ballbeam20110127
所属分类：matlab编程
开发工具：matlab
文件大小：64KB
下载次数：33
上传日期：2011-02-04 01:35:45
上 传 者：
hamlin_dsouza
说明： BALLBEAM demonsrates Proportional-Derivative (PD) control as applied to a ball and beam simulation experiment. Execute by calling with no arguments.
P and PD controllers are implemented which manipulates the beam angle in response to the position of the ball on the beam. The setpoint is indicated by the red marker and adjusted using the slider at the bottom of the figure. The control gain, Kc, and the Derivative Time constant, Td, are adjusted by a sliders located in the right hand control panel.
Simulation data is stored in ballbeam.mat for subsequent analysis and parameter estimation.
This demo was originally developed with Matlab 5.3 and Matlab 6.0. Some of the user interface code was shamelessly ripped out of the standard Matlab demos. The demo is now updated for Matlab 2010b with additional documentation and suggested exercises for classroom use.
文件列表:
ballbeam.m (17377, 2011-01-27)
ballbeam.mat (16124, 2011-01-27)
html (0, 2011-01-21)
%% Ball & Beam Demo
%
% The ball & beam demo was created as a lecture and homework demonstration
% of basic modes of proportional and proportional-derivative control. It
% was originally written in 2001, and most recently tested in 2011 using a current
% version of Matlab. These notes describe basic concepts incorporated in
% the demo and possible homework exercises.
%% Operation
%
% The ballbeam.m file is a function that can be run with no arguments. To
% start the demo simply enter |ballbeam| at the Matlab command prompt.
ballbeam
%% User Interaction
%
% The demo starts up in manual mode. The vertical slider moves the end of
% the beam up and down. The bottom slider adjusts the setpoint indicated by
% the red marker. Push the |Run| button to start the simulation. The ball
% will roll back and forth on the beam as you move the beam position up and
% down. The simulation is stopped by pushing the |Stop| button or when the
% ball rolls off either end of the beam. A summary of the simulation
% results is shown in the plot.
%
% *Exercise*: Move the setpoint to a new place, press |Run|,
% and manipulate the beam position to settle the ball over the new
% setpoint.
%% Plotting Simulation Data
%
% Simulation data is stored in a file |ballbeam.mat| after each run. The
% data can be loaded and plotted as follows:
load ballbeam
clf
subplot(211);
plot(tdata,xdata,'b',tdata,xspdata,'r');
legend('Ball Position','Setpoint','Location','NW');
xlabel('Time (Sec.)');
subplot(212);
plot(tdata,udata);
legend('Beam Position','Location','NW');
xlabel('Time (Sec.)');
%% Dynamics
%
% The position of the ball is governed by a second order differential
% equation of the form
%
% $$ \frac{d^2x}{dt^2} = K_{beam} u$$
%
% *Exercise*: Design and perform a simulation experiment to
% estimate the parameter $K_{beam}$.
%% Proportional Control
%
% As the name suggests, under proportional control the beam position is set
% in proportion to the difference between the ball position and desired
% setpoint.
%
% $$ u = K_p(x_{sp}-x) $$
%
% Under the |Mode| menu, select proportional control (P) and use the slider
% controls to adjust $K_p$. Adjust the setpoint, then push |Run|. You can
% adjust the setpoint and control gain during the course of a |Run|.
%
% *Exercise*: What type of behavior do you observe? Substituting the the
% expression for the control action into the dynamical model leads to a
% second order differential equation. What is the solution to that
% equation?
%
% *Exercise*: Use the results of the above exercise to estimate the value
% of $K_{beam}$.
%% Proportional-Derivative Control
%
% Proportional control alone leads to an oscillatory response.
% Proportional-Derivative (PD) control adds
% additional damping through a derivative term in the control law
%
% $$ u = K_p(x_{sp}-x) - K_p\tau_d\frac{dx}{dt} $$
%
% where $\tau_d$ is the derivative 'time-constant'. Under the |Mode| menu,
% select proportional-derivative control (PD) and adjust the parameters
% with the associated sliders.
%
% *Exercise*: Set $K_p = 0.1$. How large does $\tau_d$ need to be to
% completely suppress overshoot of the setpoint?
%
% *Exercise*: Explore the response of the controlled system to a step
% change in the setpoint. Would you prefer an underdamped, critcally
% damped, or overdamped control system? Explain.
%
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