microconrollers
Question #1 (60 pts): A closed-loop digital control system having a proportional controller is given in the following figure ?1 (?) = 1 − exp(−??) ?(? + 1) , ?2 (?) = 1 ? , ?3 (?) = 1 − exp(−??) ?(? + 2) where exp(⋅) denotes the standard exponential function. a) (20 pts) Obtain the overall transfer function of the closed-loop system. b) (20 pts) Obtain the range of proportional gain (i.e., K) that guarantees the system stability via Jury’s Stability Test. c) (20 pts) Assume that the input of the system is a unit step input (i.e., ?(?) = ??(?)), obtain the gain value from the range obtained in (b) that provides the least possible steady-error (i.e., lim ?→∞ ?[?]) value. What is the least possible steady-state error value for your selection?
Homework Answers
Request Answer!
We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
A closed-loop digital control system having a proportional controller is given in the following figure ?1 (?) = 1 − exp(−??) ?(? + 1) , ?2 (?) = 1 ? , ?3 (?) = 1 − exp(−??) ?(? + 2) where exp(⋅) denotes the standard exponential function. a) (20 pts) Obta
Question #1 (60 pts): A closed-loop digital control system having a proportional controller is given in the following figure\(G_{1}(s)=\frac{1-\exp (-T s)}{s(s+1)}, G_{2}(s)=\frac{1}{s}, G_{3}(s)=\frac{1-\exp (-T s)}{s(s+2)}\)where \(\exp (\cdot)\) denotes the standard exponential function.a) Obtain the overall transfer function of the closed-loop system.b)Obtain the range of proportional gain (i.e., \(\mathrm{K}\) ) that guarantees the system stability via Jury'sStability Test.c) Assume that the input of the system is a unit step input (i.e., \(r(t)=u_{s}(t)\) ), obtain the gain value from the range obtained in...
Problem 3 (25%): The closed-loop system has the block diagram shown below. Controlle Process Sensor s + l (a) (5%) Sketch the root locus of the closed-loop system. (b) (5%) Determine the range of...
Problem 3 (25%): The closed-loop system has the block diagram shown below. Controlle Process Sensor s + l (a) (5%) Sketch the root locus of the closed-loop system. (b) (5%) Determine the range of K that the closed-loop system is stable. (c) (5%) Find the percentage of overshoot and the steady state error due to a unit step input of the open loop system process. (d) (5%) Find the steady-state error due to a unit step input of the closed-loop...
Spring 2019 3. Given a closed-loop control system with unity feedback is shown in the block...
Spring 2019 3. Given a closed-loop control system with unity feedback is shown in the block diagram. G(s) is the open-loop transfer function, and the controller is a gain, K. 1. (20) Calculate the open-loop transfer function tar →Q--t G(s) (10) Calculate the steady-state error to a step input of the open-loop system. 7. (in Bode Form) from the Bode plot. (10) Calculate the shortest possible settling time with a percentage overshoot of 5% or less. 8. 2. (10)Plot the...
yUCni ias the block diagram shown below. Controller Process Sensor (a) (5%) Sketch the root locus of the closed-loop system. (b) (5%) Determine the range of K that the closed-loop system is stabl...
yUCni ias the block diagram shown below. Controller Process Sensor (a) (5%) Sketch the root locus of the closed-loop system. (b) (5%) Determine the range of K that the closed-loop system is stable. (c) (5%) Find the percentage of overshoot and the steady state error due to a unit step input of the open loop system process. (d) (5%) Find the steady-state error due to a unit step input of the closed-loop syste as a function of the design parameter...
PARTB 4. You are designing a system to enable a robot to stand on a trapeze. For small rotations, the robot can be assu...
PARTB 4. You are designing a system to enable a robot to stand on a trapeze. For small rotations, the robot can be assumed to obey the following differential equation d2 θ (t) dP--θ (t) = F(t) dt2 where θ(t) is the output angle (between the robot and a vertical reference) and F(1) is the input force exerted by a motor. a) Write the transfer function for the robot (ie a plant that converts the input to the output) b)...
Question #4 (25 points): Consider the open loop system that has the following transfer function 1 G(S) = 10s+ 35 Us...
Question #4 (25 points): Consider the open loop system that has the following transfer function 1 G(S) = 10s+ 35 Using Matlab: a) Plot the step response of the open loop system and note the settling time and steady state 15 pts error. b) Add proportional control K 300 and simulate the step response of the closed loop 15 pts system. Note the settling time, %OS and steady state error. c) Add proportional derivate control Kp 300, Ko 10 and...
G) r(t) Figure 1: Feedback control system A pulley and belt transmission has a linearized relationship between the driven pulley angle θ(t) in degrees and the input torque u(t) in Newton meters given...
G) r(t) Figure 1: Feedback control system A pulley and belt transmission has a linearized relationship between the driven pulley angle θ(t) in degrees and the input torque u(t) in Newton meters given by the following differential equation du(t) A feedback control system (illustrated in Figure 1) needs to be designed such that the closed-loop system is asymptotically stable and such that the following design criteria are met: 1. the gain crossover frequency a should be between and a 2....
Q.3(a) Transfer function model of a plant is, G(s) The controller is Ge(s)-K, where K is a constant. Find the value of K such that steady-state error for unit ramp input is 0.1. Find the gain margin...
Q.3(a) Transfer function model of a plant is, G(s) The controller is Ge(s)-K, where K is a constant. Find the value of K such that steady-state error for unit ramp input is 0.1. Find the gain margin and the phase mar gin (6 marks) (b) What are the effects on gain margin, phase margin and steady-state error, if the gain K is increased? (3 marks (c) Can the closed loop be unstable if the controller of Q.3(a) is implemented digi...
Problem 1 An inverted pendulum driven by a d-c motor is governed by the following differential...
Problem 1 An inverted pendulum driven by a d-c motor is governed by the following differential and algcbraic equa tions: (a) Determine the transfer function of the process. (b) It is proposed to control the process using "proportional control": where yr is a constant reference value. Determine the value Kmir for which the gain K must exceed in order that the closed-loop system be stable. (c) Determine the value of K for which the magnitude of the error is less...
1) Use Lyapunov stability criterion to find range of K for which a proportional feedback system...
1) Use Lyapunov stability criterion to find range of K for which a proportional feedback system with gain K and an open loop transfer function G(S) = 1/(S2+S-20) is stable. (12 pts.)
Problem 3 (25%): The closed-loop system has the block diagram shown below. Controlle Process Sensor s + l (a) (5%) Sketch the root locus of the closed-loop system. (b) (5%) Determine the range of K that the closed-loop system is stable. (c) (5%) Find the percentage of overshoot and the steady state error due to a unit step input of the open loop system process. (d) (5%) Find the steady-state error due to a unit step input of the closed-loop...
Spring 2019 3. Given a closed-loop control system with unity feedback is shown in the block diagram. G(s) is the open-loop transfer function, and the controller is a gain, K. 1. (20) Calculate the open-loop transfer function tar →Q--t G(s) (10) Calculate the steady-state error to a step input of the open-loop system. 7. (in Bode Form) from the Bode plot. (10) Calculate the shortest possible settling time with a percentage overshoot of 5% or less. 8. 2. (10)Plot the...
yUCni ias the block diagram shown below. Controller Process Sensor (a) (5%) Sketch the root locus of the closed-loop system. (b) (5%) Determine the range of K that the closed-loop system is stable. (c) (5%) Find the percentage of overshoot and the steady state error due to a unit step input of the open loop system process. (d) (5%) Find the steady-state error due to a unit step input of the closed-loop syste as a function of the design parameter...
PARTB 4. You are designing a system to enable a robot to stand on a trapeze. For small rotations, the robot can be assumed to obey the following differential equation d2 θ (t) dP--θ (t) = F(t) dt2 where θ(t) is the output angle (between the robot and a vertical reference) and F(1) is the input force exerted by a motor. a) Write the transfer function for the robot (ie a plant that converts the input to the output) b)...
Question #4 (25 points): Consider the open loop system that has the following transfer function 1 G(S) = 10s+ 35 Using Matlab: a) Plot the step response of the open loop system and note the settling time and steady state 15 pts error. b) Add proportional control K 300 and simulate the step response of the closed loop 15 pts system. Note the settling time, %OS and steady state error. c) Add proportional derivate control Kp 300, Ko 10 and...
G) r(t) Figure 1: Feedback control system A pulley and belt transmission has a linearized relationship between the driven pulley angle θ(t) in degrees and the input torque u(t) in Newton meters given by the following differential equation du(t) A feedback control system (illustrated in Figure 1) needs to be designed such that the closed-loop system is asymptotically stable and such that the following design criteria are met: 1. the gain crossover frequency a should be between and a 2....
Q.3(a) Transfer function model of a plant is, G(s) The controller is Ge(s)-K, where K is a constant. Find the value of K such that steady-state error for unit ramp input is 0.1. Find the gain margin and the phase mar gin (6 marks) (b) What are the effects on gain margin, phase margin and steady-state error, if the gain K is increased? (3 marks (c) Can the closed loop be unstable if the controller of Q.3(a) is implemented digi...
Problem 1 An inverted pendulum driven by a d-c motor is governed by the following differential and algcbraic equa tions: (a) Determine the transfer function of the process. (b) It is proposed to control the process using "proportional control": where yr is a constant reference value. Determine the value Kmir for which the gain K must exceed in order that the closed-loop system be stable. (c) Determine the value of K for which the magnitude of the error is less...
1) Use Lyapunov stability criterion to find range of K for which a proportional feedback system with gain K and an open loop transfer function G(S) = 1/(S2+S-20) is stable. (12 pts.)
Most questions answered within 3 hours.
-
Please explain steps:
An 80 kg swimmer steps off a platform 10 m above the water...
asked 6 minutes ago -
A lottery exists where balls numbered 1 to 17 are placed in an
urn. To win,...
asked 9 minutes ago -
26) Briefly describe, using words or simple diagrams, the
chemiosmotic theory for coupling oxidation to phosphorylation...
asked 2 hours ago -
Suppose that XX is a random variable with mean 16 and standard
deviation 5 . Also...
asked 2 hours ago -
Calculate the number density of argon gas at a temperature of
24C and a pressure of...
asked 6 hours ago -
Alternative
Classification
How to Estimate
Probabilities from Data? ( For continuous Attributes)
And How to generate...
asked 6 hours ago -
An explosion breaks a 20.0-kg object into three parts. The
object is initially moving at a...
asked 7 hours ago -
Calculate the approximate number of residues of Rubisco, which
is involved in carbon fixation in plants,...
asked 8 hours ago -
Other decisions about scientific claims can have a much broader
impact.ENERGYarrow-10x10.png, environment, health, security - all...
asked 8 hours ago -
I need to write a research paper and work cited about this
topic: The United States...
asked 9 hours ago -
Hello! I was wondering if I could have some help?
If the vapor pressure of carvone...
asked 9 hours ago -
An economist wants to estimate the mean per capita income (in
thousands of dollars) for a...
asked 9 hours ago