Suppose as in the picture if I have an input change there is a change in the output how I can calculate the disturbance response. Can you explain?
The answer depends upon the system characteristics. The following questions may help: Is it a linear or non-linear system? Time-varying or time-invariant? Do you have a reasonably accurate mathematical model of the system or not?
You'll also have to determine where in the system the disturbance acts as an input?
The input signal will also have to be defined.
For a linear time-invariant system the disturbance can be calculated using linear models (analytical or simple Matlab simulation). For a non-linear and/or time-varying system you may have to create a non-linear simulation model and estimate the response to a specified disturbance by running a simulation.
Do you have a block diagram of your system, in the Laplace domain? If you do, then derive the transfer function F(s) = Y(s)/D(s), that links the system output Y(s), to the disturbance input D(s). Do this by "block diagram reduction". To get the Laplace transform of the output signal Y(s), simply multiply F(s) by the Laplace transform of the input disturbance, e.g. D(s) = 1/s for a unit step disturbance. Finally, take the inverse Laplace transform to get the output response y(t) in the time domain - this may involve a "partial fraction expansion", or simply use a sym alg pkg.
If you are using Simulink, as your plot suggests, then that is much easier, just connect a step input to the point where you would like the disturbance to enter your system, and hook up a scope where you would like to tap out the output.
If you are using Matlab/Simulink, then you may add input/output points form tools-linear analysis. After that plot obtained form linear analysis, you can check amount of rejection at each frequency in bode plot.
As the system type is not specified so
In general find mathematical expression which indicates the system output as a function of the disturbance, which can be evaluated for any type of disturbance using either by hand calculations or MATLAB
ONE SUCH EXAMPLE IN THE CASE OF LTI SYSTEMS IS THE OUTPUT TO DISTURBANCE TRANSFER FUNCTION. IN CASE OF NONLINEAR SYSTEMS YOU MAY CALCULATE THE EFFECTS (RESPONSE) OF DISTURBANCE IN OVERALL OUTPUT OF THE SYSTEM, BY THE VIRTUE OF STABILITY ANALYSIS ETC.
I've used etc because no such generalized rules exist for non-linear system. One have to find out one which is suitable and appropriate and do not violate any physical or mathematical fact.
Dear Coleg, I think you can study about disturbance-output sensitivity functions.
Prof. Ioan Dore Landau and co. (but not only) have a lot of papers in this area.
Please refer to these articles:
https://www.researchgate.net/publication/313576646_From_PID_to_Nonlinear_State_Error_Feedback_Controller
https://www.researchgate.net/publication/312046377_Improved_Sliding_Mode_Nonlinear_Extended_State_Observer_based_Active_Disturbance_Rejection_Control_for_Uncertain_Systems_with_Unknown_Total_Disturbance
https://www.researchgate.net/publication/309655805_On_the_Improved_Nonlinear_Tracking_Differentiator_based_Nonlinear_PID_Controller_Design
Article From PID to Nonlinear State Error Feedback Controller
Article Improved Sliding Mode Nonlinear Extended State Observer base...
Article On the Improved Nonlinear Tracking Differentiator based Nonl...
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