A first order system unit step response is described by the equation
where A is the gain and is the time constant of the system. The objective of this experiment is to estimate the values of A and recursively from the sampled data. That is, the estimates of A and are improved in real-time as each new data point is measured.
Following the approach presented in  and , we obtain a first-order Taylor series expansion of () about a point . Then we minimize the sum of squared differences between the measured data and the model in () with respect to the parameters A and . This process leads to the recursive algorithm described next.
The recursive algorithm begins with an initial estimate of and . The next values of A and are computed by solving for the updates and in ()
The first order system used in the experiment is the RC circuit shown in Figure . The objective is to estimate the parameters A and by observing the output voltage when the input voltage is a unit step function. In this circuit, and . The parameter estimates are updated in real-time as each data point is measured. Data collection can be stopped when the estimates have converged.
Figure: RC circuit.