Control Theory
1. Determine (i) the loop transfer function, ( ii ) the control ratio, (iii) the error ratio. ( iv ) the primary feedback ratio, ( v ) the characteristic equation, for the feedback control system shown in figure ( 1 ), where K1 and K2 are constants.
Homework Answers
Task: 4 (35 Marks) The block diagram representation of a CNC machine speed control system is...
Task: 4 (35 Marks) The block diagram representation of a CNC machine speed control system is shown in Figure 4 with the gain of K, and the feedback value of K2. R(s) + cls 100 1 + 0.2s G1=6.5 K1=14.5 K2=0.55 R=3 L=7 C=0.5 Figure 4 (i). Evaluate the closed loop transfer function of the CNC speed control system; (i). Estimate the value of time constant (T) and dc gain K for the CNC speed control system; Note: Each student...
Problem 51: (25 points) Figure 5 is an example of a feedback control system that is designed to r...
Problem 51: (25 points) Figure 5 is an example of a feedback control system that is designed to regulate the angular position θ(t) of a motor shaft to a desired value θr(t). The signal e(t) represents the error between the measured shaft angle θ(t) and the desired shaft angle θ (t). The Laplace transforms ofa,(t), θ(t), and e(t) are denoted as ΘR(s), θ(s), and E(s), respectively. The control gains Ki and K2 are chosen by the control engineer to achieve...
Question three The figure below shows a unit step response of a second order system. From...
Question three The figure below shows a unit step response of a second order system. From the graph of response find: 1- The rise timet, 2- The peak timet, 3- The maximum overshoot Mp 4- The damped natural frequency w 5. The transfer function. Hence find the damping ratio ζ and the natural frequency ah-Find also the transfer function of the system. r 4 02 15 25 35 45 Question Four For the control system shown in the figure below,...
3. For the feedback control system shown in Figure Q3 below, the forward-path transfer function given...
3. For the feedback control system shown in Figure Q3 below, the forward-path transfer function given by G(s) and the sensor transfer function is given by H(s). R(s) C(s) G(s) H(s) Figure Q3 It is known that G(s) -- K(+20) S(+5) H(s) = and K is the proportional gain. (S+10) i. Determine the closed-loop transfer function and hence the characteristic equation of the system. [6 marks] ii. Using the Routh-Hurwitz criterion, determine the stability of the closed-loop system. Determine the...
Rt)+ e(t) y(t) K1 S +4 Figure 3: A closed-loop control system with an inner feedback loop. Comput...
rt)+ e(t) y(t) K1 S +4 Figure 3: A closed-loop control system with an inner feedback loop. Compute the closed-loop transfer function Gal (s) -Y(s)/R(s) for the system shown in Figure 3
rt)+ e(t) y(t) K1 S +4 Figure 3: A closed-loop control system with an inner feedback loop. Compute the closed-loop transfer function Gal (s) -Y(s)/R(s) for the system shown in Figure 3
P4: The car model of a cruise control system is given in the following transfer function...
P4: The car model of a cruise control system is given in the following transfer function block diagram ms + b Where v is the car speed u is the control force m is the mass of the vehicle, 1000 kg b is the damping coefficient, 50 N s/m More details are available here (1) Derive the differential equation relating y(t) to u(t) (2) Determine the time constant of the car dynamics (from u to v) If a proportional feedback...
A unity feedback system is shown in Fig. 1. The closed-loop transfer function ?(?) of this...
A unity feedback system is shown in Fig. 1. The closed-loop
transfer function ?(?) of this system is given as
?(?)=?1?4+2?3+(?2+1)?2+?2?+?1.
a) (20%) Using Routh-Hurwitz criteria, find expression (in
terms of ?1 and ?2) and range of value of ?1 and ?2 such that the
above system is stable.
b) (4%) It is desired to achieve steady-state error of less
than 0.3 with a unit ramp input. Find an additional constrain in
terms of ?1 and ?2 such that the...
Problem 1: Steady-state error analvsis (a) A block diagram of a feedback control system is given ...
The Class Name is: MAE 318 System Dynamics and Control I
Problem 1: Steady-state error analvsis (a) A block diagram of a feedback control system is given below. Assuming that the tunable constant Khas a value that makes this closed-loop system stable, find the steady-state error of the closed-loop system for (a a step reference input with amplitude R, r(t)- R u(t) (ii) a ramp reference input with slope R, r(t) = Rt-us(t) R(s) Y(s) (s+2)(s +5) (b) A block...
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...
C(8) for the system shown in Figure 1. R(S Find the equivalent transfer function, Geg (s)...
C(8) for the system shown in Figure 1. R(S Find the equivalent transfer function, Geg (s) 1 Cix) Figure 1. Block diagram 2s+1 s(5s+6Ge(s) = and Figure 2 shows a closed-loop transfer function, where G(s) 2. proper H(s) K+s. Find the overall closed-loop transfer function and express is as rational function. C(s) Ea (s) Controller R(s) +/ Plant G(s) Ge (s) Feedback H(s) Figure 2. Closed loop transfer function Construct the actuation Error Transfer Function associated with the system shown...
Task: 4 (35 Marks) The block diagram representation of a CNC machine speed control system is shown in Figure 4 with the gain of K, and the feedback value of K2. R(s) + cls 100 1 + 0.2s G1=6.5 K1=14.5 K2=0.55 R=3 L=7 C=0.5 Figure 4 (i). Evaluate the closed loop transfer function of the CNC speed control system; (i). Estimate the value of time constant (T) and dc gain K for the CNC speed control system; Note: Each student...
Problem 51: (25 points) Figure 5 is an example of a feedback control system that is designed to regulate the angular position θ(t) of a motor shaft to a desired value θr(t). The signal e(t) represents the error between the measured shaft angle θ(t) and the desired shaft angle θ (t). The Laplace transforms ofa,(t), θ(t), and e(t) are denoted as ΘR(s), θ(s), and E(s), respectively. The control gains Ki and K2 are chosen by the control engineer to achieve...
Question three The figure below shows a unit step response of a second order system. From the graph of response find: 1- The rise timet, 2- The peak timet, 3- The maximum overshoot Mp 4- The damped natural frequency w 5. The transfer function. Hence find the damping ratio ζ and the natural frequency ah-Find also the transfer function of the system. r 4 02 15 25 35 45 Question Four For the control system shown in the figure below,...
3. For the feedback control system shown in Figure Q3 below, the forward-path transfer function given by G(s) and the sensor transfer function is given by H(s). R(s) C(s) G(s) H(s) Figure Q3 It is known that G(s) -- K(+20) S(+5) H(s) = and K is the proportional gain. (S+10) i. Determine the closed-loop transfer function and hence the characteristic equation of the system. [6 marks] ii. Using the Routh-Hurwitz criterion, determine the stability of the closed-loop system. Determine the...
rt)+ e(t) y(t) K1 S +4 Figure 3: A closed-loop control system with an inner feedback loop. Compute the closed-loop transfer function Gal (s) -Y(s)/R(s) for the system shown in Figure 3
rt)+ e(t) y(t) K1 S +4 Figure 3: A closed-loop control system with an inner feedback loop. Compute the closed-loop transfer function Gal (s) -Y(s)/R(s) for the system shown in Figure 3
P4: The car model of a cruise control system is given in the following transfer function block diagram ms + b Where v is the car speed u is the control force m is the mass of the vehicle, 1000 kg b is the damping coefficient, 50 N s/m More details are available here (1) Derive the differential equation relating y(t) to u(t) (2) Determine the time constant of the car dynamics (from u to v) If a proportional feedback...
A unity feedback system is shown in Fig. 1. The closed-loop
transfer function ?(?) of this system is given as
?(?)=?1?4+2?3+(?2+1)?2+?2?+?1.
a) (20%) Using Routh-Hurwitz criteria, find expression (in
terms of ?1 and ?2) and range of value of ?1 and ?2 such that the
above system is stable.
b) (4%) It is desired to achieve steady-state error of less
than 0.3 with a unit ramp input. Find an additional constrain in
terms of ?1 and ?2 such that the...
The Class Name is: MAE 318 System Dynamics and Control I
Problem 1: Steady-state error analvsis (a) A block diagram of a feedback control system is given below. Assuming that the tunable constant Khas a value that makes this closed-loop system stable, find the steady-state error of the closed-loop system for (a a step reference input with amplitude R, r(t)- R u(t) (ii) a ramp reference input with slope R, r(t) = Rt-us(t) R(s) Y(s) (s+2)(s +5) (b) A block...
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...
C(8) for the system shown in Figure 1. R(S Find the equivalent transfer function, Geg (s) 1 Cix) Figure 1. Block diagram 2s+1 s(5s+6Ge(s) = and Figure 2 shows a closed-loop transfer function, where G(s) 2. proper H(s) K+s. Find the overall closed-loop transfer function and express is as rational function. C(s) Ea (s) Controller R(s) +/ Plant G(s) Ge (s) Feedback H(s) Figure 2. Closed loop transfer function Construct the actuation Error Transfer Function associated with the system shown...
Most questions answered within 3 hours.
-
1a. The __________ functional group often triggers our sense of
smell.
1b. The geometry around a...
asked 3 minutes ago -
A uniform plank of length 2.00 m and mass 34.0 kg is supported
by three ropes,...
asked 4 minutes ago -
Suppose a floor on a hospital has 12 physicians at any given
time. You are brought...
asked 18 minutes ago -
Compartmentalization
in eukaryotic cells facilitates chemical reactions happening faster
due to... Select all
Substrates needed for...
asked 4 minutes ago -
The deltaH for the solution process when solid sodium
hydroxide dissolves in water is 44.4 kJ/mol....
asked 7 minutes ago -
a. Discuss the reciprocal/opposite “hormonal” regulation of the
most highly regulated steps of these two pathways....
asked 25 minutes ago -
Members of unions had mounted campaigns to persuade customers
not to shop at a company because...
asked 27 minutes ago -
Why is the alpha carboxyl group pka value 2 ?
And why is an alpha amino...
asked 35 minutes ago -
Identify and assess an intrapreneurial
opportunities within Bank of America and
intrapreneurial assessment. Assess its impact...
asked 41 minutes ago -
How do I figure out the range of possible numbers that can be
represented by the...
asked 43 minutes ago -
A 0.48-kg metal sphere oscillates at the end of a vertical
spring. As the spring stretches...
asked 46 minutes ago -
If a block of Si is doped with 10^17 Boron atom/cm^3 and 5X10^16
Arsenic atoms/cm^3,
(a)...
asked 1 hour ago