Consider a system with a mathematical model given by the differential equation: d²y dy 3 dt² +2 dt +y= u(t) a) Express t

[answerhappygod]

Consider A System With A Mathematical Model Given By The Differential Equation D Y Dy 3 Dt 2 Dt Y U T A Express T 1 (105.47 KiB) Viewed 23 times

Consider a system with a mathematical model given by the differential equation: d²y dy 3 dt² +2 dt +y= u(t) a) Express this equation in state space form. (5 Marks) b) Find the roots of the system and sketch them on the s-plane. Is the system stable? (5 marks) c) The system is to be controlled as a regulator system with state variable feedback, as shown in Fig. 4. u B S -K Fig. 4: A Regulator System (i) What is a Regulator System? (1 mark) (ii) The closed-loop system should respond to an impulse with a settling time of 3s and a maximum overshoot of 15%. Find the state feedback gain necessary to give the desired system response. (9 marks)