Question

5., A controller in Figure 4-18 is required to produce a steady-state output, do, that is within 2 percent of the commanded input, r). As the control en- gineer, you can introduce an amplifier with gain K. Determine the minimum value of Kc that would meet the requirement. Confirm your design using SIMULINK.

Answer 1

As per control theory implies c(s)/R(s) = k_c times 3(s + 2)/(s + 3) (s + 1)/ 1 + k_c times 3(s + 2)/(s + 3) (s + 1) = 3k_c(s + 2)/3 k_c(s + 2) + (s + 3) (s + 1) implies 1 - c(s)/R(s) = R(s) - c(s)/R(s) = E(s)/R(s) = (s + 3) (s + 1)/3 k_c(s + 2) + (s + 3) (s + 1) therefore Vertical-bar steady - state output error Vertical-bar lessthanorequalto 5 times 0.02 Vertical-bar = 0.1 (Given in the problem) implies Vertical-bar E(infinity) Vertical-bar lessthanorequalto 0.1 implies Vertical-bar lim_s rightarrow 0 S E(s) Vertical-bar lessthanorequalto 0.1 implies - 0.1 lessthanorequalto lim_s rightarrow 0 s E(s) lessthanorequalto 0.1 therefore E(s) = (s + 3) (s + 1) (R(s) = 5/s)/3 k_c(s + 2) + (s + 3) (s + 1) form i and ii we have implies - 0.1 lessthanorequalto lim_s rightarrow 0 s (s + 3) (s + 1) [(1/s) times 5[/3k (s + 2) + (3 + 0(s +) lessthanorequalto 0.1 implies - 0.1 lessthanorequalto 3 times 5/(2 times 3 k_c) + 3 lessthanorequalto 0.1 implies - 0.1 lessthanorequalto 15/(6k_c + 3) lessthanorequalto 0.1 assuming that the value of k_c
For further help, please write in the comments.