Lab 2: Real-Time Automotive Suspension system Simulator

Transcription

1 ENGG*4420 Real Time System Design Lab 2: Real-Time Automotive Suspension system Simulator TA: Matthew Mayhew Due: Fri. Oct 12 th / Mon Oct 15 th ENGG*4420 1

2 Today s Activities Lab 2 Introduction. Lab 1 Demos. Start work on Lab 2. Note that some numbering is repeated for a few of the equations in the lab manual section for Lab 2. Equations referenced in this presentation match the numbering currently used. ENGG*4420 2

3 Lab 2 Development Environment HP PC LabVIEW 2009 software ENGG*4420 3

4 Introduction Types of vehicle suspension systems Passive Suspension System. Active Suspension System. Semi-Active Suspension System. SASS. Road disturbance Step Input. Harmonic Input. ENGG*4420 4

5 Passive Suspension System Standard vehicle suspension system. Employed in the majority of commercial vehicles. Advantages: Low cost. Simple implementation. Disadvantages: Purely passive elements. On-line performance optimization not possible. k s Vehicle body k t b s Tire z u z r z s ENGG*4420 5

6 Active Suspension System Fully active system. Computer controlled active element (F a ). Advantages: Offers excellent performance. Allows for control and performance optimization at any point during lifetime. Disadvantages: High cost. Major safety issues. High power demand. Vehicle body k t Tire F a z s z u z r ENGG*4420 6

7 Semi-Active Suspension System Hybrid system (Passive + Active elements). Provides excellent fail safe mechanism. Relatively low cost. Provides a performance comparable to the active system. Very low power demand. k s Vehicle body b s k t Tire z s b semi z u z r ENGG*4420 7

8 Quarter-Car Suspension Model z s z s m s m s Active element k s b s z u k s b s b semi z u m u m u z r z r k t k t Passive Suspension System Semi-Active Suspension System ENGG*4420 8

9 Quarter-Car Suspension Model cont. The system can be modeled using state space representation: Passive: Semi-Active: X & = AX + Lz& r & = AX + NXb + Lz& semi r X The two models are equivalent when the variable damper coefficient is set to 0.,, ENGG*4420 9

10 State Space Model X & = AX + NXb + Lz&, eq 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 ENGG*

11 State Space Model = = = Tire deflection sprung mass Velocity of Suspension deflection 2 1 s u s z z z z z x x x X & ENGG* mass unsprung Velocity of Tire deflection 4 3 u r u z z z x x & - Derivative of the state vector over the sampling time. - Derivative of the road disturbance over the sampling time. X & Z & r

12 Road Disturbance Step Input: Isolated sudden disturbance. Ex. Curb with a height of 10 cm. Z r = 0.1m Road Input Z r (t) 0 Time (t) ENGG*

13 Road Disturbance cont. Harmonic Input: Simple road profile. Modeled as a Sine wave with: Freq. 1 Hz. Amp. 10 cm. Phase 0. ENGG*

14 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. ENGG*

15 Linear Quadratic Regulator (LQR) The controller works towards minimizing the performance index given in equation (2.13). J T = lime T x& 2 + ρ1x1 + ρ 2x2 + ρ3x3 + ρ 4x4 eq The controller determines the required ideal active force (F a ) to stabilize the vehicle. ENGG*

16 Linear Quadratic Regulator (LQR) Cont. The active force (F a ) can be calculated using Equation (2.14) in the lab manual. G 1 = R T ( B P+ S0 ) F a = G X eq The representation of G is shown in Equation (2.15). eq ENGG*

17 Semi-Active Control Law (LQR) The optimal control law is determined using Fig 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 ENGG*

18 Semi-Active Control Law (LQR) cont. The LQR control method is summarized in table 2.2. ENGG*

19 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). ENGG*

20 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 (ρ i values in Eqn. 2.15) and observe the change in performance of the SASS. 3. Provide a measure to differentiate the difference in performance of the two systems (% difference?). ENGG*

21 Requirements 1. Fully functional passive and semiactive 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 of the lab manual. Step Harmonic ENGG*

22 Requirements 3. The following performance graphs must be present on the front panel: Vehicle ride quality ( 2). Suspension deflection response (X 1 ). Tire deflection response (X 3 ). Input disturbance to the system. 4. LQR control must be performed using a separate Task (loop with a timing VI) from the plant system. Time LabVIEW NOT required. X & ENGG* Real-

23 Notes Matlab Script Nodes The matrices 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 definition. ENGG*

24 Notes Matlab Script Nodes Matrices can be multiplied and added as long as the dimensions are consistent. To transpose a matrix add a after the matrix variable. Element wise multiplications can be performed using a.*. Matrix multiplication can be performed with a *. Dot products can be determined with the dot(x,y) function. ENGG*

25 Notes Matrix 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. Allows for the use of LabVIEW VIs to perform operations. Values may also be entered as an array and converted to Matrix form. ENGG*

26 Notes Plant/Controller synchronization A requirement of the lab is to implement the controller in a separate task than the plant system. Synchronization between the two systems can be accomplished using: Semaphores, or Occurrences. Task 1 Task 2 SASS Plant LQR Controller synchronization ENGG*

27 Notes - Structures Queues can be used to pass values between loops. Found in the Data Communication palette. ENGG*

28 Notes - Structures Flat Sequences can be used to make sure operations occur in order. Timing VIs can be found in a sub-palette of Programming. ENGG*

29 Notes - Structures MatLAB nodes can be found in the Structures sub-palette. Arrays and Matrixes found in the Programming palette. ENGG*

30 Demo Front Panel Performance Metrics Controls Passive Control Semi-Active Control Road Profile Task Communication ENGG*

31 Report Can use general structure similar to first lab. Implementation of model and controller. Communication/Synchronization between tasks. Implementation challenges and solutions. Performance Metrics. Semi-Active vs. Active Control. Effect of road profile. Weighting Factors. ENGG*

32 Deadlines and Marking Lab 2 is worth 8%. 4% for the report, and 4% for the demo. The Demo is due Oct 12 th /Oct. 15 th, 2012 in the Lab. The Report is due Oct 12 th /Oct. 15 th, 2012 in the Lab. Physical and Electronic copy. A signed group evaluation sheet must be submitted with the lab report. Do NOT include student numbers with the lab report. ENGG*