This document discusses the design and analysis of a controller for a standard dexterous arm model. It analyzes the step responses of the arm model using different controller types, including PI, PD, and PID controllers. The PID controller provided the best performance with the fastest rise time, lowest settling time, and minimal overshoot. Specifically: 1) A standard dexterous arm model is simulated using MATLAB to analyze different controller designs. 2) PI, PD, and PID controllers are implemented and their step responses analyzed and compared. 3) The PID controller provided the best performance metrics with rise time of 0.164 seconds, settling time of 0.792 seconds and overshoot of 1.16.

1. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 6, Issue 1, January (2015), pp. 73-78 © IAEME
73
CONTROLLER DESIGN AND OPTIMIZED SYSTEM
ANALYSIS FOR STANDARD DEXTEROUS ARM MODEL
Swati Barui1
, Debasmita Manna2
, Subhasish Ghosh3
, Biswarup Neogi4
1
Dept. Electronics & Communication Engineering,
Narula Institute of Technology, Agarpara, Kolkata-109, India,
2
Dept. Electronics & Communication Engineering,
Dr.Sudhir Chandra Sur Degree Engineering College DumDum,
Kolkata-74, India,
3
Dept. Electronics & Communication Engineering,
Narula Institute of Technology, Agarpara, Kolkata-109, India,
4
Dept. Electronics & Communication Engineering,
JIS College of Engineering, Kalyani, Nadia,India,
ABSTRACT
Prostheses are typically used to replace body parts lost by injury (traumatic) or missing from
birth (congenital) or to supplement defective body parts.The recent development of dexterous arm is
remodeled with different implementations of Biomedical Control Engineering. A prosthetic limb
needs to be well connected to the original connecting organ for faithful function of overall system.
One of the advanced concepts of designing of prosthetic arm is proposed by the concept of a virtual
prosthetic control system of prosthetic arm presented by the analysis of a grasp motion or dexterity.
This informative paper designates a standard dexterous arm model for designing of controller section
with transfer functional approach.
Keywords: Prosthetic Arm, Dexterity, PD, PI, PID controller, Step Response, Transfer Function
1. INTRODUCTION
Dexterity is commonly used in application to motor skills of hands and fingers. The
generalized meaning of dexterity is skill and grace in physical movement, especially in the use of the
hands. The “Prosthetic” word is originated from Prostheses mean anaesthetics. It is an artificial
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6464(Print), ISSN 0976 – 6472(Online), Volume 6, Issue 1, January (2015), pp. 73-78 © IAEME
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extension that replaces a missing body part [1]. Within science fiction and more recently within the
scientific community, there has been consideration given to using advanced prostheses to replace
healthy body parts with artificial mechanisms and systems to improve function [2]. Although no such
"enhancement prosthetics" have yet been created and demonstrated to work for healthy individuals,
the morality and desirability of such technologies is debated. Body parts such as legs, arms, hands,
feet, and most other body parts can be replaced. So in the point of view of welfare in society the
Artificial Limb/Arms system is considered. The technology is based on Electro Myo-Graphic (EMG)
signals and error control system. Prosthesis, prosthetic, or prosthetic limb is an artificial device
extension that replaces a missing body part. The concept of the artificially generated limb connected
to the nervous system to be in immediate contact to the concerned limb and lastly to brain system
able to make the overall control of the total living system was introduced in the new prospective [1].
In the present work a standard dexterous arm model has considered for designing of controller
section. Firstly, the step responses are studied for different controller by simulation and further
different control parameters are also compared.
2. DEXTEROUS ARM MODEL CONFIGURATION
The standard dexterous arm model is shown in Fig.1 .The value of Km is 1[4]. Here,
appropriate controller design is intended to obtain the optimized result.
Fig.1: Standard dexterous arm model [4]
The transfer function of the PID controller is as follows:
‫݌ܭ‬ +
௄௜
ௌ
+ ‫ܵ݀ܭ‬ =
௄ௗௌమା௄௣ௌା௄௜
ௌ
(1)
Where Kp is the proportional gain, Ki is the integral gain, and Kd is the derivative gain. For PI
controller, Kd = 0. So the controller transfer function is
௄௣ௌା௄௜
ௌ
. For PD controller, Ki = 0.So the
controller transfer function is
௄ௗௌమା௄௣ௌ
ௌ
[5].Now, the entire model can be represented by the block
diagram shown in Fig.2.

3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 6, Issue 1, January (2015), pp. 73-78 © IAEME
75
+
R(s) Y(s)
-
Fig.2: Block diagram of standard dexterous arm model
The effect of Kp, Ki, Kd on the closed-loop system is very important for analysing the
control parameters. A large Kp will have the effect of reducing the rise time and will reduce (but
never eliminate) the steady-state error. Integral control (Ki) will have the effect of eliminating the
steady-state error, but it will make the transient response worse. If integral control is to be used, a
small Ki should always be tried first. Derivative control will have the effect of increasing the
stability of the system, reducing the overshoot, and improving the transient response [6]. The effects
on the closed-loop response of adding to the controller terms Kp, Ki and Kd are listed in Table 1.
Table 1: Effects of kp, ki, kd [5]
3. TRANSFER FUNCTION FORMATION BY SIMULATION APPROACH
All the results are extracted by designing the different Controller Transfer Function to get
response through simulation using MATLAB.
3.1 Case 1: PI Controller
The overall system step response with PI controller is shown in Fig.3.
Fig.3: Step response of the model with PI controller
CLOSED LOOP
RESPONSE
RISE TIME OVERSHOOT SETTLING TIME
Kp Decreases Increases No Changes
Ki Decreases Increases Increases
Kd No Changes Decreases Decreases
‫ܵܦܭ‬ଶ
+ ‫ܵܲܭ‬ + ‫ܫܭ‬
ܵ
1
‫ݏ(ݏ‬ + 5)(‫ݏ‬ + 10)

4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 6, Issue 1, January (2015), pp. 73-78 © IAEME
76
Here,
Kp=100;
Ki=10;
Kd=0
The corresponding system transfer function can be calculated as
௒(௦)
ோ(௦)
=
ଵ଴଴௦ାଵ଴
௦మ(௦ାହ)(௦ାଵ଴)
(2)
3.2 Case 2: PD Controller
The overall system step response with PD controller is shown in Fig.4.
Fig.4: Step response of the model with PD controller
Here,
Kp=340;
Kd=95;
Ki=0
The corresponding transfer function can be calculated as
௒(௦)
ோ(௦)
=
ଽହ௦మାଷସ଴௦
௦మ(௦ାହ)(௦ାଵ଴)
(3)
3.3 Case 3: PID Controller
The overall system step response with PID controller is shown in Fig.5.
Fig.5: Step response of the model with PID controller

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6464(Print), ISSN 0976 – 6472(Online), Volume 6, Issue 1, January (2015), pp. 73-78 © IAEME
77
Here,
KP=500;
KI=10;
KD= 100;
The corresponding system transfer function can be calculated as
௒(௦)
ோ(௦)
=
ଵ଴଴௦మାହ଴଴௦ାଵ଴
௦మ(௦ାହ)(௦ାଵ଴)
(4)
4. COMPARATIVE ANALYSIS FOR CONTROLLER SELECTION
The corresponding Control parameters for all three cases are shown in Table 2,Table 3 and
Table 4.
Table 2: Control parameters for case 1
Table 3: Control parameters for case 2
Table 4: Control parameters for case 3
Here for all the three types of controller the system is stable as all the responses reach its unit
steady state value, but for PI controller the settling time is more than the other two cases. So, it
would not be opted for further analysis. In between PD and PID controller, system parameters for
PID controller are better than the PD controller. So, the system with PID controller is best in
performance and selected for further tuning for the reduction of steady state error.
5. CONCLUSION
This work involves the selection of controller for a standard dexterous arm model through
simulation approach. Taking a comparison it can be concluded that PID controller is best for the
Different Parameters Value
Maximum Overshoot 1.14
Settling Time 9.89s
Rise Time 0.637s
Different Parameters Value
Maximum Overshoot 1.05
Settling Time 0.82s
Rise Time 0.2s
Different Parameters Value
Maximum Overshoot 1.16
Settling Time 0.792s
Rise Time 0.164s

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system in terms of rise time, settling time, overshoot. As a result, the transfer function of the system
with PID controller is more effective because of its fastest response. This transfer function would be
effective for further tuning to get more accurate error free response for designing the actual system.
Proper controller selection made the system useful for tuning parameter value selection through
computational approach. In future different optimization techniques would be adopted to get the
more optimized system response by minimizing the steady state error. Also discretization of the
system for performance analysis in discrete domain would have been done for the design aspect of
dexterous arm.
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