Prelab Answer the following questions 1. What is the unit-step response of a system with trans fer function G(s)- ST +1 where and τ are constants > 0? 2. Make a hand-sketch of the response of the...
5. (30) Find the unit step response of the system where its transfer function is defined as s + 10 G(s) = 20 (s2 + 165 + 100)(s + 1)(s + 2) Sketch the time response of this system roughly.
(25 points) Find the discrete time unit step response of the system with transfer function G(2) = 2(2+1)
Find the discrete time unit step response of the system with transfer function G(z) = (z−1)/z(z+1)
2. When a unit step is applied to a system at 0 its response is y(1) = | 4 +-e-3,-e-2,(2 cos 41 + 3 sin 41) | u(t) (a) What is the transfer function of the system? (b) What is the governing differential equation for this system?
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s)X2 (s)/F(s) (b) Does the system oscillate with a unit step input (f (t))? Explain the reason (c) Decide if the system(x2 (t)) is stable with a unit step input (f (t))? Explain the reason 1. 320) 8 kg 2 N/m 4N-s/m 2N-s/m Fig. 1 2. There are two suspensions for a car as shown in Fig. 2 (a) Find the equations of each...
x(t)-A()x(t) + B(t)u(t) 2. Consider the following system y(t)-C(t)x(t) where A(t)- 0 1) Derive the state transition matrix Φ(t, τ). 2) Derive the impulse response function g(t, z). x(t)-A()x(t) + B(t)u(t) 2. Consider the following system y(t)-C(t)x(t) where A(t)- 0 1) Derive the state transition matrix Φ(t, τ). 2) Derive the impulse response function g(t, z).
Find the zero-state response of the linear system with transfer function with an > 0 and 0 <くく1, when the input u(t) is the unit step, that is, u(t)-1(t), for 12 o, using both 1) the transfer function approach and 2) the convolution approach Find the zero-state response of the linear system with transfer function with an > 0 and 0
Consider the transfer function of a DC motor given by G(s) = 1 / s(s+2) 3. Consider the transfer function of a DC motor given by 1 G(s) s (s2) The objective of this question is to consider the problem of control design for this DC motor, with the feedback control architecture shown in the figure below d(t r(t) e(t) e(t) C(s) G(s) Figure 4: A feedback control system (a) Find the magnitude and the phase of the frequency response...
Q.4 A position control system is shown in Figure Q4. Assume that K(s) = K, the plant 50 s(0.2s +1) transfer function is given by G(s) s02s y(t) r(t) Figure Q4: Feedback control system. (a) Design a lead compensator so that the closed-loop system satisfies the following specifications (i) The steady-state error to a unit-ramp input is less than 1/200 (ii) The unit-step response has an overshoot of less than 16% Ts +1 Hint: Compensator, Dc(s)=aTs+ 1, wm-T (18 marks)...
2. (30) Answer the questions for the following distributions: (G) Normal(0, 1) (ii) t(15) (ii) x(12) (iv) F(4, 34) (a) Write down the probability density function (pdf (b) Sketch the pdf using hand drawing or R program. (c) At 5% significance level, indicate the rejection region of the right-tailed test. You may use R. 2. (30) Answer the questions for the following distributions: (G) Normal(0, 1) (ii) t(15) (ii) x(12) (iv) F(4, 34) (a) Write down the probability density function...