PID Controller Simulator Design for Polynomials Transfer Function

Department of Avionics Engineering
AE-3452
Modern Control Systems
Experiment No. 12
PID Controller Simulator Design for Polynomials
Transfer Function
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PID Controller Simulator Design for Polynomials Transfer Function
Objective:
• To compute responses at different values of PID for a transfer function for both open
loop and Closed Loop Simulation.
Theory
PID controller is a controller used to determine precision of a system instrument employing
feedback of the system. The component of PID control can be applied simultaneously or singly
depends on the response we desired from a plant. However, there is problem in analyzing planned
system response; how to get transfer function from a system and analyze it quickly and easily. As
of today, control system engineers still encounter difficulty in analyzing system response
especially for transfer function using polynomial equations of degree greater than two and
employing trial and error method when analyzing response in the simulation. Thus, the writers
design a simulator to solve this problem by using Graphical User Interface. The design of the
program can be used for polynomial transfer function and installed directly to computer with
smaller memory capacity. Hence, it is more user-friendly and not slowing down the operating
system of computer. To ensure that the output of simulation correctly generated, we implemented
block diagram modeling in Simulink. In the future, the result of this research can be implemented
as reference to easily understand the characteristics of PID controller especially for polynomials
transfer function.
Introduction
PID Controller is one of the controllers that widely used in almost 90% process of industrial
system. The system is easily affiliated with other control methods such as Fuzzy and Robust, which
makes it better control system. PID Controller consists of the combination of three controllers; P
(Proportional) Controller, I (Integral) Controller, and D (Derivative) Controller, and each
has its respective tuning parameters to properly operate called constants.
Each type has its advantages and disadvantages. It is difficult and boring to view a response of a
system with a variety of combination from input signal and control action. The process needs high
accuracy and calculation, yet the description of the output oftentimes is inaccurate, especially for

polynomial transfer functions. To address this issue, we need simulation software to acquire
response from a system with convenience and time efficiency. One of the software that is
appropriate for this
PID Simulator:
GUI stands for Graphical User Interface, a display application containing tasks, commands, or
components of a program that makes it easy for users to run a program. In this GUI has perfected
a Graphical User Interface to make it easier to analyze the PID controller, the view of the GUI can
be seen in the image below:
Figure 1: GUI PID Controller
Input Values:
In the Input Panel and there are 2 text boxes for transfer function and the other 2 boxes for the
feedback.
Loop system
In a control system, there are two types of control system namely closed loop system and open
loop system where in the GUI PID controller that has been created can choose either for closed
loop system or open loop system or both.

Example:
Proportional – integral controller simulation with Simulink
Polynomial equations for this simulation are
H (S) = 1; Kp = 1; Ki = 0.5; input = 1; Time = 4 seconds. The data Input process can be seen in
the image:
Figure 2: Block Diagram for proportional integral control
Figure 3: Output response for Kp = 1 and Ki = 0.5
System response from figure 4 shows that proportional integral controls have the characteristic of
reducing up time, adding overshoot and down time, as well as eliminating the steady state.

Proportional – integral controller simulation with graphic user interface
The same simulation is done for proportional and integral controllers by entering the
following equation (1). Where H (S) = 1; Kp = 1; Ki = 0.5; input = 1; Time = 4 seconds. The
data Input process can be seen in the image:
Task 1:
Use the following equation:
H (S) = 1; Kp = 18; Ki = 12,811 Kd = 6.3223; input = 1. Time = 15 seconds.
Task 2:
𝑪(𝒔)
𝑹(𝒔)
= 𝑮(𝑺) =
𝟓𝟎. 𝟗
𝒔𝟑 + 𝟏𝟎𝟏. 𝟑𝟐𝒔𝟐 + 𝟏𝟑𝟐𝒔

Check is this system is stable and give the desired Values or not?

PID Controller Simulator Design for Polynomials Transfer Function

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PID Controller Simulator Design for Polynomials Transfer Function