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--- lego_rip_modeling [2016/04/30 18:10] – joaomatos
+++ lego_rip_modeling [2017/07/21 15:37] (current) – joaomatos
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-**SYSTEM MODELING**
+===== System Modeling =====
-This section is divided as following:
+After following this tutorial you will be able to find the full state feedback gains to be used on the NQC Code to control your Lego Rotary Inverted Pendulum.
-  * SELECTING THE CONTROL METHOD - FULL STATE FEEDBACK USING LQR
+The first derivation is for the virtual simulation using Simulink - The output is the Torque. The second derivation is for your real project , that will use the DC-motor voltage as output.
-  * STATE-SPACE REPRESENTATION
-  * FINDING THE STATE-SPACE REPRESENTATION
-  * CALCULATING THE OPTIMAL GAIN MATRIX USING MATLAB
-After reading this steps , you will find the full state feedback gains to be used on the NQC Code to control our Rotary Inverted Pendulum.
+**References**
+[[http://www.saadat.us/download/3_Inverted_Pendulum_Project.pdf|[1]]]
+[[http://engineering.nyu.edu/mechatronics/Control_Lab/ROTPEN_SE.pdf|[2]]]
+[[http://file.scirp.org/pdf/WJET_2015052217370851.pdf|[3]]]
+[[http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac11-proceedings/data/html/papers/2933.pdf|[4]]]
+[[http://www.iop.vast.ac.vn/theor/conferences/nctp/proc/37/243-249.pdf|[5]]]
-----
+**You can find the Matlab Script to run the [K] matrix calculation here **
+{{:rip_kit.rar|}}
-**SELECTING THE CONTROL METHOD - FULL STATE FEEDBACK USING LQR**
-{{::rip_pap_1.jpg?direct|}}
 ----
-**STATE-SPACE REPRESENTATION **
+===== Derivation for Simulink Simulation =====
-{{::rip_pap_2.jpg?direct|}}
+Use this derivation if you want to simulate the system virtually trough Simulink. This derivation will neglect the friction in the motor rotation , friction in the pendulum rotation and will USE TORQUE as input to the state-space representation . The real model , have rotation friction , and use Voltage in the DC motor as input ( you can find this derivation on this same page).
+{{ ::rip_der_sim1.jpg |}}
+{{ ::rip_der_sim2.jpg |}}
+{{ ::rip_der_sim3.jpg |}}
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+{{ ::rip_der_sim5.jpg |}}
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+{{ ::rip_der_sim8.jpg |}}
+{{ ::rip_der_sim9.jpg |}}
-{{::rip_pap_3.jpg?direct|}}
 ----
-**FINDING THE STATE-SPACE REPRESENTATION **
+===== Derivation for Real Project =====
-{{::rip_pap4.jpg?direct|}}
-{{::rip_pap5.jpg?direct|}}
+This derivation is closer to reality the output from the state-space representation is the DC voltage, that is applied to the Lego Motor.
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+{{ ::rip_der_real1.jpg |}}
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+{{ ::rip_der_real10.jpg |}}
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+{{ ::rip_der_real16.jpg |}}
-----
-**CALCULATING THE OPTIMAL GAIN MATRIX USING MATLAB**
-{{::rip_pap17.jpg?direct|}}
-{{::rip_pap18.jpg?direct|}}
-{{::rip_pap19.jpg?direct|}}
-{{::rip_pap20.jpg?direct|}}