ACS Assignment 2023/2024
Module AE03 – Automotive Control and Simulation
Design Exercise – Range Extender Speed Controller
A range extender is a specialist engine designed to provide auxiliary power to a battery electric vehicle. Conventional engines designed to produce high torques, but for a range extender, we are more interested in designing something that can provide optimal efficiency. A typical range extender runs at a steady speed at a high-efficiency point in its operating envelope driving a generator connected to the system’s battery.
In this exercise, you will design a speed control system for a range extender. The problem has been simplified, but it should still give you a feel for some of the things that are involved. As an input, you are given a throttle demand – this represents the input to a throttle actuation mechanism, in the range 0–1. You will notice that the model experiences changes in torque load that you do not know or measure. You can measure the engine speed but the sensor – like most real-world sensors – is ‘noisy’.
You will be taken through a design exercise through a series of five questions. You will start by obtaining models suitable for control design, then you will design and test controllers with different techniques. At the end of the assignment, you should have a good practical understanding of the concepts required to design a feedback controller
The Intended Learning Outcomes for the Module are:
1. Evaluate an automotive system (in terms of its performance, robustness, and sensitivity to noise and disturbances) using classical control concepts and methods.
2. Design feedback control algorithms to meet specified performance requirements using frequency-domain ‘loop-shaping’ methods and PID techniques, and to understand trade-offs and limitations on what can be achieved.
3. Create Simulink simulations of multi-domain automotive systems suitable for performance analysis and control system design and assess control systems with these models.
4. Evaluate operating points and construct linearized state-space and transfer function modules using MATLAB and Simulink.
5. Construct a linear observer (state estimator) using pole-placement methods and inspect its behaviour using MATLAB and Simulink.
As you undertake the assignment, you will quickly see the relationship with these ILOs. As well as letting us prove your new capabilities, this exercise is intended to provide a further learning opportunity. It may take you a while to get your head round some of the ideas, but once it ‘clicks’, you’ll understand it for life. Good luck, and please enjoy the exercise!
acs2023_assignment_brief 1/6 October 2023
Handing this work in
I ask students to submit a write-up on this assignment. It’s not a formal ‘report’ – it just needs to have answers to the questions. You will need to include enough of your working – your thoughts, calculations, MATLAB code and Simulink models – so that I can see that you’ve thoroughly answered each question. I cannot mark what I do not see, so if in doubt, please put it in.
You do not need to hand in a printed copy, and you do not need to hand in electronic copies of your MATLAB and Simulink files. (You should give enough detail on these in your write- up.)
You must upload your work on this assignment via Canvas as instructed there. If your work is late, you risk having your mark capped at 50% or – if it’s very late – failing with a zero mark.
Please contact your Student and Academic Support Lead with any questions about handing work in.
You have a week to complete the assignment. Please use this time wisely. Candidates who leave this assignment to the last minute often struggle, sometimes with disastrous consequences. It’s considered good teaching practice to allow you some time ‘on your own’ to try to tackle the problem, but I will be willing to provide help to students with any questions via the discussion forum and assignment feedback seminars. Please do make good use of this opportunity. Often, when students are struggling, it’s only a small problem that is getting in their way of their progress, and I can usually very quickly help. Remember that this exercise is supposed to be ‘hard’. But please also remember that most students do succeed, and their hard work pays off with good results. This exercise is a key part of your deep learning: hopefully, you will enjoy it, too.
How this work will be marked
Please bear in mind the university mark scheme for subjective assignments. Design is a subjective task, and there is rarely a single unique answer to a question.
To get ‘excellent’ marks on a question, it is necessary to ‘push the boundaries’ in your answer. Candidates who get excellent marks typically display an unusual level of thoroughness and insight. Obviously, I’d encourage you to strive towards this if you can. If you don’t quite manage this, a reasonably thorough attempt with no serious mistakes can get a ‘very good’. Work with more serious mistakes or omissions, but that still indicates a reasonable understanding will be graded as ‘good’ or ‘satisfactory’. Incomplete answers and seriously incorrect work are graded at ‘poor’ or lower. Each question is graded separately: the marks are added to get a total mark, then rounded to the nearest whole number.
Candidates should attempt any question: bear in mind that an absent answer gets a zero mark, even a ‘poor’ answer can be worth up to 40% of the question’s marks. It really is worth having a go at every question.
acs2023_assignment_brief 2/6 October 2023
The course director has set the minimum mark for this assignment at 50%. Please try to pass first-time: at Cranfield, retakes are an emergency provision, and not ‘normal’.
Good luck, and enjoy the experience! ☺ D. J. Auger
October 2023
acs2023_assignment_brief 3/6 October 2023
Questions
1. A permanent magnet DC motor such as the generator attached to the range extender can be represented using the electrical schematic shown in the diagram below.
Assume that the electrical parameters of the motor are Ra = 0.12 ohms, La = 0.0012 H, kE = 0.2 units, and the motor’s rotor has a moment of inertia Jm = 0.25 kg m2.
a) Write down the differential equations describing the relationship between the rotor’s angular velocity and angular displacement in response to a voltage input.
b) By finding an expression for the angular acceleration in terms of other variables and then integrating this, implement a Simulink model of the motor. By considering step inputs of up to 48 V, use the model to illustrate the effects of ‘back EMF’ in the motor current. (You may need to read up on motors to do this.)
c) Using Laplace transforms, convert your differential equation into a transfer function. Comment on the locations of any poles and zeros and explain how these relate to your observed simulation behaviour.
[20 marks]
2. You have been given a set of Simulink models representing the range extender rig. The main one is called ‘m01_plant_model.slx’.
a) Examine the model, and briefly answer the following questions:
(i) Which (if any) blocks in the model represent nonlinearities? Is the overall model linear or nonlinear?
(ii) How are noise and disturbances modelled? (iii) What are the model’s states?
acs2023_assignment_brief 4/6 October 2023
b) Write a MATLAB program to trim and linearize the version of the model in the file ‘m02_linearization_model.slx’ for a steady-state speed of 2500 rpm. (You can use the supplied trimming function to help you.) Include a listing for your program in your write-up, as well as the transfer function. Use Simulink to compare the linear model with the original nonlinear one.
If you can’t solve this question, there is a MATLAB file containing the outputs you would have got, which you can use for the rest of the assignment.
[20 marks]
3. Use frequency domain loop-shaping to design a feedback controller for the range extender’s speed. Aim for:
A stable system, with phase margin >= 60 degrees.
Steady-state disturbance rejection better than 25 rpm.
Peak-peak noise in throttle signal < 0.025
At least 450 rpm response to 500 rpm demand from a starting point of 2500 rpm in 2 sec.
Peak overshoot < 2%.
Your answer should include plots, code samples, etc., that illustrate your design process. You should ensure that you include a Bode plot showing your gain and phase margins, Bode magnitude plots showing T(s), S(s) and C(s) S(s) – if you use a prefilter, you should also include R(s) = T(s) Q(s).
You should test your controller in Simulink, showing a screenshot of your model’s top level and relevant plots. Consider small speed demands (a few tens of rpm) and larger demands. How big can the angle be before you see significant effects from nonlinearities in your system?
[20 marks]
4. Repeat Question 3, but this time use a PID controller using the following controller structure:
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How does this relate to the ‘PID weights’ in the lecture notes? (Algebra is required here!)
Design your controller in the frequency domain using proportional, PI and PD weights, as shown in lectures. Do not use a prefilter.
In addition to answering the specifics asked for in Question 3, comment on and the advantages and disadvantages of the simplified PID method compared to the ‘full’ frequency-domain loop-shaping method.
(Do not use the MathWorks PID Tuner – the resulting controllers are not ‘pure’ PID controllers.)
[20 marks]
acs2023_assignment_brief 5/6 October 2023
5. Using the pole placement method, design an observer that can estimate the state variables. Implement this in Simulink and determine how effective it is.
Your answer should include the following:
a) The state space model you use, with the states clearly identified.
b) Relevant code snippets showing how you found the observer gains.
c) Your Simulink model with the observer added. (Don’t forget to account for the operating point input u0 in your implementation.)
d) A comparison between your observer’s state estimates and the state measurements from the model’s measurement bus. Comment on how effective this is.
[20 marks]
acs2023_assignment_brief 6/6 October 2023
