An Analysis of CAN Performance in Active Suspension Control System for Vehicle

Transcription

1 icc An Analysis o CAN Perormance in Active Suspension Control System or Vehicle Mohd Badril Nor Shah, Abdul Rashid Husain, Amira Sarayati Ahmad Dahalan Faculty o Electrical Engineering, Universiti Teknologi Malaysia This paper addresses the analysis o control perormance or vehicle active suspension via Controller Area Network (CAN) based on ull vehicle model. The dynamic model o the system is developed based on our sets o suspension which constitutes state variables communicated through si CAN nodes. The Linear Quadratic Regulator () technique is used to reduce heave, pitch and roll variation to achieve desired perormance o active suspension. The simulation work is perormed by using Matlab/Simulink with TrueTime toolbo. Various system perormances are analyzed by varying CAN data speed, CAN loss probability, nodes sampling time, clock drit and scheduling techniques. Based on the analysis, the setup o the proposed CAN network or the system meet the system requirements.. Introduction Active suspension is an automotive technology that virtually eliminates heave, pitch and roll variation o onboard systems in many driving situation such as cornering, accelerating, braking and uneven road surace. This technology has always been applied in luury car, oers a greater degree o ride comort and car handling. Active suspension consists o spring, viscous damper and actuator, preerably hydraulic actuator, equipped with movement sensors to collect and send amount o inormation to onboard engine control unit (ECU) to calculate control signal or actuators. Actuators then generate an appropriate orce to compensate heave, pitch and roll variation to achieve a great perormance o active suspension. In practical situation, control o active suspension in car is done through network This constitutes a typical networked control system. All sensors, actuators and controllers are communicated through a shared bus. This type o architecture oer aa many advantages, such as reduce compleity o wiring, lower installation cost, enable mobile operation and easy or diagnosis and troubleshooting. However, employing such architecture give arise a new problems, that are time delay and data dropout which can degrade the control perormance. CAN Controller Area Network (CAN) is an advanced serial bus system with high speed, high reliability and low cost or distributed real time control applications. It was initially developed or automotive use in late 98s by Robert Bosch, but now CAN is widely utilized in most real time automation system due to robustness to electrical intererences, ability to sel diagnose and data errors repair, high perormances, low cost and suitable or harsh environment. CAN uses carrier sense multiple access protocol with collision detection (CSMA/CD) and arbitration on message priority as its communication protocol to that ensures that a message is successully transmitted to particular node. 9-

2 icc In this work, analysis o CAN perormance will be done. In order to achieve this, mathematical model o active suspension is irst developed based on ull car model as discussed in Section. Section 3 deal with the design o Linear Quadratic Regulator () controller or regulation o active suspension. Section show the simulation results and the discussion o the results are also provided. Finally, Section 5 contains the conclusion.. Mathematical model o active suspension based ull car model The model o ull-vehicle suspension system is adopted rom [], as illustrated in Figure as =. Each set o suspension consists o a spring, a shock absorber and a hydraulic actuator at each corner o the sprung mass (vehicle body). The suspensions connects the sprung mass to the our unsprung masses (ront-let, ront-right, rear-let and rear-right wheels). This coniguration allows sprung mass to heave, pitch and roll reely and enable the unsprung masses are to bounce vertically with respect to the sprung mass. With assumption that all displacements o heave, pitch and roll angles are small, the suspensions between the sprung mass and unsprung masses are modeled as linear viscous dampers while the tires are modeled as simple linear springs = "" "" + "" + "" + " + " = + " + " " + " + " " + " " + " " + " + " + " + = "" + "" " " " " " = " " " + " + " " + " " + " " " " + " + = " " " " + " + " " " " + " + " " " " " " + " " + " = = " + " " " + " + " " " " + z _" = " " = " + " " " " " " " " " + z _" = " " = " + " + " + " + " + " " " " " + z _" " = " () " = " + " + " + " " " " " " " + z _ 9-3

3 icc w K " " m K w φ m K z " _" " m B " Figure : Active suspension system or ullvehicle model springs without damping. Thus, the linearized equation o ull-vehicle suspension system is represented as Equation (). Equation () then is arranged in orm o state space equation such that t = A t + Bu t + B d(t) y(t) = C(t) () where y(t) is the measured output, u(t) is orce input and d(t) is disturbance inputs. u(t) and d(t) are deine as u t = " t " t " t (t) d t = t t t z _ (t) Note that the subscript l, r, rl and rr are reerring to ront-let, ront-right, rear-let and rear right o wheels respectively. The state variables (t) are assigned as listed in Table. 3. Controller design a The controller is designed based on continuous optimal state eedback strategy without consider time delay and packet dropout. By considering a state space equation o ull-vehicle active suspension system represented in Equation (), the control input will be in the orm o u = G t (3) Table : State variables description o active suspension system or ull-vehicle model. θ b z _ K z " _ K " m " B " z m _ K B " B " K K State variables = z = z = θ = θ = φ = φ = = = " = = " = " = z _ " = z _ where heave position heave velocity pitch angle pitch angular velocity Description roll angle roll angular velocity ront-let wheel unsprung mass height ront-let wheel unsprung mass velocity ront-right wheel unsprung mass height ront-right wheel unsprung mass velocity rear-let wheel unsprung mass height rear-let wheel unsprung mass velocity rear-right wheel unsprung mass height rear-right wheel unsprung mass velocity u = [u u u u ], t = [. " ] with G is an optimal gain which obtained by solving Linear Quadratic Regulation () problem that minimizes the cost unction J = t Q t + u t Ru t dt () where Q and R are symmetric positive matrices which penalize the deviation o the state rom the origin and the magnitude o the control signal, respectively. The gain G is given by G = R B X (5) and X = X is the unique positive semideinite solution o the algebraic Riccati equation A X + XA XBR B X + Q = (6) The solution o the Riccati equation (6) will lead to the solution o the controller gain G that takes the system to zero state ( t = ) in an optimal controller eort. However, there in an eicient way emerge recently to solve Equation (6) based on Linear Matri Inequality (LMI). By the LMI technique, the problem can be rephrased as an optimization problem such that [] 9-

4 icc A X + XA + Q XB B X R > (7). Simulation results and discussion The simulation is done by using Matlab/Simulink with TrueTime toolbo. The parameter o suspension systems are given as shown in Table. For solving the LMI problem o (7), YALMIP/SeDuMi conve problem solver is used instead o using standard LMI toolbo in Matlab. YALMIP/SeDuMi is among the newly developed conve problem solver which is proven to produce a less conservative solution and a higher convergence rate [3]. Q and R are arbitrarily assigned as Q = diag( ) R = diag(....) Thus, value o G is obtained by using YALMIP/SeDuMi solver such that G = To measure the perormance o active suspension compare to passive suspension and continuous direct control, integral o Table : Parameters value o active system suspension system o ull-vehicle model [] Sprung mass, m Unsprung mass, m Descriptions Value 5 kg 59 kg Front suspension spring stiness, K " 35 N/m Rear suspension spring stiness, K " 38 N/m Tire spring stiness, K 9 N/m Front suspension damping, B " N/m/s Rear suspension damping, B " N/m/s Roll ais moment o inertia, I 6 kg m Pitch ais moment o inertia, I 6 kg m Length between ront o vehicle and center o gravity o sprung mass, a. m Length between rear o vehicle and center o gravity o sprung mass, b.7 m Width o sprung mass, w 3 m square o error (ISE) unction is used, which deined as ISE = r t c(t) dt (8) where r(t) is set point and c(t) is the output parameters that need to measure their perormance. In this case, r t =, while heave displacement, pitch angle and roll angle are chosen to evaluate the controlled active suspension perormance which is deine in (8). The system is simulated by inserting road disturbance unction at the ront-right suspension set. The road disturbance d t will be in orm o d t =.5 cos 8πt i.5 t.75 otherwise (9) Four nodes are used to collect necessary inormation rom each our sets o suspension and also responsible to send control signal to actuator o corresponding suspension set. While the other node is used to read sensors or heave, pitch, roll and their derivatives values. All these nodes are communicating with an ECU which calculate a control signal o and send it back to corresponding nodes. The coniguration o the nodes is shown in Figure and the tasks details at each node is shown in Table

5 icc Rear-right suspension Rear-let suspension Front-right suspension Front-let suspension ", " u, " u, " u, u Node 6 Node 5 Node Node 3,, Vehicle body,, Node Get rom network:,,,.. " Node (ECU) Send to network: u, u, u, u Figure : Nodes coniguration o networked control system or ull-vehicle model active suspension system The system is evaluated in several cases as the ollowing and the results are shown in Table and Figure 3 to Figure : Case : Sensors sampling time =.6s, Controller sampling time =.s, message length = 8 bits, CAN bandwidth = Mbps, deploying Dateline Monotonic (DM) scheduling technique or each nodes, no data loss in CAN. Case : Sensors sampling time =.6s, Controller sampling time =.s, message length = 8 bits CAN bandwidth = kbps, deploying DM scheduling technique or each nodes, no data loss in CAN. Case 3: Sensors sampling time =.s, Controller sampling time =.s, message length = 8 bits CAN bandwidth = Mbps, deploying DM scheduling technique or each nodes, no data loss in CAN. Case : Sensor sampling time =.s, Controller sampling time =.s, message length = 8 bits CAN bandwidth = Mbps, deploying DM scheduling technique or each nodes, no data loss in CAN. Case 5: Sensor sampling time =.6s, Controller sampling time =.s, message length = 8 bits CAN bandwidth = Mbps, deploying DM scheduling technique or each nodes, no data loss in CAN, network always CONTROLLER AREA NETWORK (CAN) be interrupt by nodes that contain high priority and random tasks. Case 6: Sensor sampling time =.6s, Controller sampling time =.s, message length = 8 bits CAN bandwidth = Mbps, DM scheduling technique or each nodes, CAN data loss probability =.55. Case 7: Sensor sampling time =.6s, Controller sampling time =.s, message length = 8 bits CAN bandwidth = Mbps, added with three new task at all nodes with.5s eecution time each and period time.s,.5s and s respectively, deploying Earliest Deadline First (EDF) scheduling technique at all nodes, no data loss in CAN. Case 8: Sensor sampling time =.6s, Controller sampling time =.s, message length = 8 bits, CAN bandwidth = Mbps, DM scheduling technique or each nodes, no data loss in CAN, Node 3 eperience clock drit at rate. (local time driting % aster than nominal time). The eect o active suspension control perormance via CAN with respect to sampling time and CAN data speed are shown in Figure 3 to Figure 6. From the simulation, it is ound that the acceptable sensors-controller delay should not be more than.5s. Any time delay longer than this value continuously will destabilize the system. In order to obtain good control perormance, sampling time and CAN speed must be properly selected. In this case, at sampling time.6s and CAN speed Mbps, the control perormance o or active suspension is almost same with direct control without using network (Figure 3). Increasing sampling time and CAN speed will lead to longer data transmission delay thus degrade the control perormance (Figure, Figure 5). The delay 9-6

6 icc Table 3: Nodes coniguration o networked control system or ull-vehicle model active suspension system Task Message Eecution Period Node Tasks type Priority* Time (ms) (ms) Received reading or all state variables, calculate control signal o and send it to Node 3, Node, Node 5 and Node 6. Get heave displacement sensor reading and send it to Node Get heave velocity sensor reading and send it to Node Get pitch displacement sensor reading and send it to Node Get pitch velocity sensor reading and send it to Node Get roll displacement sensor reading and send it to Node Get roll velocity sensor reading and send it to Node Get unsprung displacement sensor reading o ront-let suspension and send it to Node Get unsprung velocity sensor reading o ront-let suspension and send it to Node Receive control signal rom Node and send it to actuator o ront-let suspension Get unsprung displacement sensor reading o ront-right suspension and send it to Node Get unsprung velocity sensor reading o ront-right suspension and send it to Node Receive control signal rom Node and send it to actuator o ront-right suspension Get unsprung displacement sensor reading o rear-let suspension and send it to Node Get unsprung velocity sensor reading o rear-let suspension and send it to Node Receive control signal rom Node and send it to actuator o rear-let suspension Get unsprung displacement sensor reading o rear-right suspension and send it to Node Get unsprung velocity sensor reading o rear-right suspension and send it to Node Receive control signal rom Node and send it to actuator o rear-right suspension * Priority no. is reserved or intererence node Case,,, Table : Perormance comparison o passive suspension and active suspension Passive Suspension Heave Pitch Roll Direct Control Control via CAN Passive Suspension Direct Control Control via CAN.78-5 Passive Suspension Direct Control Control via CAN Case Case Case Case Case Case Case behavior is random but periodic and bounded at certain range.

7 icc Reducing sampling time may ulill a real time perormance, but it might cause a network become saturated and overloaded. Data transmission delay will increase with time, thus destabilizes the active suspension system as shown in Figure 6. Figure 7 shows the simulation is done by inserting ive intererence nodes which it injects some high priority and messages at random time into CAN. It is ound the delay becomes random and the control perormance is signiicantly degraded. In CAN, i the data losses occur due to some reason, i.e. error in transmission, or hardware ailure, the node will attempt to retransmit the message. This process will increase a delay transmission and become random. Figure 8 shows when the system with loss probability at 55%, sensorscontroller delays more than.ms and in random manner. The control perormance is signiicantly degraded and even become unstable i loss probability more than 7%. Scheduling technique also inluence the data transmission delay in a system. In Figure 9, it can be seen that deploying EDF scheduling technique or all nodes will introduce a random and unpredictable sensors-controller delay. However, the control perormance is not obviously degraded. Control perormance in a system also can be aected by clock drit phenomenon inside nodes. In Figure, it is ound the control perormance degrade slightly when Node 3 eperiences clock drit at rate o %. This rate value is chosen since under temperature variation - o C to 5 o C, drit rate can reach up until % due to the sensitivity o quartz clock to temperature []. At this rate, sensors-controller delay behavior is random but periodic and at certain period, the delay eceed than ms. From the simulations, the active suspension system using technique is working well under various conditions. With a proper sampling period and CAN data speed, the system preserves the stability when CAN is interrupted by random and high priority tasks, CAN data loss not more than 5% and clock drit at typical rate in particular node Passive suspension Direct continuous control Real time control via CAN Figure 3: control perormance o active suspension or Case Figure : control perormance o active suspension or Case Figure 5: control perormance o active suspension or Case

8 icc Figure 6: control perormance o active suspension or Case Figure 7: control perormance o active suspension or Case 5 Figure 8: control perormance o active suspension or Case 6 Figure 9: control perormance o active suspension or Case in CAN (s) in CAN (s) in CAN (s) Figure : control perormance o active suspension or Case 8 5. Conclusion The article shows a control o active suspension system using technique. The controller is designed based on continuous system and then be applied into real time system o CAN with help o TrueTime simulator. It is ound that the system works well under various conditions and the results also illustrates where the perormance o active suspension system is also aected due to variation o CAN system. Reerence 6 8 [] S. Ikenaga, F.L. Lewis, J. Campos, L. Davis, Active suspension control o ground vehicle based on ull-vehicle model, Proceeding o the America Control Conerence (ACC), Chicago, USA, 999. [] Abdul Rashid Husain, Multi-objective sliding mode control o active magnetic bearing system, PhD thesis, Universiti Teknologi Malaysia, 9 [3] J. Loberg, YALMIP: A Toolbo or Modeling and Optimization in MATLAB, in Proceeding o the CACSD Con, Taiwan,. [Online]. Available: [] Aurélien Monot, Nicolas Navet, Bernard Bavou, Impact o clock drit on CAN rame response time distribution, Proceedings o IEEE Conerence on Emerging Technologies and Factory Automation, Authors: Mohd Badril Nor Shah, Abdul Rashid Husain, Amira Sarayati Ahmad Dahalan Company: Universiti Teknologi Malaysia Address: Faculty o Electrical Engineering, 83 Skudai, Johor Bahru, Malaysia Phone: Fa: bad_z8@yahoo.com, rashid@ke.utm.my, amira_sarayati@yahoo.com Website: 9-9