mirror of
https://github.com/ME-561-W20-Quadcopter-Project/Quadcopter-Control.git
synced 2025-09-03 14:03:15 +00:00
Code Cleanup & Project Name Update
- Cleanup LQR.m and add whitespaces - Change project name in README and home - Add Source Code section to home.md describing each file
This commit is contained in:
Sravan Balaji
@@ -2,7 +2,7 @@
|
||||
|
||||
UMICH EECS / MECHENG 561: Design of Digital Control Systems WN 2020
|
||||
|
||||
Full State Feedback and Control of a Quadcopter Drone
|
||||
A Comparison of Quadcopter Drone Control Methods
|
||||
|
||||
## Documentation
|
||||
|
||||
|
||||
21
docs/home.md
21
docs/home.md
@@ -1,8 +1,9 @@
|
||||
# Full State Feedback and Control of a Quadcopter Drone <!-- omit in toc -->
|
||||
# A Comparison of Quadcopter Drone Control Methods <!-- omit in toc -->
|
||||
|
||||
## Table of Contents <!-- omit in toc -->
|
||||
- [Contributors](#contributors)
|
||||
- [Documents](#documents)
|
||||
- [Source Code](#source-code)
|
||||
|
||||
## Contributors
|
||||
|
||||
@@ -23,3 +24,21 @@
|
||||
|
||||
1. [Project Proposal](1.%20ME%20561%20Project%20Proposal.pdf)
|
||||
2. [Final Report - Overleaf (Read-Only)](https://www.overleaf.com/read/kyjvdsxkfnmg)
|
||||
|
||||
## Source Code
|
||||
|
||||
### [LQR.m](../src/LQR.m) <!-- omit in toc -->
|
||||
|
||||
Finite and infinite time horizon LQR implementation in MATLAB. Gains determined for linearized discrete time system, then simulated on nonlinear system (see LQRNonlinearSim.slx below).
|
||||
|
||||
### [LQRNonlinearSim.slx](../src/LQRNonlinearSim.slx) <!-- omit in toc -->
|
||||
|
||||
Simulink nonlinear model that is run from within LQR.m. Takes gain matrix **K** and initial condition **x_0** as input.
|
||||
|
||||
### [PlantModel.m](../src/PlantModel.m) <!-- omit in toc -->
|
||||
|
||||
Parameters for PID controller (see PlantModelSim.slx below).
|
||||
|
||||
### [PlantModelSim.slx](../src/PlantModelSim.slx) <!-- omit in toc -->
|
||||
|
||||
PID control of nonlinear and linear system.
|
||||
|
||||
61
src/LQR.m
61
src/LQR.m
@@ -1,9 +1,14 @@
|
||||
% Clear workspace
|
||||
clear all; close all; clc;
|
||||
clear all;
|
||||
close all;
|
||||
clc;
|
||||
|
||||
% Parameters source: https://sal.aalto.fi/publications/pdf-files/eluu11_public.pdf
|
||||
g = 9.81; m = 0.468; Ix = 4.856*10^-3;
|
||||
Iy = 4.856*10^-3; Iz = 8.801*10^-3;
|
||||
g = 9.81;
|
||||
m = 0.468;
|
||||
Ix = 4.856*10^-3;
|
||||
Iy = 4.856*10^-3;
|
||||
Iz = 8.801*10^-3;
|
||||
|
||||
% States:
|
||||
% X1: x X4: x'
|
||||
@@ -69,31 +74,31 @@ continuous = ss(A, B, C, D);
|
||||
T_s = 0.01;
|
||||
discrete = c2d(continuous, T_s);
|
||||
|
||||
%Check if this works
|
||||
% Check if this works
|
||||
impulse(discrete, 0:T_s:1);
|
||||
|
||||
%We should see that U1 gets us only translation in z, U2 couples Y2 and Y4,
|
||||
%U3 couples Y1 and Y5, and U4 gets us Y6
|
||||
% We should see that U1 gets us only translation in z, U2 couples Y2 and Y4,
|
||||
% U3 couples Y1 and Y5, and U4 gets us Y6
|
||||
|
||||
%% Define goals
|
||||
%Goal 1: settle at 1m height <2s
|
||||
% Goal 1: settle at 1m height <2s
|
||||
x_0_up = [0, 0, -1, ...
|
||||
0, 0, 0, ...
|
||||
0, 0, 0, ...
|
||||
0, 0, 0]'; %Redefine origin!
|
||||
|
||||
%Goal 2: Stabilize from a 10-degree roll and pitch with <3deg overshoot
|
||||
% Goal 2: Stabilize from a 10-degree roll and pitch with <3deg overshoot
|
||||
x_0_pitchroll = [0, 0, 0, ...
|
||||
0, 0, 0, ...
|
||||
10*(pi/180), 10*(pi/180), 0, ...
|
||||
0, 0, 0]'; %Pitch and roll of 10 degrees
|
||||
0, 0, 0]'; %Pitch and roll of 10 degrees (convert to radians)
|
||||
|
||||
x_0_roll = [0, 0, 0, ...
|
||||
0, 0, 0, ...
|
||||
0, 10*(pi/180), 0, ...
|
||||
0, 0, 0]'; %Roll of 10 degrees
|
||||
0, 0, 0]'; %Roll of 10 degrees (convert to radians)
|
||||
|
||||
%Goal 3: Move from position (0,0,0) to within 5 cm of (1,1,1) within 5 seconds.
|
||||
% Goal 3: Move from position (0,0,0) to within 5 cm of (1,1,1) within 5 seconds.
|
||||
x_0_trans = [-1, -1, 0, ...
|
||||
0, 0, 0, ...
|
||||
0, 0, 0, ...
|
||||
@@ -101,7 +106,7 @@ x_0_trans = [-1, -1, 0, ...
|
||||
|
||||
%% Finite-Time Horizon LQR for Goal 1
|
||||
|
||||
%Define Q and R for the cost function. Begin with nominal ones for all.
|
||||
% Define Q and R for the cost function. Begin with nominal ones for all.
|
||||
Q = diag([1000, 1000, 1000, ... % x, y, z
|
||||
1, 1, 100, ... % x', y', z'
|
||||
200, 200, 1, ... % roll, pitch, yaw
|
||||
@@ -109,15 +114,15 @@ Q = diag([1000, 1000, 1000, ... % x, y, z
|
||||
|
||||
R = diag([10, 20, 20, 1]); % upward force, pitch torque, roll torque, yaw torque
|
||||
|
||||
%Calculate number of timesteps.
|
||||
% Calculate number of timesteps.
|
||||
tSpan = 0:T_s:2;
|
||||
nSteps = length(tSpan);
|
||||
|
||||
%Determine gains
|
||||
% Determine gains
|
||||
[K, P] = LQR_LTI(discrete.A, discrete.B, Q, R, nSteps);
|
||||
FiniteLQR_Goal_1_K = K;
|
||||
|
||||
%Simulate nonlinear model
|
||||
% Simulate nonlinear model
|
||||
[x0, y0, z0, xdot0, ydot0, zdot0, phi0, theta0, psi0, phidot0, thetadot0, psidot0] = unpack(x_0_up);
|
||||
set_param('LQRNonlinearSim', 'StopTime', '2')
|
||||
simout = sim('LQRNonlinearSim', 'FixedStep', '.01');
|
||||
@@ -158,7 +163,7 @@ for i = 1:nSteps
|
||||
K(:,:,i) = K_const;
|
||||
end
|
||||
|
||||
%Simulate nonlinear model
|
||||
% Simulate nonlinear model
|
||||
[x0, y0, z0, xdot0, ydot0, zdot0, phi0, theta0, psi0, phidot0, thetadot0, psidot0] = unpack(x_0_up);
|
||||
set_param('LQRNonlinearSim', 'StopTime', '2')
|
||||
simout = sim('LQRNonlinearSim', 'FixedStep', '.01');
|
||||
@@ -186,14 +191,14 @@ Q = diag([0, 0, 0, ... % x, y, z
|
||||
|
||||
R = diag([10, 20, 20, 1]); % upward force, pitch torque, roll torque, yaw torque
|
||||
|
||||
%Calculate number of timesteps.
|
||||
% Calculate number of timesteps.
|
||||
tSpan = 0:T_s:4;
|
||||
nSteps = length(tSpan);
|
||||
|
||||
%Determine gains
|
||||
% Determine gains
|
||||
[K, P] = LQR_LTI(discrete.A, discrete.B, Q, R, nSteps);
|
||||
|
||||
%Simulate nonlinear model
|
||||
% Simulate nonlinear model
|
||||
[x0, y0, z0, xdot0, ydot0, zdot0, phi0, theta0, psi0, phidot0, thetadot0, psidot0] = unpack(x_0_pitchroll);
|
||||
set_param('LQRNonlinearSim', 'StopTime', '4')
|
||||
simout = sim('LQRNonlinearSim', 'FixedStep', '.01');
|
||||
@@ -234,7 +239,7 @@ for i = 1:nSteps
|
||||
K(:,:,i) = K_const;
|
||||
end
|
||||
|
||||
%Simulate nonlinear model
|
||||
% Simulate nonlinear model
|
||||
[x0, y0, z0, xdot0, ydot0, zdot0, phi0, theta0, psi0, phidot0, thetadot0, psidot0] = unpack(x_0_pitchroll);
|
||||
set_param('LQRNonlinearSim', 'StopTime', '4')
|
||||
simout = sim('LQRNonlinearSim', 'FixedStep', '.01');
|
||||
@@ -262,14 +267,14 @@ Q = diag([1000, 1000, 1000, ... % x, y, z
|
||||
|
||||
R = diag([1, 20, 20, 1]); % upward force, pitch torque, roll torque, yaw torque
|
||||
|
||||
%Calculate number of timesteps.
|
||||
% Calculate number of timesteps.
|
||||
tSpan = 0:T_s:5;
|
||||
nSteps = length(tSpan);
|
||||
|
||||
%Determine gains
|
||||
% Determine gains
|
||||
[K, P] = LQR_LTI(discrete.A, discrete.B, Q, R, nSteps);
|
||||
|
||||
%Simulate nonlinear model
|
||||
% Simulate nonlinear model
|
||||
[x0, y0, z0, xdot0, ydot0, zdot0, phi0, theta0, psi0, phidot0, thetadot0, psidot0] = unpack(x_0_trans);
|
||||
set_param('LQRNonlinearSim', 'StopTime', '5')
|
||||
simout = sim('LQRNonlinearSim', 'FixedStep', '.01');
|
||||
@@ -310,7 +315,7 @@ for i = 1:nSteps
|
||||
K(:,:,i) = K_const;
|
||||
end
|
||||
|
||||
%Simulate nonlinear model
|
||||
% Simulate nonlinear model
|
||||
[x0, y0, z0, xdot0, ydot0, zdot0, phi0, theta0, psi0, phidot0, thetadot0, psidot0] = unpack(x_0_trans);
|
||||
set_param('LQRNonlinearSim', 'StopTime', '5')
|
||||
simout = sim('LQRNonlinearSim', 'FixedStep', '.01');
|
||||
@@ -332,11 +337,11 @@ plot_states(state, tSpan);
|
||||
%% Helper Functions
|
||||
|
||||
function [K, P] = LQR_LTI(A, B, Q, R, nSteps)
|
||||
%Set P up
|
||||
% Set P up
|
||||
P = zeros(size(Q, 1), size(Q, 2), nSteps);
|
||||
%Initial value of P
|
||||
% Initial value of P
|
||||
P(:, :, nSteps) = 1/2 * Q;
|
||||
%Set K up, initial K is 0, so this is fine.
|
||||
% Set K up, initial K is 0, so this is fine.
|
||||
K = zeros(length(R), length(Q), nSteps);
|
||||
|
||||
for i = nSteps-1:-1:1
|
||||
@@ -348,7 +353,7 @@ function [K, P] = LQR_LTI(A, B, Q, R, nSteps)
|
||||
end
|
||||
|
||||
function [ulqr, xlqr] = propagate(nInputs, nStates, nSteps, x_0, K, A, B)
|
||||
%Set up for propagation
|
||||
% Set up for propagation
|
||||
ulqr = zeros(nInputs, nSteps);
|
||||
xlqr = zeros(nStates, nSteps);
|
||||
xlqr(:, 1) = x_0;
|
||||
|
||||
Reference in New Issue
Block a user