Dear All,
I developed a very simple SD model (using iThink) to demonstrate how perception delay combined with quick action cause instability in a feedback system: i.e., long perception delay (“time to perceive”) coupled with quick action (“time to adjust”) cause instability.
I found that the model (“output) is either stable or unstable whether the first or third order exponential smoothing functions are used for the perceived output. If the “perceived output” is modeled using the first order exponential smoothing, the output is stable (SMTH1). However, the output is unstable if the third order exponential smoothing (SMTH3) is used.
I appreciate any comments about the model below. I'm sorry I could not attach the model below because this forum doesn't allow ithink file attached. I believe that this model is very simple and it won't take more than 1 minute to build.
Thanks.
Sangdon Lee, Ph.D.,
GM Tech. Center,
Here is the model in iThink:
Output(t) = Output(t  dt) + (Adjust_Output) * dt
INIT Output = 0
INFLOWS:
Adjust_Output = Error/Time_to_adjust
Desired_Output = STEP(5,1)
Error = Desired_OutputPerceived_Output
Perceived_Output = SMTHN(Output, Time_to_perceive, SMTH_Nth, 0)
SMTH_Nth = 3 {3=for third order delay}
Time_to_adjust = 1
Time_to_perceive = 4
Comments:
 Simulation duration: 0 to 40 days, 4th order RungeKutta method.
 SMTHN is an iThink command for the nth order exponential smoothing, which is specified by the value of “SMTH_Nth” in the model above. The value of one or three for “SMTH_Nth” is for first order or third order exponential smoothing, respectively.
