Compensator Assignment (Without introduction and conclusion)

Abstract
In this assignment, lead compensator is implemented to reduce the percentage of peak overshot to less than 5% and the settling time to 2 second with 2% accuracy. First of all, to implement lead compensators into a circuit, a pole–zero pair is introduced into the open loop transfer function. Lead compensator is a component in a control system that improves an undesirable frequency response in a feedback and control system. Besides that, it also provides phase lead in its frequency response. Lead compensator also helps to improve transient response and a small change in steady-state accuracy.Therefore, modification of the circuit are to be taken place to meet the desired performance specification.
Introduction

Product Design Description

Figure 1: The circuit of the assignment before modification

Bill Of Material ( BOM )
Item
Designation
Component Description
Value
Maker/Part Number
Supplier
Quantity
Per Unit Cost (RM)
Total Unit Cost (RM)

Original Part
1
R1
Resistor, Lead Type
1kΩ
N/A
I.E
4
0.05
0.20
2
R2
Resistor, Lead Type
1MΩ
N/A
I.E
1
0.05
0.05
3
R3
Resistor, Lead Type
500kΩ
N/A
I.E
1
0.05
0.05
4
R4
Resistor, Lead Type
400kΩ
N/A
I.E
2
0.05
0.10
5
R3
Resistor, Lead Type
80kΩ
N/A
I.E
1
0.20
0.05
6
C1
Ceramic Capacitor
1μF
N/A
I.E
3
0.20
0.60
7
TL082
Op-Amp
N/A
TL082
I.E
2
0.80
1.60
Gain Part
8
Ra
Resistor, Lead Type
500Ω
N/A
I.E
1
0.05
0.05
9
Rb
Resistor, Lead Type
620kΩ
N/A
I.E
1
0.05
0.05
Compensator Part
10
R1
Resistor, Lead Type
21kΩ
N/A
I.E
1
0.05
0.05
11
R2
Resistor, Lead Type
2.4kΩ
N/A
I.E
1
0.05
0.05
12
C1
Ceramic Capacitor
22μF
N/A
I.E
1
0.20
0.20 Total Amount:
RM 3.05

Part by Part Derivation

The Figure below shows the block diagram of the system before modification.

Based on the derivation part by part, we know that:
Open Loop Gain =