Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
In this system, the muscle has been modelled as a linear system which has a relation between the tension it performs (muscle-tendon force, fmt (t)) and the length of the same, x(t). This force can be stimulated by a stimulation system, FES. The system is designed with the purpose to obtain a desired length of the muscle, xa(t). This value is compared in real time with the effect obtained, providing an error, e(t), which must be corrected by the use of controller, Ge(s). xa(t) e(t) fmt(t) x(t) Ge(s) H(s) Figure 5 Control system for FES ks fs fe fmt fr Figure 6 Linear muscle model The Hill model can be used to describe the behaviour of the muscle as a mechanical system (Figure 6). Different forces that appear in the behaviour of the muscle have been considered. An interpretation, according classical mechanics, has been performed. Resistance to elongation or contraction can be described as a spring with a constant ks (generating a force f, ), acting in parallel with a damper with damping factor c, which develops a force fc. In addition, we must consider the force of friction of Coulomb, fr(t), and the force of the muscle-tendon assembly, fmt- The resulting model can be described with the following equation, obtained from the application of Newton's laws 2i = fmt - fr-fs-fe = më Being: fr = umgi fs = kgx fe = cx The system is to be regulated in order to obtain the desired distance. In order to get this goal, a strain gauge is used as sensor. Assume that H(s)%=1 and the following parameter values are given: m = 100 g, ks = 20 m' %3D Ns c = 4,g= m 9.81,u = 0.1. In this scenario, answer the following questions. a) What is the length of muscle if the desired length of muscle is 10cm and G.(s) = 4. b) It is stated that the system response to a unit step input should have an overshoot below 20% and a settling time below 2s. Can a proportional controller satisfy these specifications? Explain. c) Design a phase lead controller such that the response to a unit step input would have an overshoot below 15% and a settling time below 1.5s.

In this system, the muscle has been modelled as a linear system which has a relation between the tension it performs (muscle-tendon force, fmt (t)) and the length of the same, x(t). This force can be stimulated by a stimulation system, FES. The system is designed with the purpose to obtain a desired length of the muscle, xa(t). This value is compared in real time with the effect obtained, providing an error, e(t), which must be corrected by the use of controller, Ge(s). xa(t) e(t) fmt(t) x(t) Ge(s) H(s) Figure 5 Control system for FES ks fs fe fmt fr Figure 6 Linear muscle model The Hill model can be used to describe the behaviour of the muscle as a mechanical system (Figure 6). Different forces that appear in the behaviour of the muscle have been considered. An interpretation, according classical mechanics, has been performed. Resistance to elongation or contraction can be described as a spring with a constant ks (generating a force f, ), acting in parallel with a damper with damping factor c, which develops a force fc. In addition, we must consider the force of friction of Coulomb, fr(t), and the force of the muscle-tendon assembly, fmt- The resulting model can be described with the following equation, obtained from the application of Newton's laws 2i = fmt - fr-fs-fe = më Being: fr = umgi fs = kgx fe = cx The system is to be regulated in order to obtain the desired distance. In order to get this goal, a strain gauge is used as sensor. Assume that H(s)%=1 and the following parameter values are given: m = 100 g, ks = 20 m' %3D Ns c = 4,g= m 9.81,u = 0.1. In this scenario, answer the following questions. a) What is the length of muscle if the desired length of muscle is 10cm and G.(s) = 4. b) It is stated that the system response to a unit step input should have an overshoot below 20% and a settling time below 2s. Can a proportional controller satisfy these specifications? Explain. c) Design a phase lead controller such that the response to a unit step input would have an overshoot below 15% and a settling time below 1.5s.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
See similar textbooks
icon
Related questions
Question
In this system, the muscle has been modelled as a linear system which has a relation between the tension it performs (muscle-tendon force, fmt (t)) and the length of the same, x(t). This force can be stimulated by a stimulation system, FES. The system is designed with the purpose to obtain a desired length of the muscle, xa(t). This value is compared in real time with the effect obtained, providing an error, e(t), which must be corrected by the use of controller, Ge(s). xa(t) e(t) fmt(t) x(t) Ge(s) H(s) Figure 5 Control system for FES ks fs fe fmt fr Figure 6 Linear muscle model The Hill model can be used to describe the behaviour of the muscle as a mechanical system (Figure 6). Different forces that appear in the behaviour of the muscle have been considered. An interpretation, according classical mechanics, has been performed. Resistance to elongation or contraction can be described as a spring with a constant ks (generating a force f, ), acting in parallel with a damper with damping factor c, which develops a force fc. In addition, we must consider the force of friction of Coulomb, fr(t), and the force of the muscle-tendon assembly, fmt- The resulting model can be described with the following equation, obtained from the application of Newton's laws 2i = fmt - fr-fs-fe = më Being: fr = umgi fs = kgx fe = cx The system is to be regulated in order to obtain the desired distance. In order to get this goal, a strain gauge is used as sensor. Assume that H(s)%=1 and the following parameter values are given: m = 100 g, ks = 20 m' %3D Ns c = 4,g= m 9.81,u = 0.1. In this scenario, answer the following questions. a) What is the length of muscle if the desired length of muscle is 10cm and G.(s) = 4. b) It is stated that the system response to a unit step input should have an overshoot below 20% and a settling time below 2s. Can a proportional controller satisfy these specifications? Explain. c) Design a phase lead controller such that the response to a unit step input would have an overshoot below 15% and a settling time below 1.5s.
Transcribed Image Text:In this system, the muscle has been modelled as a linear system which has a relation between the tension it performs (muscle-tendon force, fmt (t)) and the length of the same, x(t). This force can be stimulated by a stimulation system, FES. The system is designed with the purpose to obtain a desired length of the muscle, xa(t). This value is compared in real time with the effect obtained, providing an error, e(t), which must be corrected by the use of controller, Ge(s). xa(t) e(t) fmt(t) x(t) Ge(s) H(s) Figure 5 Control system for FES ks fs fe fmt fr Figure 6 Linear muscle model The Hill model can be used to describe the behaviour of the muscle as a mechanical system (Figure 6). Different forces that appear in the behaviour of the muscle have been considered. An interpretation, according classical mechanics, has been performed. Resistance to elongation or contraction can be described as a spring with a constant ks (generating a force f, ), acting in parallel with a damper with damping factor c, which develops a force fc. In addition, we must consider the force of friction of Coulomb, fr(t), and the force of the muscle-tendon assembly, fmt- The resulting model can be described with the following equation, obtained from the application of Newton's laws 2i = fmt - fr-fs-fe = më Being: fr = umgi fs = kgx fe = cx The system is to be regulated in order to obtain the desired distance. In order to get this goal, a strain gauge is used as sensor. Assume that H(s)%=1 and the following parameter values are given: m = 100 g, ks = 20 m' %3D Ns c = 4,g= m 9.81,u = 0.1. In this scenario, answer the following questions. a) What is the length of muscle if the desired length of muscle is 10cm and G.(s) = 4. b) It is stated that the system response to a unit step input should have an overshoot below 20% and a settling time below 2s. Can a proportional controller satisfy these specifications? Explain. c) Design a phase lead controller such that the response to a unit step input would have an overshoot below 15% and a settling time below 1.5s.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 9 steps with 9 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Mathematical Modeling of Mechanical System
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS