http://amsjournal.ams-mss.org
MODELLING AND SIMULATION
eISSN 2600-8084 VOL 2, NO. 2, 2018, 70-75
70
Simulation and Real-Time Analysis of Active Suspension System over Controller Area Network
Tahmida Islam1,2, Leila Rajabpour1, Roy E. A. Leon1,3 and Abdul Rashid Husain1*
1School of Electrical Engineering, Faculty of Engineering, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia.
2Khulna University of Engineering & Technology, Khulna 9203, Bangladesh.
3Escuela Superior Politécnica del Litoral, Ecuador.
*Corresponding author: [email protected]
Abstract: This paper discusses the simulation of network-based control of active car suspension system. The suspension is modelled as of a class of linear and the states of the system are treated as the node to transmit in data in the Controller Area Network (CAN) – based network. The designed PID controller is also connected to the CAN network with additional sending/receiving node. In order to guarantee the timeliness of the messages, a few scheduling approaches namely Fixed Priority, Deadline Monotonic and Earliest Deadline First are tested to schedule the messages. The performance of a quarter car model is observed through a simulation study based on specialised Real-time Truetime Toolbox in Matlab/Simulink. In this work, road disturbance is also introduced to the system so as the ride controller presented by the movement of the wheel and car body can also be accessed as the mean to measure the system performance. The simulations results show that for this class of system, the performance of the system are relatively similar for all the scheduling methods which imply that for dynamic system with less package rate, selection of scheduling algorithm is less critical.
Keywords: CAN; Full-car model; Quarter-car model; Road profile; Suspension system; Truetime scheduling.
1.INTRODUCTION
Suspension system in car consists of mechanical mounting of tyres, air pressure in tyre, springs, shock absorbers and linkage that connects a vehicle to its wheels and allows relative motion between the two connected systems. In other meaning, suspension system is a mechanism that physically separates the car body from the car wheel [1-2]. Vehicle suspensions systems is typically rated by its ability to provide good road handling, load carrying and improve passenger comfort. The suspension system is meant to absorb shock caused by the irregular road profile, drag forces, drivetrain or engine vibrations, wheel and also the non-uniformity of the tires. Unexpected speed bumps and pot holes along the roadway where a vibrational oscillation subjected to the wheels transmitted to the axel causing vehicle body vibration.
Current automobile suspension uses a passive suspension system in which the movement of the quarter-car model is being determined entirely by the road surface. A passive suspension has the ability to store energy via a spring and dissipate it via a damper. Its parameters are generally fixed, being chosen to achieve a certain level of compromise between road handling, load carrying and ride comfort. Whereby, the active suspension is said to pose the ability of reducing the traditional design as a compromise between handling and comfort by directly controlling the suspensions force actuators [3]. Active suspension consists of spring, viscous damper and actuator, preferably hydraulic actuator, equipped with movement sensors to collect and send amount of information to onboard engine control unit (ECU) to calculate control signal for actuators. Actuators then generate an appropriate force to compensate heave, pitch and roll variation to achieve a great performance of active suspension [4].
A modern vehicle may have many ECUs in different subsystems for various purposes. In a full car suspension system, there are four wheels with their own controller unit attached. All these wheels need to be balanced in term of position and speed coordination for proper suspension application. Improved electronic control system can improve relaxation experienced by passengers and vehicle dynamics. However, there are some new challenges such as the body wiring sophistication, space constraints, and reliability as the interconnected system required to be coordinated properly. Communicating among dependent subsystems is very crucial. The exchange of particular performance and position advice between subsystems within defined communication latency is necessary. Thus, a simple and effective real-time communication protocol is required and further it requires a means of scheduling approach to so-called manage the exchange of data communication. The work in [5] also highlights some of the requirement of the system and [6-7] covers an excellent review of network in dynamic system.
A real-time system based on network is one in which the correctness of a result not only depends on the logical correctness of the calculation but also upon the time at which the result is made available i.e. every task has timing constrain [8]. CAN bus
can offer a simple but effective real-time communication protocol between controls, actuators, sensors, and other subsystems.
However, CAN itself does not provide any scheduling approach to manage the exchanges of messages between the nodes in the dynamic system. In this work, the quarter car suspension system connected via CAN bus is explored where the nodes of the system (to the wheels) are communicated to a centralised PID based controller to achieve the overall system performance.
The outline of the article is as follows: Section 2 covers the model of the suspension system in a class of linear system. Section 3 describes the design of the PID controller and the set-up of the networked suspension system on Truetime environment.
Section 4 covers the discussion of the result and Section 5 is the conclusion of the work.
2.SYSTEMDESCRIPTION
Most of the past active suspension designs were developed based on the quarter-car model as in Figure 1. The fundamental components of the suspension system are the sprung mass (car body), spring damper and actuator and unsprung mass which is the tyres and its mounting system. For this work, a linear quarter-car model is considered as it is simple to model, yet the basic elements of the suspension system can be observed as seen from Figure 2 which 𝑀2 and 𝑀1 are the masses of the car body (sprung mass) and wheel (unsprung mass), respectively, 𝑋 𝑠 and 𝑋 𝑡 are the displacements of car body and wheel, respectively, 𝐾 𝑎 and 𝐾 𝑡 are the spring coefficients, and 𝐶 𝑎 is the damper coefficient.
Based on Figure 2, the mathematical model of the active suspension system behavior is further described by a complete set of differential equations. This is to aid in the analysis of the behavior of the dynamic system before designing the controller.
The model is constructed according to functional principles in view of the demand and is required to represent the kinematic and dynamic behavior of the system in an equation [2, 4].
𝑀1𝑋̈𝑤= −𝐾1(𝑋𝑤− 𝑟) + 𝐾𝑎(𝑋𝑠− 𝑋𝑤) + 𝐶𝑎(𝑋̇𝑠− 𝑋̇𝑤) − 𝑈𝑎 (1) 𝑀2𝑋̈𝑠= −𝐾𝑎(𝑋𝑠− 𝑋𝑤) − 𝐶𝑎(𝑋̇𝑠− 𝑋̇𝑤) + 𝑈𝑎 (2) where 𝑋̈𝑠, 𝑋̇𝑠, 𝑋𝑠 and 𝑋̈𝑤, 𝑋̇𝑤, 𝑋𝑤 are the acceleration, velocity and displacement of the car body and car wheel, respectively, and 𝑟 is the road condition.
For the given system, four state variables are defined such that two variables give the displacement of the two masses and the other two give the velocities of the respective masses. Let the states to be defined as follows:
𝑋1= 𝑋𝑠− 𝑋𝑤; 𝑋̇1= 𝑋̇𝑠− 𝑋̇𝑤≈ 𝑋2− 𝑋4
Figure 1. Quarter car model
Figure 2. Active suspension model
72 𝑋2= 𝑋̇𝑠; 𝑋̇2= 𝑋̈𝑠
𝑋3= 𝑋𝑤− 𝑟; 𝑋̇3= 𝑋̇𝑤− 𝑟̇ ≈ 𝑋4− 𝑟̇
𝑋4= 𝑋̇𝑤; 𝑋̇3= 𝑋̈𝑤
where 𝑋1, 𝑋2, 𝑋3, and 𝑋4 are the displacement and velocity of mass M1 and the displacement and velocity of mass M2, respectively. Then the dynamic equations can be arranged in state-space form as
[ 𝑋̇1
𝑋̇2
𝑋̇3 𝑋̇4]
= [
0 1 0 −1
−𝐾𝑎
𝑀2 −𝐶𝑎
𝑀2 0 𝐶𝑎
𝑀2
0 0 0 1
𝐾𝑎 𝑀1
𝐶𝑎 𝑀1 −𝐾𝑡
𝑀1 −𝐶𝑎
𝑀1] [
𝑋1
𝑋2
𝑋3 𝑋4
] + [
0
1 𝑀2
01 𝑀1]
𝑈𝑎+ [ 0 0
−1 0
] 𝑟̇ (3)
The values of the parameters are defined in Table 1. The parameter values of both the models such as the mass, damping coefficient and spring stiffness used in the simulation using Matlab/Simulink are shown in Table 1.
3. CONTROLLER DESIGN
For this system, PID controller is used to perform the closed-loop control of the suspension system for all the four wheels of the car. In order to perform the exchange of the messages between the nodes which include the states’s node, controller node and the actuator node, CAN network is used and to maintain the synchronicity and to achieve the real-time performance requirement. Both of these aspects are covered as below:
3.1 PID Controller Design
The objective of this section is to design a proper PID controller for the active suspension system. By considering the state space equation of full-vehicle active suspension system (3) as the following form:
𝑋̇(𝑡) = 𝐴𝑋(𝑡) + 𝐵𝑢𝑎(𝑡) + 𝐿𝑟̇(𝑡)
𝑦(𝑡) = 𝐶𝑋(𝑡) (4) where 𝑦(𝑡) is the measured output, 𝑢𝑎(𝑡) is force input and 𝐿𝑟̇(𝑡) is disturbance inputs. Considering the PID controller of the following form:
𝑢𝑎(𝑡) = 𝑘𝑝𝑒(𝑡) + 𝑘𝑖∫ 𝑒(𝑡)𝑑𝑡 + 𝑘𝑑 𝑑
𝑑𝑡𝑒(𝑡) (5) where 𝑒(𝑡) is the error between the desired and actual values of the states. In order to find the parameters of the controller, the model of the system is run in the simulation with no network, but additional disturbance with delay is introduced. By using MATLAB sisotool, the gain values can be obtained as:
𝑘𝑝= 58965.00 𝑘𝑖= 115828.90 𝑘𝑑= 0.02
Here, the system has two inputs which are road disturbance, 𝑟(𝑡), and the other one is the control input, 𝑢𝑎(𝑡), which needs to be designed to reduce the car fluctuations caused by the road disturbance. By considering the following function as the disturbance input
𝑟(𝑡) =0.1(1−cos(8𝜋𝑡))
2 , 0.5 < 𝑡 < 0.75 (6) Table 1. List of parameters
System Components Parameter Symbol Value
Sprung mass 𝑀2 (kg) 290
Un-sprung mass 𝑀1 (kg) 59
Linear damping coefficient 𝐶 𝑎 (N/(m/sec)) 1000 Linear spring stiffness coefficient 𝐾 𝑎 (N/m) 16812 Linear tire stiffness coefficient 𝐾 𝑡 (N/m) 190000
which its derivative 𝑟 will be applied to the system as the road disturbance, d, then the system transfer function from disturbance input to the output will be as follows:
𝐺𝑑−𝑦(𝑠) = 𝑠3−20.45𝑠2+227𝑠+1.512×10−12
𝑠4+20.4𝑠3+2993𝑠2+1.11×104𝑠+1.867×105 (7) and the system transfer function, from the control input, u, to the output is obtained as:
𝐺𝑢−𝑦(𝑠) = 0.01695𝑠2+0.1169𝑠+1.038×10−16
𝑠4+20.4𝑠3+2993𝑠2+1.11×104𝑠+1.867×105 (8) and the overall output would be as follows:
𝑌(𝑠) = 𝐺𝑢−𝑦(𝑠) ⋅ 𝑈𝑎(𝑠) + 𝐺𝑑−𝑦(𝑠) ⋅ 𝑟̇(𝑠) (9) It is obvious that the system is formed as a coupled linear system where the superposition can be applied for the selection of the controller parameters under any uncertainties. However, this is not discussed as it is beyond the scope of this work.
3.2 CAN Controller Design
Based on the system configuration, each wheel of the car will be considered as one node. One node is for the PID controller of active suspension and another node for the scheduling part. All of these six nodes are shown in Figure 3.
From Figure 3, we can see each car wheel node consist of a sensor and an actuator. Each sensor senses the deviation due to road conditions and sends this value to the central PID controller in node 5. The controller calculates the algorithm (5) based on the sensed values and then sends the resultant actuation value to the actuator of respective wheel. All these communication data is done by using CAN buses developed on CAN network throughout the car. As all the nodes are using the same CAN buses, there is a scheduler to help all the nodes accessing the buses. This diagram is simulated in MATLAB simulink using TRUETIME 2.0 beta [9].
There are three crucial parts in TrueTime toolbox simulation scheme: TrueTime kernel, TrueTime network and a controlled process. TrueTime kernel is the brain of CAN network which is responsible for I/O and network data acquisition or data processing and calculations. It can realise a control algorithm/logic and handle several independent tasks (periodic, non- periodic). TrueTime network is used for defining system specifications, such as network type, protocol used, network ID, nodes and data rate. The control processes schedule all the node access using different scheduling protocols [10]. The TrueTime Simulink is shown in Figure 4. The coding for each node involves the initialisation of the node and the process of transmitting/receiving the data. The arbitration process is done automatically by the CAN protocol in the Truetime toolbox.
4. RESULT AND DISCUSSION
In order to observe the performance of the system under the three scheduling algorithms, the system as shown in Figure 4 is set-up and in the coding of the network, the function ttInitKernel(‘prioDM’), ttInitKernel(‘prioFP’) and ttInitKernel(‘prioEDF’) are used where the name DM, FP and EDF are to call the Deadline Monotonic (DM), Fixed Priority (FP) and Earliest Deadline First (EDF) scheduling algorithms. When the system runs under one scheduling method, all the related codes have to be changed accordingly and repeated for all the three methods. The system responses by applying different types of scheduling algorithm including DM, EDF and FP are investigated for the system.
For all the cases, t is assumed that the disturbance is applied to the rear wheels with a delay of 0.2 sec. Figures 5-7 show the results of applying DM, EDF and FP to the system, respectively. For Figure 5(a), the timing schedule for the 6 tasks executed are shown where it can be seen tasks 5 which is the controller is the ‘busiest’ node that transmit/receive data. This is true since this is the only node that has to entertain the incoming data, perform the controller calculation time and transmit the
Figure 3. System block diagram with CAN
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resulted control value to the actuator node in node 6. It is also noticed that node 6 is less occupied and most of the time is in waiting time (idle-middle level).
Based on this schedule method, the responses of all the wheels are shown in Figure 5(b) where all the wheel deflections are much lesser than the disturbance and in the acceptable range. In a similar line, Figure 6(a) and Figure 7(a) are the timing diagrams of EDF and FP, respectively. The wheels deflections are shown in Figure 6(b) and Figure 7(b) for each of the schedule approaches. It can be noticed that in term of the suspension system performance, very little discrepancies can be noted in the three scheduling approaches. However, for the network performance, EDF seems to be more optimum since the network is less busy and the timing is rather evenly distributed. This is in the agreement with the theory since EDF is dynamic scheduling and is the most optimum as compared to other fixed scheduling approaches. Also, it is noted that no data loss occurs and this might be due to number of nodes is rather low for this 4th order system.
Figure 4. Truetime set-up configuration of the system
Figure 6(a). EDF scheduling Figure 6(b). EDF scheduling
Figure 5(a). DM scheduling Figure 5(b). System responses with DM scheduling
5.CONCLUSION
In this work, the control of an active suspension model of a full car by using PID controller was studied. The model is developed based on a quarter car model and connected via distributed network nodes. Then the applicability of the designed controller for a real time system of CAN with the help of true time simulator was examined. It was shown that the controller has a good disturbance rejection and the system works properly under different scheduling algorithms and the response is satisfactory. In all three scheduling protocols, namely FP, DM and EDF, is quite similar and no data loss occurs. This happens due to similar priority in all cases and less traffic in the network. In future works more nodes and dummy nodes will be added in the network to check the system response and to determine the most suitable scheduling protocol for car system.
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Figure 7(a). FP scheduling Figure 7(b). System responses with FP scheduling
