ENGG* 4420 Real Time System Design Lab 2: Real-Time Automotive Suspension system Simulator TA: Aws Abu-Khudhair (aabukhud@uoguelph.ca) Due: Week of Oct. 12th Aws Abu-Khudhair ENGG* 4420 1
Today’s Activities � Lab 2 Introduction. � Lab 1 Demos. � Start work on Lab 2. Aws Abu-Khudhair ENGG* 4420 2
Lab 1 Development Environment � HP PC � LabVIEW 2009 software Aws Abu-Khudhair ENGG* 4420 3
Introduction � Types of vehicle suspension systems � Passive Suspension System. � Active Suspension System. � Semi-Active Suspension System. � Road disturbance � Step Input � Harmonic Input Aws Abu-Khudhair ENGG* 4420 4
Passive Suspension System � Standard vehicle suspension z s system Vehicle body � Employed in the majority of commercial vehicles � Advantages: k s b s z u � Low cost. � Simple implementation. Tire � Disadvantages: � z r Purely passive elements. k t � On-line performance optimization not possible Aws Abu-Khudhair ENGG* 4420 5
Active Suspension System z s � Fully active system. � Computer controlled active Vehicle body element (F a ). � Advantages: F a z u � Offers excellent performance. � Allows for control and performance optimization at any point during Tire lifetime. � Disadvantages: z r k t � High cost. � Major safety issues. � High power demand. Aws Abu-Khudhair ENGG* 4420 6
Semi-Active Suspension System � Hybrid system (Passive + z s Active) Vehicle body � Provides excellent fail safe mechanism. k s b s b semi z u � Relatively low cost. � Provides a performance Tire comparable to the active system. z r k t � Very low power demand. Aws Abu-Khudhair ENGG* 4420 7
Quarter-Car Suspension Model z s z s m s m s Active element k s b s k s b s b semi z u z u m u m u z r z r k t k t Passive Suspension System Semi-Active Suspension System Aws Abu-Khudhair ENGG* 4420 8
Quarter-Car Suspension Model cont. � The system can be modeled using state space representation: � Passive: & = + & X AX L z , r � Semi-Active: & = + + & X AX NXb L z , semi r � The two models are equivalent when the variable damper coefficient is set to 0 Aws Abu-Khudhair ENGG* 4420 9
State Space Model & = + + & X AX NXb L z , eq. 2.11 semi r � In the S.S. equation: � ‘X’ – State vector. � ‘A’ – State matrix (system description). � ‘N’ – Semi-active control matrix. � ‘L’ – Input disturbance vector. � ‘Z r ’ – Road disturbance. � Matrices description is provided in the lab manual pg. 43-45 Aws Abu-Khudhair ENGG* 4420 10
State Space Model − ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ x z z Suspension deflection 1 s u ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ & x z Velocity of sprung mass ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ = = = 2 s X ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ − x z z Tire deflection 3 u r ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ & ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ x z Velocity of unsprung mass 4 u & � X - Derivative of the state vector over the sampling time. & � - Derivative of the road disturbance over Z r the sampling time. Aws Abu-Khudhair ENGG* 4420 11
Road Disturbance � Step Input: � Isolated sudden disturbance. � Ex. Curb with a height of 10 cm. Z r = 0.1m Road Input Z r (t) Time (t) 0 Aws Abu-Khudhair ENGG* 4420 12
Road Disturbance cont. � Harmonic Input: � Simple road profile. � Modeled as a Sine wave with: � Freq. 1 Hz. � Amp. 10 cm. � Phase 0°. Aws Abu-Khudhair ENGG* 4420 13
Semi-Active Suspension Control Methods � Skyhook Control. � Ground-hook control. � Optimal control based on LQR. � Fuzzy logic control: � GA-based fuzzy control. � Neural-Fuzzy control. � Adaptive Fuzzy control. Aws Abu-Khudhair ENGG* 4420 14
Linear Quadratic Regulator (LQR) � The controller works towards minimizing the performance index given in equation (2.13). ⎡ ⎤ T ∫ = + ρ + ρ + ρ + ρ 2 2 2 2 2 & ⎢ ⎥ eq. 2.13 J lim E x x x x x 2 1 1 2 2 3 3 4 4 → ∞ ⎣ ⎦ T 0 � The controller determines the required “ideal” active force (F a ) to stabilize the vehicle. Aws Abu-Khudhair ENGG* 4420 15
Semi-Active Control Law (LQR) � The optimal control law is determined using Fig. 2.6. � According to the calculated optimal active force (F a ), and the absolute velocity of the two masses, the damping coefficient (b semi ) is calculated. Fig. 2.6. Aws Abu-Khudhair ENGG* 4420 16
Semi-Active Control Law (LQR) cont. � The LQR control method is summarized in table 2.2. Aws Abu-Khudhair ENGG* 4420 17
Lab 2 – Implementation steps � Step 1: Read Chapter 2 of the lab manual (further information is given in the appendix section). � Step 2: Implement the quarter-car passive and semi-active suspension models in LabVIEW. � Step 3: Implement the two road disturbances (step and harmonic). Aws Abu-Khudhair ENGG* 4420 18
Lab 2 – Implementation steps � Step 4: Implement the LQR controller for the semi-active suspension system. � Step 5: Perform the following analysis 1. Compare the performance of the passive and semi-active suspension systems. 2. Vary the weight parameters of the LQR controller (P matrix in eq. 2.14) and observe the change in performance of the SASS. 3. Provide a measure to differentiate the difference in performance of the two systems (% difference?) Aws Abu-Khudhair ENGG* 4420 19
Requirements 1. A fully functional passive and semi- active suspension systems, with the ability to switch between the two systems in the same project. 2. Simulations performed using the two road disturbances given in section 2.2.2 of the lab manual. Aws Abu-Khudhair ENGG* 4420 20
Requirements 3. The following performance graphs must be present on the front panel: � Vehicle ride quality. � Suspension deflection response. � Tire deflection response. � Input disturbance to the system. 4. LQR control must be performed using a separate Task (loop) from the plant system. Aws Abu-Khudhair ENGG* 4420 21
Notes – Matlab Script Nodes � The matricies can be coded using the MatLAB script node in LabVIEW. � Matrix definitions are done in the following format: � X= [ xx xx xx; xx xx xx; xx xx xx] ; Note that variables can be used within the matrix defintion. Aws Abu-Khudhair ENGG* 4420 22
Notes – Matlab Script Nodes � Matricies can be multiplied and added as long as the dimensions are consistent. � To transpose a matrix add a ‘ ’ ’ after the matrix variable. � Dot product multiplications can be performed using a ‘* ’. Aws Abu-Khudhair ENGG* 4420 23
Notes - � Another method of implementing the matrices is through using the matrix variables in LabVIEW. � Matrix values must be calculated by hand and inputted in the matrices manually. Aws Abu-Khudhair ENGG* 4420 24
Note – Plant/ Controller synchronization � A requirement of the Task 1 lab is to implement the SASS Plant controller in a separate task than the plant system. synchronization � Synchronization between the two Task 2 systems can be LQR Controller accomplished using: � Semaphore, or � Occurrences. Aws Abu-Khudhair ENGG* 4420 25
Deadlines and Marking � Lab 2 is worth 8% . � 4% for the report, and 4% for the demo � The Demo is due Oct. 12 th , 2010 in the Lab. � The Report is due Oct. 12 th , 2010 in the Lab. � A signed group evaluation sheet must be submitted with the lab report � QUESTIONS? Aws Abu-Khudhair ENGG* 4420 26
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