, as in (6).
(6)
The integral control in the controller is turned on and is set to 10. The response of the system with Ki = 10 and Kp= 100 to a unit step input is shown in Fig. 10. The steady-state error of the system is eliminated by adding the integral time control, but overshoot of the response is introduced. Also, the response time of the system is shortened.
Fig. 10. Response of the system with Kp =100 and Ki =10
Third, the proportional control and the integral control of the controller are adjusted to meet the design specifications of the cruise control model.
The first design specification of the cruise control system is to have the rise time less than 5 second. Therefore, the rise time of the cruise control model needs to decrease, such that the cruise control system can reach the desired speed within a few seconds. By increasing the proportional gain constant on the controller from 100 to 500, the rise time of the system is decreased as shown in Fig. 11.
Fig. 11. Response of the system with Kp= 500 and Ti = 10
The proportional gain is further increased to 800, so the rise time is decreased to about 3.5 seconds, as shown in Fig 12. Therefore, the rise time for the cruise control system with Kp = 800 and Ki = 10 meets the design specification.
Fig. 12. Response of the system with Kp=800 and Ki=10
The second design specification of the cruise control system is having the steady state error of the response less than 2%. For the response of the system shown in Fig. 12, the steady state error is about 4%. Therefore, the value of the integral time constant is increased to further reduce the steady-state error.
When the integral time constant is changed to 40, the controller of the model essentially eliminates the steady-state error of the response. The response of the cruise control model with the controller of Kp =800 and Ki = 40 is shown in Fig. 13. There is no overshoot in the response of the system, so the third design specification is met. Since the system is overdamped, the 10-90% rise time is used and is estimated to be 2.8 sec, which meets the design specifications. Therefore, the model with the controller of Kp = 800 and Ki= 40 meets all the design specifications of the cruise control system.
Fig. 13. Response of the system with Kp = 800 and Ki = 40
Since the controller with the proportional control and the time integral control is able to achieve the desired response of the system, a derivative control is not necessary to add to the model to keep the simplicity of the controller.
4) Effect of the Weight of the Car to Cruise Control System
Cruise control system usually comes with the vehicle in two ways. One way is that the vehicle is equipped with the cruise control system as one of the features in the vehicle as a whole package from the vehicle manufacturer. This is the case mostly for the vehicles have been out in the market in these recent years. Another way is to install the cruise control system on the older models of vehicles which are not equipped with the cruise control feature. The cruise control system needs to adapt to the changes of the weight of the car, especially for those commercial available cruise control system that is to beinstalled on the car after the production. In order to see how the weight affects the response of the cruise control system, cruise control model with different weights of car are simulated on the Simulink.
First, the weight of the car is changed from 1000kg to 500kg, and the process transfer function of the model is obtained, as stated in (7).
(7)
The cruise control model is simulated with the same controller, which has Kp = 800 and Ki = 40, and the response of system is shown in Fig. 14. The steady state error of the system is slightly larger than 2%. There is no overshoot in the response, and the 10-90% rise time of the response is 1.6 sec.
Fig. 14. Response of the system with m = 500kg, Kp = 800 and Ki = 40
Since the steady state error is slightly larger than the design specification, the controller constants are varied to obtain a desired response. By increasing the integral time constant to 45, the steady state error of the response becomes 2%, while the 10– 90% rise time is still be about 1.6 sec and there is no overshoot, as shown in Fig. 15. Therefore, all the design specifications are met for the cruise control system with the car weight of 500kg.
Fig. 15. Response of the system with m = 500kg, Kp = 800, and Ki = 45
Second, the weight of the car is increased to 2000kg, so the new process transfer function of the cruise control is obtained, as stated in (8).
(8)
The model with m = 2000kg and the controller of Kp = 800 and Ki = 40 is simulated, as shown in Fig. 16. The system has no overshoot, and the rise time is about 8 sec. Also, the steady-state error is about 3.5%.
Fig. 16. Response of the system with m = 2000kg, Kp = 800 and Ki = 40
In order to meet the design specification for the steady-state error and the rise time, the control constants in the controller are adjusted to obtain a desired response.After a few combinations of different values of the contoller, Kp is picked to be 2000 and Ki is picked to be 80. The cruise control model with the new controller is simulated, and its response is shown in Fig. 17. The system has no overshoot and 1% steady-state error. Also, the rise time of the response is about 5 sec. Therefore, the design specifications of the cruise control with car weight of 2000 kg are met.
Fig.17 Response of the system with m = 2000, Kp = 2000, and Ki = 80
IV. Adaptive cruise control
Adaptive cruise control (ACC) system takes the traffic flow into considerationin controlling the speed of a vehicle. ACC system not only maintains the pre-set speed of a vehicle, likes a conventional cruise control system does, but it also maintains a constant distance between the vehicle and the vehicle ahead by adapting the speed. Vehicle equipped with ACC system has a forward-looking sensor at the front of the vehicle to detect the relative speed of the preceding vehicle and the distance in between the two vehicles. Therefore, the difference between an ACC system and a CC system is that ACC system has the ability to adapt the speed of the preceding vehicle.
A. Background
ACC system was first introduced in 1998 by Toyota on production vehicles in Japan, and it was a laser-based system for Toyota’s Progress compact luxury sedan. Then, Nissan introduced a radar-based ACC system for its Cima 41LV-2, a luxury sedan sold in Japan. Later, Jaguar also offered an ACC for its XKR coupes and convertibles sold in Germany and Britain in September 1999 [4]. Other car manufacturers, for example, Mercedes-Benz, Audi, Cadillac and BMW, have ACC feature available now in their selected models.Furthermore, the first model equipped with ACC system available in the United States was Lexus’ LS 430.
Adaptive cruise control system measures the distance to the preceding vehicle and the relative speed of the vehicles. When there is no vehicle ahead on the roadway, the ACC system works in the same way as the conventional cruise control system. When there is a preceding vehicle or another vehicle cuts in front of the host vehicle, the ACC system measures the distance from the host vehicle to the vehicle ahead. If the measured distance is less than the desired distance preset by the driver, ACC system slows down the car with a maximum deceleration of 3.5m/s^2 by closing the throttle valve and/orautomatically applying the brake until the preset distance is obtained [4], [5]. Also, if the measured distance is larger than the preset distance, the host vehicle resumes the preset speed. The basic components and subsystems in an ACC system on a traveling vehicle are shown in Fig. 18.