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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
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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.
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