Please, choose the task type:

Stabilisation Step signal Continuous trajectory

stabilisation

Plant

Observer

Controller

Initial state

User-defined control:

function [u, C_out]=control(t, x,  x_ref, C_in)
%-------------------------------------------------------------------------------------------
%t - time
%x=(theta,alpha,d_theta,d_alpha) is the system state (estimated by the observer),
%where the angle alpha=0 corresponds to the lower position of the pendulum.
%the variable C_in(out) is the internal variable of the controller (e.g. to realize integrator).
%C_in corresponds to C_out at the previous instant of time.
%The command C_out=C_in has to be included if the controller does not need an internal state.
%-------------------------------------------------------------------------------------------
%The following change of coordinate makes the state x(2)=0 corresponding to the upper
%position of the pendulum.
x(2)=mod (x(2),2*pi)-pi;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% THE USER-DEFINED CONTROLLER HAS TO BE REALIZED BELOW
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C_out=C_in;
%The static linear feedback u=K(x-x^ref) stabilizes the pendulum in the upper position
%and tracks the reference theta^ref(t)=0.3sin(t).
u=[2 -35 1.5 -3]*(x-x_ref);

User defined observer:

Initialisation of internal variables of controller and observer:

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