ME568-HW3-2024_updated

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ME 568 Vehicle Control Systems Winter 2024 1 Homework 3 (Due on Wednesday 3/13 11:59pm ET via Canvas) The tables, equations, and examples in this homework set are referring to the course textbook “ A. G. Ulsoy, H. Peng, and M. Çakmakci, Automotive Control Systems. Cambridge: Cambridge University Press, 2012 .” You may find this book online through the University of Michigan Library and download the pdf version via campus Wi-Fi. For each homework problem, whenever applicable, please also submit the code and/or the model file you created. Problem 1-Engine dynamics (25%) Consider the closed-loop idle speed control system given in Example 8.1 (see Fig. 8.3). Neglect the IP delays and the effects of sampling, and replace the controller 𝐾?/(? − 1) by the integral controller 𝐾 𝐼 /? . In Fig 8.3, the system includes fuel control based upon estimation of the mass flow rate as in Eq. (3.4). Thus, in this controller Δ𝜃 = −(𝐾 𝐼 /?) Δ𝑁 , Δ𝛿 = ? ? Δ𝑁 , and from Eq. (3.4), Δ? 𝑑 = ?𝑁 0 Δ𝑃 + ?𝑃 0 Δ𝑁 . (a) The linearized engine dynamics model without IP delays is given in Example 3.2, see Eq. (3.9-3.12). Using the above relationships for the controller, derive the closed-loop system equations: 𝒙̇ = 𝑨 𝒙 + 𝒃 𝒗 𝑣 , and ? = 𝑪 𝒙 , where 𝒙 = [ Δ𝜃 𝑚 ? Δ𝑃 Δ𝑁 ] and 𝑣 = Δ𝑇 𝑑 , ? = Δ𝑁 . What are the 𝑨 , 𝒃 𝒗 , 𝑪 matrices? Show the derivation. (b) Simulate the system to a unit step disturbance torque input for time span ? = 0: 0.01: 5 . Use the model parameter values : τ P = 0.21, 𝐾 𝑃 = 0.776, ? 𝑃 = 13.37, 𝜏 𝑅 = 3.98, 𝐾 𝑅 = 67.2,𝐾 𝑁 = 0.08, ? 𝑓 = 36.6,𝐾 𝜃 = 20 , and ? 𝛿 = 10 . The controller parameter values: ? ? = −0.005, ? = 0.000125,𝑁 0 = 600, 𝑃 0 = 12. Use the following controller integral action gains: 𝐾 𝐼 = 0.06, 0.006 and 0.0006 . Which one gives qualitatively similar response to the bottom panel of Fig. 8.4? How does the choice of 𝐾 𝐼 affect the response? (c) Use ? ? = 0 (i.e., no coordination with spark ignition control) and the controller integral action gains: 𝐾 𝐼 = 0.006 and 0.0006. Compare the results to part (b).

ME 568 Vehicle Control Systems Winter 2024 2 Problem 2-Engine dynamics (25%) Consider the same closed-loop engine in Problem 1 above, but with the following alternative control strategies: (a) Use a proportional plus integral (PI) control where Δ𝜃 = −(𝐾 𝐼 /?) Δ𝑁 − 𝐾 Δ𝑁 . What are the new A and b v matrices? Show 5-second simulation result (use same step input in Δ𝑇 𝑑 and Δ𝑁 as output), for ? 𝑠 = 0 , 𝐾 𝐼 = 0.001 , 𝐾 = 0.01 . Plot Δ𝑁 ∈ [−6, 6] . (b) Use the feedforward plus PI control, Δ𝜃 = − ( ? 𝐼 𝑠 ) Δ𝑁 − 𝐾 Δ𝑁 + Δ𝜃 𝐹 , Δ𝜃 𝐹 = 𝐾 𝐹𝐹 Δ𝑇 𝑑 (i.e., assume the disturbance Δ𝑇 𝑑 is measured or can be estimated). Determine the feedforward gain 𝐾 𝐹𝐹 , such that the non-zero throttle at the new steady state is given by the feedforward signal Δ𝜃 = Δ𝜃 𝐹 . Show 5-second simulation results with ? 𝑠 = 0 , 𝐾 𝐼 = 0.001 , 𝐾 = 0.01 and the 𝐾 𝐹𝐹 you found. Plot Δ𝑁 ∈ [−6, 6] and compare it to part (a). (c) This time u se the maximum control design degree of freedom (Spark+PI+feedforward) and tune all the gains ( ? 𝑠 , 𝐾 𝐼 , 𝐾, 𝐾 𝐹𝐹 ) until you are satisfied with the results. Explain how the controller gains were determined. Problem 3-IDM simulations (25%) Consider the following Intelligent Driver Model (IDM): 𝑣̇(𝑣, 𝑣 ? ) = ? (1 − ( 𝑣 𝑣 0 ) 𝛿 − ( ? ∗ (𝑣, 𝑣 ? ) ? ) 2 ) with ? ∗ (𝑣, 𝑣 ? ) = ? 0 + max (0, 𝑣𝑇 + 𝑣(𝑣−𝑣 𝐿 ) 2√?? ) , ? = 0.73 m/s 2 , ? = 1.67 m/s 2 , 𝛿 = 4 , 𝑣 0 = 30 m/s, ? 0 = 2 m , 𝑇 = 1.5 s. Simulate the velocity 𝑣 and the distance ? of the ego vehicle with initial velocity and 𝑣(0) = 20 m/s and initial distance ?(0) = 36 m, ? = 0: 0.1: 100 . Consider the following velocity profiles for its leading vehicle: (a) 𝑣 ? (?) = 20 + sin ? . (b) 𝑣 ? (?) = { 20 − ?, 0, ? ≤ 20 ? > 20 . Repeat (a) and (b) for ? 0 = 5 m, keep all other parameters the same. Comment on the plots of distance ? for different ? 0 Hint: Use ode45 for the simulation. You will need one more equation ?̇ = 𝑣 ? − 𝑣 . Moreover, the velocity should always be non-negative in the simulation, i.e., the car is not reversing.

ME 568 Vehicle Control Systems Winter 2024 3 Problem 4 - HEV(20%) Compare the simulation results for a series hybrid electric vehicle and a parallel hybrid electric vehicle for given drive cycle data : CYC_HWFET.mat and CYC_US06.mat The engine parameters are given in: engine_parameters.mat. You can build the simulations from the provided codes (also in the book) “ ex10_3.m ” (series) and “ ex10_5.m ” (parallel) in the homework 3 folder. “ ex10_ 2.m” and “ ex10_ 1.m” are provided for running the “ ex10_3.m ”, though they have been included in “ ex10_5.m ” already. The following figure shows the simulation results for the parallel hybrid electric vehicle on the CYC_US06.mat, if you run “ ex10_5.m ” with the default parameters given in the book. In this problem, please use the following parameters for each HEV: Series: SOC_max_power = 0.25; SOC_low = 0.35; SOC_high = 0.50; threshold_power = 42; % kW max_power = 84; % kW Battery_capacity = 2.5; % kW-hr Parallel: Battery_capacity = 2.5; % kW-hr P_ev = 20; Pe_max = 70; P_ch = 20; SOC_t = 0.35;

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ME 568 Vehicle Control Systems Winter 2024 4 For both simulations , scale down the engine by 30% and use the same battery capacity: engine_torque = engine_torque*0.7; fuel_map = fuel_map*0.7; Battery_capacity = 2.5; % kW-hr The initial SOC for both simulations is: SOC(1) = 0.5; Keep other parameters the same as in the original script. (a) Present the simulation results (similar to the figure above) for two HEVs on the data CYC_HWFET.mat. Comment on the difference between two HEVs. (b) What if we run both HEV on the data CYC_US06.mat? Present the simulation results and compare them with part (a). You may try other dataset s, e.g., urban traffic “ CYC_UDDS .mat” , and play with the parameters (not required). Project Related Assignment (5%) Please provide a brief (one paragraph) progress report on your project (e.g., modeling, simulation, controller design, etc.). Please submit this as a separate page from the rest of your homework assignment, and only submit one per team, indicate your team number.