Consider a variant of the matrix A used in Example 10-2. In this example, we used A(2,1) = -0.6.

(a) Changing this to A(2,1) = -0.9, and assuming exact same values for B and C as in the example, what changes in the impulse response do you observe and why?

(b) In Example 10-2, we used 50 data samples to estimate the system matrices such that the estimated impulse response matches the measured output perfectly. Repeat the identification with A(2,1) = -0.9, and check if we should use lesser or more number of samples to achieve the same accuracy in matching.

Example 10-2

Transcribed Image Text:

Consider the following impulse response data for a SISO discrete-time LTI system with a sampling time of T = 0.01 s. The output is measured at the sampling time instants t = 0, 0.01, 0.02, ..., 0.08, as shown in Fig. 10-2. k y(k) 0 0 1 2 0.996 -0.298 3 -0.0148 4 5 0.0338 -0.0081 6 7 -0.0011 0.0011 8 -0.0002 Our objective is to identify a similarity transformation of the system matrices A, B, and C, and the corresponding transfer function, using the given values of y(k) and with the information