代做Experiment 81 – ELEC207 coursework Design of a Stable Martian Segway 2021调试Haskell程序

Experiment 81 – ELEC207 coursework

Design of a Stable Martian Segway

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1. Mathematical Modelling

A) Please define the values for l, m and t_s that you will use for your coursework. [1E]

B) Now derive the transfer function, H(s)=θ(s)/T(s), of the Segway in terms of l, m and g. [1E]

C) Using your values for l and m along with g=3.711 ms^-2, write the transfer function with the denominator and numerator of your transfer function in polynomial form. [1E]

D) Calculate the position of the poles for your Segway and plot the poles on the complex plane. [1E]

2. Validating that the Open-loop System is Unstable

E) Insert a picture of the time-response of your Segway to the unit-step. [2E]

F) Comment on whether this time-response indicates that the open-loop system is stable. [1M]

3. Ensuring that the Closed-loop System is Stable Using PID Control

G) Write the closed-loop transfer function for your Segway in terms of K_p, K_I and K_D as a ratio of polynomials in s. Ensure that the highest order term in s in the denominator has a coefficient of unity. [3M]

H) What is the characteristic polynomial that would result in these pole positions? [1M]

I) By equating the coefficients in the closed-loop transfer function’s denominator and this characteristic function, deduce values for K_p, K_I and K_D which will ensure that the closed-loop system is stable. [3M]

4. Validating That the Closed-loop System is Stable

J) Insert a picture of the time-response of your closed-loop system to the unit-step.  [2M]

5. Optimising the Time-Response Using Root Locus

K) Calculate the positions of the open-loop zeros (ie the zeros of C(s)H(s)) for the values of l, m, K_p, K_I and K_D that you have used. [1M]

L) State the positions of the open-loop poles (ie the poles of C(s)H(s)) for the values of l and m that you have used. [2E]

M) Sketch the root locus for C(s)H(s) and identify the points on the root locus that are such that Re(s) = — 4/ts.  [3M]

N) Write the open-loop transfer function, C(s)H(s), as a ratio of polynomials in s. [1H]

O) Write  as a polynomial in s involving K.  [1H]

P) Write  as a polynomial in  involving K. [1H]

Q) Complete a Routh table for  Deduce the value of k that is such that Re(s) = — 4/ts [3H]

6. Validating the Response of Optimised System

R) Insert a picture of the time-response of your improved closed-loop system to the unit-step.  [2H]