Since the Cubli system is underactuated and you seek to use only a PID Controller, you must select which output you would like to control. This is necessary because PID control design generally works for single-input, single-output (SISO) systems.
Once a stabilizing PID controller is successfully designed, it can then be implemented on the multi-input, multi-output (MIMO) system. However, there is no guarantee that the other two outputs will be stable as well. Nevertheless, since the second output depends on the first output, if the first output is stable, the second output will also be stable.
%% Parameters
l = 0.085;
lb = 0.075;
mb = 0.419;
mw = 0.204;
Ib = 3.34e-3;
Iw = 0.57e-3;
Cb = 1.02e-3;
Cw = 0.05e-3;
Km = 25.1e-3;
g = 9.81;
%% State-space model
A = [0 1 0
(mb*lb + mw*l)*g/(Ib + mw*l^2), -Cb/(Ib + mw*l^2), Cw/(Ib + mw*l^2)
-(mb*lb + mw*l)*g/(Ib + mw*l^2), Cb/(Ib + mw*l^2), -Cw*(Ib + Iw + mw*l^2)/(Iw*(Ib + mw*l^2))];
B = [0
- Km/(Ib + mw*l^2)
Km*(Ib + Iw + mw*l^2)/(Iw*(Ib + mw*l^2))];
C = [1 0 0];
sys = ss(A, B, C, 0*C*B);
%% Transfer function model
Gp = tf(sys)
%% PID Controller
Gc = pidtune(Gp, 'PIDF')
%% Closed-loop transfer function
Gcl = minreal(feedback(Gc*Gp, 1))
sys = ss(Gcl);
op = findop(sys, y=1)
%% Response to Custom Step Input
opt = RespConfig;
opt.InputOffset = 0;
opt.Amplitude = op.u;
step(Gcl, opt), grid on
