Question

The parameters are as follows k=0.1,a=1.00,b=1,c=1.0,d=25,w_1=20,w_2=25,Kv=50

e(t) r(t) e (t) G(s) Figure 1: Feedback control system A pulley and belt transmission has a linearized relationship between the driven pulley angle e (t) in degrees and the input torque u(t) in Newton meters given by the following differential equation du(t) dt A feedback control system (illustrated in Figure 1) needs to be designed such that the closed-loop system is asymptotically stable and such that the following design criteria are met 1. the gain crossover frequency O should be between o and o 2. the steady-state error should be zero in response to a unit step reference 3. the velocity constant should be greater than Kv (in other words, the steady-state unit ramp error should be less than 1/K,) 4. the phase margin should be at least 55°. If the four performance criteria are met, further iteration of the controller may be undertaken (if you wish) to minimise the settling time of the step response from r(t) to y(t). If you cannot meet any of the design criteria, get as close as you can while ensuring closed-loop stability, and explain where and why compromises were needed. 3 Lead-Lag controller Consider a series lead and lag compensator ats+1 Ts+1 Select the parameters of the controller such that all design constraints are satisfied. Plot the c response to a unit step input, and to two sinusoidal inputs with frequencies one decade above and one decad: :lw th: gainr Ru:ny. Also ploi th: emoito th: unrap input. Hex: show that all of the required performance criteria are met, or else get as close as possible and explain where compromises have been made and why.

Answer 1

+とfe + d de U) 闪

tyi l+ kb A+C Finte v