Question: Solve and show work 1. Consider the following digital controller. 1-2-1 G(Z) = 1 - 0.25z-1 + 0.125z-2 (a) Write the difference equation for implementing

Solve and show work

1. Consider the following digital controller. 1-2-1 G(Z) = 1 - 0.25z-1 + 0.125z-2 (a) Write the difference equation for implementing this controller using the direct programming method and draw the block diagram for this implementation. (b) Write a MATLAB program using the direct method of implementation. Use the following for the input u[k] and initial conditions. k y[0] = 1, y[1] = -1, u[k] = k = 1 [k] Plot the input u[k] and output y [k] in a single figure for 0

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