School of Engineering and Applied Science
ME3050 Advanced Dynamics and Control
You have been deferred or referred in ME3050. To satisfy the deferred or referred requirement you are required to provide full solutions to the following problems.
In order that you pass this deferred or referred coursework you must provide FULL and HIGH quality solutions to BOTHPart ACoursework AND Part B Questions, answeringALL FOUR questions in Part B. Use of MatLab or Simulink is required for the Part A coursework assignment, and is allowed for the questions. However, answers to the questions must be written and explained, not just copied from MatLab output.
Untidy working, lack of explanation and misuse of units WILL be heavily penalised.
You may use any reference material available to you and have unlimited time to complete the questions.
Your report, MatLab script and solutions must be scanned in and uploaded to the ME3050 Blackboard site by 26th August 2015.
Part A: Coursework
This is an individual exercise in which you will design a control system, analyse its performance and submit a brief report (5 pages maximum firm). You will design a motion control system to align the azimuth angle for a parabolic reflector for a concentrated solar collector. The reflector weighs 2.5 kg, has a moment of inertia of 6.25 kg m2, a collection area of 20 m2, and is carried by a rover that will operate remotely on Europa, the fourth largest of Jupiter’s moons. The rover will need to move hundreds of kilometres over rough terrain, around obstacles and over hills and valleys.
As the terrain has not been mapped previously, the reflector needs to be able to align itself towards the sun to maximize the power generation during daylight hours. Europa is covered in (water) ice and has a very thin atmosphere. Clouds and winds should not affect the collector. The rotation of the reflector will be controlled using a separate system, which is not part of this project. Your control system should control the azimuth angle of the reflector to maximize net power generation while the rover is moving or stationary.
You are required to design a suitable actuation and motion control system to align the azimuth angle of the reflector for maximum net power generation as far as is practical taking into account the power consumption of the motion control system. The system should also have the minimal weight required to perform the required task in the given environment. You should determine the optimal response of the system and design it accordingly. You should also determine the time response to impulse, step and ramp input functions. Reasonable assumptions may be made, but should be stated explicitly in the report.
Rules of Engagement:
- This is an individual exercise. You must not share computer files.
- The assignment is to be submitted via Blackboard by the due date and time. Submissions must contain your final Matlab/Simulink files including any scripts, functions and data files; any spreadsheets used and a report typed in Microsoft Word. These should all be zipped in to the same folder and submitted via Blackboard.
- This assignment is worth 20% of the module total.
- Design of the motor control system and meeting design requirements: [8 marks]
- Analysis of the control system performance and simulation of time response: [8 marks]
- Report – layout, focus, quality of written English, quality of figures, referencing: [4 marks]
Part B: Questions
Q1. The mechanism in Figure 1 below is part of a weighing balance consisting of a platform suspended above an electromagnetic actuator. Data are provided in the table.
|k1||2 N A-1|
|k2||300 N m-1|
Figure 1: Actuator mechanism
The actuator exerts an upward force f on the platform that depends on the current i applied and on the vertical position z of the platform:
f = k1 i –k2 z
Mechanical damping is negligible.
- Write down the equation of motion for the mechanism and find the transfer function G(s) to relate the position Z(s) to the input current I(s). [6 marks]
- This mechanism is incorporated in a closed-loop feedback system designed to keep the platform at a set height, as shown below. Find the transfer function for this system.
- For the values of parameters given in the table below, find the value of K that will provide critical damping. [5 marks]
- Find the 2%-settling time with the value of K calculated above. [4 marks]
Q2. Figure 2 shows a DC servo motor used to position a gun turret via a pair of gears. Parameters relating to the motor are shown in the table.
|Voltage constant (=torque constant)||20 rad s-1 V-1|
|Rotary inertia||0.3 kg m2|
|Winding resistance||0.5 W|
Figure 2: Gun turret and motor parameters
- Draw an equivalent circuit for the DC motor, neglecting inductance of the windings.
- Show that the transfer function G(s) relating the angular position of the turret to the voltage applied to the motor has the form
and determine the values of the constants a and b [9 marks]
The block diagram below shows the motor incorporated into a closed-loop system using a PI controller. Work out the closed loop transfer function for this system and determine the value of K to make the system just gounstable. [8 marks]
Q3. (a) Find the transfer function G(s)=X2(s)/F(s) for the mechanical system shown in Figure 3 below, where F(s) is the Laplace transfer of f(t) and X2(s)is the Laplace transfer of x2(t).
Figure 3.Mechanical system
(b) A system has the transfer function
You are required to represent this system in state space as follows:
Find the values of the coefficients of the matrices A, BandC [8 marks].
Q4. Figure4 shows a two tank system. The liquid inflow into the upper tank can be controlled using a valve, with the flow through the valve represented as F0. The outflow from the upper tank equals the inflow to the lower tank, which is represented as F1. The outflow from the lower tanks is F2. The objective is to control the liquid level ,y(t), of the lower tank. The open loop transfer function for this system is:
The system will be controlled by a unity feedback loop, where the liquid level will be measured and compared to a set point. The resulting error will be fed to a controller toopen or close the valve feeding the upper tank, which modifies the flow F0.
- a) Design a lag compensator to obtain a steady state error of 10% for a step input with negligible effect on the system’s transient response. [12 marks]
- b) Verify that the compensated system is stable. [4 marks]
- c) Explain briefly the advantages of lag compensation over PI compensation. [4 marks]
Formula Sheet For Use In ME3050 Examinations
whereu(t) is the unit step function
Damping ratio and phase margin:
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