Q6 U(s) Y(s) G₁(s) G₂(s) (a) H₁(s) H₂(s) Figure Q6 Using Routh test determine if the system shown in Figure Q6 will be stable when: G₁(s) = H₁(s)=2 1 G₂(s)== 2s+2 3 H₂(s)²+3
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- A system has the following characteristic equation: s+ s+ 3s+ 2s + 2 = 0 Using the Routh-Hurwitz method, checka. How many roots are to the right of the imaginary axis?b. Is the system stable?.Which one is the linearized modelling equation of the given system. 5-3Nm Your answer: O 22 + +72= fa(t) O2+6+11r fa(t) O 2+62 +9r= Ja(1)5. Determine the validity of a second-order approximation of the system below: 450 / [(s +9)*(s² + 3s +70)]. If valid, give the approximation.
- 1 Problem 5 4 State, x(t) SAWNO-Nw. ● ● Case 1 O 2 6 Time, sec. underdamped critically damped State, x(t) • overdamped 54321 ONS TY Case 2 2 ▷ Time, sec. 8 10 State, x(t) 5 2 + 3 4 Case 3 2 ▷ 6 Time, sec. 5432 State, x(t) & A & No. 2 Match each of the resposes above to one of the following second-order system types: • undamped Case 4 ▷ Time, sec.The Routh-Hurwitz criterion to be used to determine the stability of a system with a characteristic equation given by 85 + 2s4 + 2s3 + 4s² + 11s + 10 Comment on the stability of the system. Neutral Stable UnstableQ5. For a point at distance 50 m and angle 450 to the axis which of the following statements are correct? Consider an infinite baffled piston of radius 5 cm driven at 2 kHz in air with velocity 10 m/s. You may choose multiple options. a. The constant term is given by 515.03 b. The distance dependent term is given by e-jk50/50 c. The directivity term is given by j1(Ka sin 450)/sin 450 d. There is no time dependent term.
- b) G₂ (s) = K(s+1)(s+3) (s²-2s+4) In Problem 1(b), find the range/value of K, such that the system has a) poles on the jw-axis; b) poles in the right half-plane; c) poles not on the real-axis.Draw by hand the Bode plot of the following systems. 1. 50 G(s) : s(s² + 4s + 8) 2. 20(s + 1) s(s² + 2s + 10)(s + 5) G(s) =2- Using Matlab, what are the step response curves of the closed-loop system, as shown in fig.1. the feedback represents the second-order dynamic system. (fill in the following table) For=0.4 Wn 1 3 6 9 10 R(S) 0.1 0.3 0.6 0.9 1 For w 5 rad/sec 3 Settling time Peak response 2 Wn s(s+23wn) Settling time Peak response C(s) Discuss the follow Which parameters or w occur on the rise time of the response? Which parameter increases the speed of response? Which parameters can be decreases the response amplitude? Which parameter decreases the steady error state? fig.2
- s)- Characteristic equation for a 5th order system is given as: s5 + 4s4 + 3s3 + s? + 2s + 10 Using Routh-Hurwiz stability criteria, determine if the system is stable or unstable (show your work)xa 0- 1 point) Which of the systems presented on Fig. 2 is stable and which unstable? (a) t Fig. 2. System response (b) AO 1::09 O [Template] Ho... -> Homework For the system shown in figure below, Find the range of K for stable system. R K(s + 2) C s(s +5)(s² + 2s + 5) II