Description
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Objective
The main goal of this assignment is to design and implement controller for inverted pendulum system using state feedback controller and dominant pole method.
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Your responsibility
Your responsibility is to answer all questions which have been asked throughout this assignment and submit all your answers in addition to Matlab codes and Simulink results.
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Questions
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Using the linearized model introduced in previous lab, and coe cients in the lab manual, nd matrices A; B; C; D of state space representation of the system, and de ne them in matlab.
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Using matlab nd the transfer function of the system.
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Using system’s transfer function and the command pzmap, nd the place of poles of the system. Is the system stable?
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Using eig(A) compare the place of eigen values of matrix A with poles of the system.
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Check, whether or not your system is controllable.
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1
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Describe whether or not we should check observability conditions.
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Choose your design parameters (maximum overshoot and settling time), determine the place of two dominant poles of your desired system using following set of equations.
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P |
D1 |
;D23:9 |
n |
! |
n |
p |
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= :! |
1 2 |
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ts = |
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:!n |
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= |
s |
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2 + ln(pMp)2 |
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ln(M )2 |
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8. |
Using the place of dominant poles, determine the place of non-dominant poles of your desired |
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system.(choose non-dominant poles 5 to 15 times further than dominant poles from the |
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origin.) |
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9. |
Using the command place, nd state feedback gains. |
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10. |
Using calculated gains, implement a state feedback controller in the Simulink for the physical |
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system which uses cart’s position, cart’s velocity, angel of pendulum, and angular velocity. |
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(Hint: You should use low pass lter after derivative blocks). |
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11. |
Using the switch block in Simulink, design a mechanism to disconnect the controller when |
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the angle exceeds 10 . |
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12. |
Is your system able to stabilize pendulum around zero degree? If not, change your design |
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parameters and iterate over the steps until you achieve a proper controller. |
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13. |
You can ne tune your controller(manually), if you don’t change a gain by more than 5% of |
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its initial value. |
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14. |
Include all of the gains and parameters of your nal controller. Using the scope, show the |
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performance of your controller. (and all four states) |
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15. |
Changing each of the 4 di erent gains individually, describe intuitively the e ect of each of |
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these gains on the performance of your controller. |
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