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--- pid_vs_lqr_ballandbeam [2016/02/02 00:30] – joaomatos
+++ pid_vs_lqr_ballandbeam [2016/07/13 14:59] (current) – joaomatos
@@ Line 1: / Line 1: @@
-** __PID CONTROL__ **
+===== Lego Ball and Beam =====
+**Keywords:**Lego,NXT,Ball and Beam,PID,LQR.
- We can analyze the whole system into two distinct transfer functions , one for the ball and beam , and one for the motor. After , we can analyze the whole system putting these two transfer functions together in a block diagram.
- ** Ball and Beam Transfer Function Derivation**
+----
-{{ ::ball_system.jpg?direct&400 |}}
- Analyzing the equilibrium we have:
+===== Motivation and Audience =====
- {{::ball_derivation_1.jpg?direct&500|}}
+Motivation and Audience: This tutorial's motivation is to study about the mechanisms behind the control of a classical ball and beam problem,using Lego to build the structure and the NXT Brick to program the balance code using NXC(Not Exactly C) language and the Matlab environment. Readers of this tutorial assumes the reader has the following background and interests:
- {{:ball_derivation_2.jpg?direct&500|}}
- {{:ball_derivation_3.jpg?direct&600|}}
+.Automatic Controls Theory (PID and LQR)
+.Controls Programming using lego NXT Brick (NXC language).
+.Controls Programming using Matlab.
-** Motor Transfer Function Derivation **
- One easy way to get the motor's transfer function is to plot and analyze its response to an input , and by a graphical analysis get the parameters to derive its transfer function. We can program an algorithm to read and save ( using file saving functions ) the motor position during its operation. The following code was used to save and after plot the motor response until it get to the desired angle.
+----
+===== Parts List and Source =====
+[[ballandbeam_parts|Parts List]]
+----
+===== Construction Instructions =====
+{{::new_instructions_ball_and_beam.rar| Step by Step Building}}
+----
+===== System Modeling =====
+. [[ballandbeam_modelling|System Modeling.]]
+----
+===== Programming =====
+. [[ballandbeam_code|Programming]]
+----
-{{::motor_code_save.jpg?direct&500|}}