Obtain a state-space representation of the system shown in Fig.3(a), where uuu is the input and y1y_1y1 and y2y_2y2 are the outputs. Assume that the rollers are frictionless.
Why linearization is necessary? Linearize the nonlinear system z=x2+8xy+3y2z = x^2 + 8xy + 3y^2z=x2+8xy+3y2 in the region 2≤x≤42 \le x \le 42≤x≤4, 10≤y≤1210 \le y \le 1210≤y≤12. Find out the Linearization error at (4, 12).
A closed-loop control system has the characteristics equation s5+3s4+5s3+4s2+s+3=0s^5 + 3s^4 + 5s^3 + 4s^2 + s + 3 = 0s5+3s4+5s3+4s2+s+3=0. Using Routh's stability criterion, determine whether the system is stable or unstable. If unstable how many unstable roots are there?
What types of signals are used as test signal? Find out unit-step response of a first order system.
Draw a typical unit-step response of a 2nd2^{nd}2nd order system and mention the related terminology.
Consider the negative feedback system having the gain G(s)=ks(s+1)(s+2)G(s) = \frac{k}{s(s+1)(s+2)}G(s)=s(s+1)(s+2)k, H(s)=1H(s) = 1H(s)=1. Determine the root loci on the real axis.
Why root locus plots are important? Mention the conditions for finding root locus. A negative feedback system has G(s)=k(s+1)(s+2)G(s) = \frac{k}{(s+1)(s+2)}G(s)=(s+1)(s+2)k, H(s)=1H(s)=1H(s)=1. Determine the root loci on the real axis.
Apply Routh's stability criterion on the feedback control system as in Fig. 3(b) and find out the value of kkk for stability.
Linearize the nonlinear system z=x2+8xy+3y2z = x^2 + 8xy + 3y^2z=x2+8xy+3y2 in the region defined by 2≤x≤42 \le x \le 42≤x≤4 and 10≤y≤1210 \le y \le 1210≤y≤12 and find out the linearization error at (4, 12).
Define the building blocks of a hydraulic system. Show that hydraulic capacitance is proportional to cross-sectional area of the capacitor.
Draw a typical unit step response of 2nd order system with necessary terminology.
A servo system is shown in Fig. 4(c). Determine the values of gain kkk and velocity feedback constant khk_hkh so that the maximum overshoot in the unit-step response is 0.2 and the peak time is 1 sec. with these values of kkk and khk_hkh obtain in rise time and settling time. Assume that J=1 kg-m2J = 1 \text{ kg-m}^2J=1 kg-m2 and B=1 N-m/rad/secB = 1 \text{ N-m/rad/sec}B=1 N-m/rad/sec.
Consider the characteristic equations s4+2s3+(4+k)s2+9s+25=0s^4 + 2s^3 + (4+k)s^2 + 9s + 25 = 0s4+2s3+(4+k)s2+9s+25=0 Using Routh's stability criterion, determine the range of K for stability.
Compare between modern control theory and conventional control theory.
Consider the block diagram in Figure 2(c). Simplify the diagram and find out C(s)/R(s)C(s)/R(s)C(s)/R(s).
Define the following term of a measurement system: Accuracy Sensitivity Repeatability Resolution
Draw a typical unit-step response of a 2nd2^{nd}2nd order system and show related specifications of the response.
Describe the principle and working of piezoelectric sensor.
A control system has the following characteristics equation: 3s7+9s6+6s5+4s4+7s3+8s2+2s+6=03s^7 + 9s^6 + 6s^5 + 4s^4 + 7s^3 + 8s^2 + 2s + 6 = 03s7+9s6+6s5+4s4+7s3+8s2+2s+6=0. Using Routh's stability criteria determine whether the system is stable or unstable. If unstable, how many poles are in the right half of s-plane.
Draw a typical unit-step response of a second order system and show related specifications of the response.
Consider a system having G(s)=ks(s+1)(s+2)G(s) = \frac{k}{s(s+1)(s+2)}G(s)=s(s+1)(s+2)k and H(s)=1H(s) = 1H(s)=1. Determine the root loci on the real axis for the system.
How a proportional controller rectify the error in a system?
Determine the range of kkk for stability of a unity feedback control system whose open-loop transfer function is G(s)=ks(s+1)(s+2)G(s) = \frac{k}{s(s+1)(s+2)}G(s)=s(s+1)(s+2)k.
Consider a PID controlled system shown in Figure 6(c). Determine the value of kpk_pkp, TiT_iTi and TdT_dTd for the controller using Ziegler-Nichols tuning rule.
A servo system exhibits a standard second-order response against a step input. Considering the value of damping ration of 0.6 and undamped natural frequency of 5 rad/sec, calculate the value of rise time peak time maximum overshoot 5% settling time.
Determine the range of KKK for stability of a unity feedback control system whose open-loop transfer function is G(s)=Ks(s+1)(s+2)G(s) = \frac{K}{s(s+1)(s+2)}G(s)=s(s+1)(s+2)K.
Draw the second-order response curve against step input for the condition: 0<ζ<10 < \zeta < 10<ζ<1 ζ=1\zeta = 1ζ=1 ζ>1\zeta > 1ζ>1
Determine the magnitude and phase of the output from a system when subjected to a sinusoidal input of 5sin(4t+60∘)5\sin(4t + 60^\circ)5sin(4t+60∘) if it has a transfer function of G(s)=4s+1G(s) = \frac{4}{s+1}G(s)=s+14.
Why root-locus method is used in control engineering? Write down the angle and magnitude conditions of the method.
Consider a PID controlled system shown in Fig 6(c). Determine the values of KpK_pKp, TiT_iTi and TdT_dTd using Ziegler-Nichols tuning rule.