Q1) Design an operational amplifier circuit that give the transfer function of the a first order...
Q1) Design an operational amplifier circuit that give
the transfer function of the a first
order system:
G(s) = 100/s + 100
Q2)Assuming the reduced transfer function fo the
closed loop system is given as the
following, find the value of K that makes the system has a percent
overshoot of 15% ? Transfer function is the attached in the
figure
Homework Answers
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Q1) Design an operational amplifier circuit that give
the transfer function of the a first
order...
2. You are given the motor whose transfer function is shown in Figure 2(a). s) e(s) Amplifier Mot...
Control system
2. You are given the motor whose transfer function is shown in Figure 2(a). s) e(s) Amplifier Motor C(s) 15 Tachometer Кр Figure 2 a) If this motor were the forward transfer function of a unity feedback system, calculate the percent overshoot and settling time that could be expected. b) You want to improve the closed-loop response. Since the motor constants cannot be changed and you cannot use a different motor, an amplifier and tachometer are inserted into...
Q2 (a) Consider the control system shown in Figure Q1 (a). Obtain the closed-loop transfer function...
Q2 (a) Consider the control system shown in Figure Q1 (a). Obtain the closed-loop transfer function of this system and by using MATLAB obtain the unit step response of this closed loop system - R(S) c(s) 36+1) (s + 1) Figure Q2 (a) (b) A sampler and a zero-order hold element were inserted into the system in Figure Q1(a) as shown in Figure Q1(b). Obtain the closed-loop pulse transfer function of this system and by using MATLAB or otherwise, obtain...
Problem 52: (25 points) Operational amplifiers are important building blocks in a wide spectrum of electronic systems such as amplifiers and filters. The concept of feedback control is of central imp...
Problem 52: (25 points) Operational amplifiers are important building blocks in a wide spectrum of electronic systems such as amplifiers and filters. The concept of feedback control is of central importance in understanding the design of operational amplifier circuits. For without feedback, operational amplifiers behave as comparators. This problem shows why it is necessary to connect the output of an operational amplifier to its inverting input. Negative feedback produces a circuit that is BIBO stable. Figure 1(A) shows the circuit...
Q1. Show analytically that the Root Locus for the unity feedback system with open loop transfer f...
Q1. Show analytically that the Root Locus for the unity feedback system with open loop transfer function: (a) [10 marks] K(s 4) (s + 2) is a circle, and find the centre and the radius. Determine the minimum value of the damping ratio and the corresponding value of K (b) The root locus of the open loop transfer function: [10 marks] s(s26s +15) is depicted in Figure Q1(b). Find the minimum value of gain K that will render the system...
s+0. 4. The transfer function for a controller is Ge identify and implement the controller with an operational amplifier. Assuming a capacitor of 100 μF is available. s+0. 4. The transfer fu...
s+0. 4. The transfer function for a controller is Ge identify and implement the controller with an operational amplifier. Assuming a capacitor of 100 μF is available.
s+0. 4. The transfer function for a controller is Ge identify and implement the controller with an operational amplifier. Assuming a capacitor of 100 μF is available.
Problem 1. A unity feedback system with forward transfer function G(s) is operating with a closed...
Problem 1. A unity feedback system with forward transfer function G(s) is operating with a closed-loop step response that has 20.5% overshoot. G)-(+8)6 + 25) G(s) (a) Design a PD compens ator to decrease the settling time of the closed-loop system by a factor of four
Problem 1. A unity feedback system with forward transfer function G(s) is operating with a closed-loop step response that has 20.5% overshoot. G)-(+8)6 + 25) G(s) (a) Design a PD compens ator to decrease...
The open loop transfer function of a unity negative feedback system is given by : G(s)...
3. The open loop transfer function of a unity feedback system is given by \(G(S)=\frac{K}{S(1+S T)}\) Where Tand \(\mathrm{K}\) are constants having positive values. By what factor the amplifier gain be reduced so that (a) peak overshoot of unit step response of the system is reduced from \(75 \%\) to \(25 \% .\) b) The damping ratio increases from \(0.1\) to \(0.6\).
Consider the electro-mechanical feedback control system shown in Figure 3. The voltage Ea(s) - Liea(t)) is...
Consider the electro-mechanical feedback control system shown in Figure 3. The voltage Ea(s) - Liea(t)) is generated by an amplifier whose transfer function is Ga(s) -5 The position sensor has a transfer function H(s) 1 and the pre-compensator transfer function is pot X (s) Ea(s) The "Electro-Mechanical System" block, is X(s) Ea(s) 5.05s3 101s2 +505.2s 100 R(s) Amplifier, |Ea(S)Electro-MechanicalX(S) Controller, Gc(s) K, pot Ga(s) System, G(s) Encoder H(s) Figure 3: Electro-mechanical control system for Question 3 Consider a proportional controller...
Not all second-order systems are designed to give a standard 2"d order response. Consider the pow...
Not all second-order systems are designed to give a standard 2"d order response. Consider the power steering for an automobile. The feedback system can be modeled as the block diagram shown in the figure below. For a unit step input A(s), find values of K1 and K2 for which the response w(t) is critically damped and has a steady-state gain of 0.4 unit. Repeat for a damping ratio of 0.7 and a steady-state gain of 0.2 unit. 7) Control Steering...
2. The following second-order transfer function was obtained via an identification experiment performed in a small...
2. The following second-order transfer function was obtained via an identification experiment performed in a small neighborhood of a particular stead-state operating condition of a nonlinear process: G(s) = (3s +1)(6s1) (a 5pts.) Use direct synthesis method to design a controller. Assume that the desired closed-loop transfer function is first order and the desired closed-loop time constant is Td = 4. (b 5pts.) Suppose as a consequence of the nonlinearity, this process sometimes passes through a region of operation where...
Control system
2. You are given the motor whose transfer function is shown in Figure 2(a). s) e(s) Amplifier Motor C(s) 15 Tachometer Кр Figure 2 a) If this motor were the forward transfer function of a unity feedback system, calculate the percent overshoot and settling time that could be expected. b) You want to improve the closed-loop response. Since the motor constants cannot be changed and you cannot use a different motor, an amplifier and tachometer are inserted into...
Q2 (a) Consider the control system shown in Figure Q1 (a). Obtain the closed-loop transfer function of this system and by using MATLAB obtain the unit step response of this closed loop system - R(S) c(s) 36+1) (s + 1) Figure Q2 (a) (b) A sampler and a zero-order hold element were inserted into the system in Figure Q1(a) as shown in Figure Q1(b). Obtain the closed-loop pulse transfer function of this system and by using MATLAB or otherwise, obtain...
Problem 52: (25 points) Operational amplifiers are important building blocks in a wide spectrum of electronic systems such as amplifiers and filters. The concept of feedback control is of central importance in understanding the design of operational amplifier circuits. For without feedback, operational amplifiers behave as comparators. This problem shows why it is necessary to connect the output of an operational amplifier to its inverting input. Negative feedback produces a circuit that is BIBO stable. Figure 1(A) shows the circuit...
Q1. Show analytically that the Root Locus for the unity feedback system with open loop transfer function: (a) [10 marks] K(s 4) (s + 2) is a circle, and find the centre and the radius. Determine the minimum value of the damping ratio and the corresponding value of K (b) The root locus of the open loop transfer function: [10 marks] s(s26s +15) is depicted in Figure Q1(b). Find the minimum value of gain K that will render the system...
s+0. 4. The transfer function for a controller is Ge identify and implement the controller with an operational amplifier. Assuming a capacitor of 100 μF is available.
s+0. 4. The transfer function for a controller is Ge identify and implement the controller with an operational amplifier. Assuming a capacitor of 100 μF is available.
Problem 1. A unity feedback system with forward transfer function G(s) is operating with a closed-loop step response that has 20.5% overshoot. G)-(+8)6 + 25) G(s) (a) Design a PD compens ator to decrease the settling time of the closed-loop system by a factor of four
Problem 1. A unity feedback system with forward transfer function G(s) is operating with a closed-loop step response that has 20.5% overshoot. G)-(+8)6 + 25) G(s) (a) Design a PD compens ator to decrease...
3. The open loop transfer function of a unity feedback system is given by \(G(S)=\frac{K}{S(1+S T)}\) Where Tand \(\mathrm{K}\) are constants having positive values. By what factor the amplifier gain be reduced so that (a) peak overshoot of unit step response of the system is reduced from \(75 \%\) to \(25 \% .\) b) The damping ratio increases from \(0.1\) to \(0.6\).
Consider the electro-mechanical feedback control system shown in Figure 3. The voltage Ea(s) - Liea(t)) is generated by an amplifier whose transfer function is Ga(s) -5 The position sensor has a transfer function H(s) 1 and the pre-compensator transfer function is pot X (s) Ea(s) The "Electro-Mechanical System" block, is X(s) Ea(s) 5.05s3 101s2 +505.2s 100 R(s) Amplifier, |Ea(S)Electro-MechanicalX(S) Controller, Gc(s) K, pot Ga(s) System, G(s) Encoder H(s) Figure 3: Electro-mechanical control system for Question 3 Consider a proportional controller...
Not all second-order systems are designed to give a standard 2"d order response. Consider the power steering for an automobile. The feedback system can be modeled as the block diagram shown in the figure below. For a unit step input A(s), find values of K1 and K2 for which the response w(t) is critically damped and has a steady-state gain of 0.4 unit. Repeat for a damping ratio of 0.7 and a steady-state gain of 0.2 unit. 7) Control Steering...
2. The following second-order transfer function was obtained via an identification experiment performed in a small neighborhood of a particular stead-state operating condition of a nonlinear process: G(s) = (3s +1)(6s1) (a 5pts.) Use direct synthesis method to design a controller. Assume that the desired closed-loop transfer function is first order and the desired closed-loop time constant is Td = 4. (b 5pts.) Suppose as a consequence of the nonlinearity, this process sometimes passes through a region of operation where...
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