system_ctrl_design.py File Reference

This file outlines the controller design process for my balancing platform system. More...

Namespaces
	system_ctrl_design

Functions
def	system_ctrl_design.plot_sim (sim, title='', xlabel='', ylabel1='', ylabel2='', fig_size=(4, 5))
	This function creates an appropriately formatted system test plot. More...
def	system_ctrl_design.comp_plot_sim (sim1, sim2, ylim1='auto', ylim2='auto', title='', subtitle1='', subtitle2='', xlabel='', ylabel1='', ylabel2='', fig_size=(13, 6))
	This function creates an appropriately formatted system test plot. More...
def	system_ctrl_design.plot_pole (p, title, fig_size)
	This function creates an appropriately formatted system test plot. More...

Variables
	system_ctrl_design.A = np.asmatrix(np.loadtxt('A.txt',delimiter=','))
	system_ctrl_design.B = np.asmatrix(np.loadtxt('B.txt',delimiter=',')).transpose()
	system_ctrl_design.C = np.matrix()
int	system_ctrl_design.D = 0
	system_ctrl_design.sys_full_OL = control.StateSpace(A,B,C,D)
	system_ctrl_design.A_p = np.matrix([[A[1,1], A[1,3]], [A[3,1], A[3,3]]])
	system_ctrl_design.B_p = np.matrix([[B[1,0]], [B[3,0]]])
	system_ctrl_design.C_p = np.matrix()
int	system_ctrl_design.D_p = 0
	system_ctrl_design.sys_plat_OL = control.StateSpace(A_p,B_p,C_p,D_p)
	system_ctrl_design.plat_OL_pole = control.pole(sys_plat_OL)
	system_ctrl_design.Q_plat = np.diag([1,1])
	system_ctrl_design.R_plat = np.diag([1])
	system_ctrl_design.K
	system_ctrl_design.S
	system_ctrl_design.E
	system_ctrl_design.K_plat_0 = np.matrix(K)
	system_ctrl_design.A_p_CL0 = A_p - (B_p*K_plat_0)
	system_ctrl_design.sys_plat_CL0 = control.StateSpace(A_p_CL0,0*B_p,C_p,D_p)
	system_ctrl_design.plat_CL0_pole = control.pole(sys_plat_CL0)
	system_ctrl_design.T = np.arange(0,3,.001)
list	system_ctrl_design.X0 = [5*3.14159/180, 0]
	system_ctrl_design.R_plat_CL0 = control.initial_response(sys_plat_CL0,T,X0)
	system_ctrl_design.fig = plt.figure()
	system_ctrl_design.title
	system_ctrl_design.xlabel
	system_ctrl_design.ylabel1
	system_ctrl_design.ylabel2
	system_ctrl_design.K_plat_1 = np.matrix(K)
	system_ctrl_design.A_p_CL1 = A_p - (B_p*K_plat_1)
	system_ctrl_design.sys_plat_CL1 = control.StateSpace(A_p_CL1,0*B_p,C_p,D_p)
	system_ctrl_design.plat_CL1_pole = control.pole(sys_plat_CL1)
	system_ctrl_design.R_plat_CL1 = control.initial_response(sys_plat_CL1,T,X0)
	system_ctrl_design.subtitle1
	system_ctrl_design.subtitle2
	system_ctrl_design.sys_OL_pole = control.pole(sys_full_OL)
	system_ctrl_design.Q_sys = np.diag([1,1,1,1])
	system_ctrl_design.R_sys = np.diag([1])
	system_ctrl_design.K_sys_0 = np.matrix(K)
	system_ctrl_design.A_CL0 = A - (B*K_sys_0)
	system_ctrl_design.sys_CL0 = control.StateSpace(A_CL0,0*B,C,D)
	system_ctrl_design.sys_CL0_pole = control.pole(sys_CL0)
	system_ctrl_design.R_sys_CL0 = control.initial_response(sys_CL0,T,X0)
	system_ctrl_design.K_sys_1 = np.matrix(K)
	system_ctrl_design.A_CL1 = A - (B*K_sys_1)
	system_ctrl_design.sys_CL1 = control.StateSpace(A_CL1,0*B,C,D)
	system_ctrl_design.sys_CL1_pole = control.pole(sys_CL1)
	system_ctrl_design.R_sys_CL1 = control.initial_response(sys_CL1,T,X0)

Detailed Description

This file outlines the controller design process for my balancing platform system.

Author

E. Nicholson

Date

March 10, 2021

I completed a symbolic kinematic and kinetic analysis of the system on paper to define my equations of motion. I then used MATLAB as a symbolic algebra tool to simplfy / linearize my system and place it in state space form. This script pulls the most recent matrix output from my MATLAB script and uses it to design two full state feedback controllers. One controller is used to balance the platform by itself. The other is used to balance the platform and ball together.

The source code for this file can be found here:

LINK