State Space Model - First Order Open Loop Frequency - Phase Lead Compensator - Mathematics Assignment Help

Assignment Task:

TASKS 
 
Task 1: First-Order Open-Loop Frequency Response 

a) From your knowledge of K and T , and the background theory, plot the asymptotic Bode diagram of the first-order open-loop system with input θi and output ω o on linear-log paper.  

b) Plot the experimental Bode diagram of the first-order open-loop system using the data of the open-loop frequency response test on linear-log paper. Hence estimate the value of the system gain K and the system time constant T . 
 
Task 2: Second-Order Open-Loop Frequency Response  

a) Determine the Bode diagram of the second-order open-loop system with angular position output using the data of the closed-loop frequency response test.  

b) Determine the phase crossover frequency, phase margin and estimate the value of the damping ratio. 
 
Task 3: Step Response of the Second-Order System 

a) Using the second-order open-loop transfer function obtained in Task 2

b) a model of the unity negative feedback system can be obtained and its step response simulated using MATLAB.

c) Use the simulated step response of the closed-loop system in Task 3a) to justify the need for a controller for the system and an appropriate type of controller. 
 
Task 4: Design via Frequency Response

a) Design a phase-lead compensator for the complete second-order open-loop system with angular position output.  

b) Use MATLAB to simulate the step response of the compensated system and verify your design by showing it meets the specifications. Give your evaluation of your compensator design. 
 
Task 5: Design via State Space 

a) Derive a state-space model of the complete second-order open-loop system with angular position output. Use this model to design a state feedback controller for the system. Explain how the design could be implemented using tacho feedback.

b) Assuming tacho feedback is not available, derive the compensator for observed state feedback using the state feedback controller and evaluate the compensator using MATLAB. Give your comparative evaluation of your observed state feedback design with your phase lead compensator design. 
 
Task 6: Conclusions: Given your conclusions with respect to your designed controllers and any insights gained from carrying out the assignment. 
 
In your design, you should be aiming for a maximum percentage overshoot of 5% and a settling time (to 2%) of less than 0.5 seconds. 
 
NOTE: all frequency response plotting should be done by hand. You may also confirm your hand-plotted results using the exported plots using Discovery software. 
 
The focus of the tasks to be done outside of the laboratory is the design. This work should be carried out individually and the tasks set are intended to encourage students to work with techniques presented in the term 1 lecture contain all the information needed to complete the tasks. You may discuss your ideas and problems in a general way with other students, but you must not copy or share text, calculations, etc. Any material ‘cut and paste’ from the web, or copied from any source, must be presented as a quotation (e.g. within “quotation marks”) and clearly referenced at the point where it occurs in the report. Violation of these rules is regarded as plagiarism which will result in misconduct. You may wish to arrange a time to go into the laboratory and implement your state feedback controller design using tacho feedback and proportional control, obtain the step response of the resulting closed-loop system, and compare your simulated and experimental step responses and evaluate state feedback control in comparison with phase lead control. However, no marks are given for this.

This EE3050 - Mathematics Assignment has been solved by our Mathematics Experts at My Uni Paper. Our Assignment Writing Experts are efficient to provide a fresh solution to this question. We are serving more than 10000+ Students in Australia, UK & US by helping them to score HD in their academics. Our experts are well trained to follow all marking rubrics & referencing style.

Be it a used or new solution, the quality of the work submitted by our assignment experts remains unhampered. You may continue to expect the same or even better quality with the used and new assignment solution files respectively. There’s one thing to be noticed that you could choose one between the two and acquire an HD either way. You could choose a new assignment solution file to get yourself an exclusive, plagiarism (with free Turnitin file), expert quality assignment or order an old solution file that was considered worthy of the highest distinction.