Problem 3 Consider the system presented in the figure below. (a) Show the Nyquist diagram for K = 0.2. (b) What is the gain margin of the Nyquist diagram in (a)? (c) Explain the dependence of stability on the gain K. R E 1 K C s(s+25+1)

As an entry engineer you are assigned the task of designing an averaging circuit of three voltage signals. The signals can come from various sources, like sensors. You decide to design an operational amplifier-based circuit as the one shown below: RE R₁ V10- www R₂ V20 V30 R3 વ્ઝ ટ્રાંસ્ક્રાઇબ કરેલ ટેક્સ્ટ બતાવો C -vo Why would you select an operational amplifier-based circuit? Determine an expression for the output voltage in terms of the input voltages. Determine the relationship between the components of the circuit such that it acts as an averaging system. Select values of components to realize the averaging system.

LOOP GAIN( NEED ONLY HANDWRITTEN SOLUTION PLEASE OTHERWISE DOWNVOTE).

3. In this problem, use the two closed loop systems given in the figure to answer the questions below. 4 R(s) K₁ 0.0099 In thin K₂ Y(s) R(s) K₁ 4 S(s) = 0.09 K₂ 0.09 (a) Show that these two systems have the same transfer function for K₁ = K₂ = 100 (b) Using the definition of sensitivity, S(s), for each system calculate the sensitivity to the parameter K₁ with K₁ and K₂ as variables. Recall: Y(s) OG G OG Gal (c) Substitute K₁ = K₂ = 100 into each S(s) and compare the sensitivities to parameter K₁.