1.0 INTRODUCTION 1.0 INTRODUCTION
1.1 History of PID 1.1 History of PID
PID
PID concontrotrolleller r was first been was first been useused d in in autautomaomatic ship tic ship stesteeriering ng whiwhich ch devdeveloeloped ped by by NicNicolaolass Minorsky in 1922 . He designed the controller for the U.S navy. Based on what he had observed, Minorsky in 1922 . He designed the controller for the U.S navy. Based on what he had observed, he
he madmade e a a matmathemhematiatical cal equequatiation on to to simsimpliplify fy his beliefhis beliefs. s. The The proproporportiotional nal concontrotrol l he he madmadee provides
provides the the stability stability against against small small disturbances disturbances yet yet not not for for great great disturbances. disturbances. In In order order toto overcome the problem, the addition of integral term next with derivative term was established. overcome the problem, the addition of integral term next with derivative term was established.
At first, the PID controller was made by using electronic analog PID control loops. Yet, this At first, the PID controller was made by using electronic analog PID control loops. Yet, this system have some problems and may not shows the accurate and precise performance. Thus the system have some problems and may not shows the accurate and precise performance. Thus the digital PID controller were implemented to reduce the problems and to increase the performance digital PID controller were implemented to reduce the problems and to increase the performance in the control loops.
in the control loops.
1.2 PID Controller Theory and Equation 1.2 PID Controller Theory and Equation
u(t) = MV(t) =
u(t) = MV(t) = e(t)e(t)
dτ dτ d d K K )d )d e( e( K K e(t) e(t) K K tt 0 0 d d ii p p
Kp =Kp = ProporProportional gain, a tional gain, a turniturning parameter ng parameter
Ki = Intetgral gain Ki = Intetgral gain
Kd =
Kd = DeriDerivative gainvative gain
e = error, (SP - PV) e = error, (SP - PV)
t = time for instantaneous time t = time for instantaneous time
τ = variable of integration, from 0 to t τ = variable of integration, from 0 to t
PID control is a process system which consists of three different terms that can be manipulate. This three terms are proportional, integral and derivative terms. This terms are summed in order to get the final output of the controller. Each terms plays the important role to achieve the targeted output. Any disturbances or error in a process system can be adjusted to be as what as desired by manipulating this three terms. Thus, it can be said that it is applicable in order to controls the problem and perform the process with very high satisfactorily.
1.3 Description of PID and Death Time
Proportional Term
It was called as proportional term because it produced the output value proportional to the value of current error. The proportionality is gain by Kc. The controller determined how much output changes for the given changes in error. The disadvantage of this term when controlling alone is it will leave an offset error. This error then can be eliminated by the addition of integral term.
p(t) = p’ + K Ce(t)
Integral Term
Its depending on the error and the duration of the error. Integral term is calculated by dividing the time of error with instantaneous error. This term is called as accumulated error which then been multiplied with the integral gain, Ki. It helps to remove the error that occurs in the proportional based controller.
p(t) = p’ + K C
t 0 i et (dt*)* τ e(t)Derivative Term
It used to predict the system behavior with the helps to increase the stability of the system. It can be determine by slope of the error and time. It gives the controller the capability to anticipate
where the process is heading by calculating the derivative error.
p(t) = p’ +
dt de(t) τDS
Death Time
Death time is a delay variable which occurs as a problem to process the signal output. Large death time is such a very big problem to the process control since its delay the output for that time to other forward time. Death time in PID controller need to be eliminate in order to get the significance output value on the right time.
1.4 Effect of manipulating the value of PID towards the response
Increasing the parameters, then vice versa
Term Rise Time Overshoot Settling time Steady state error
stability
Proportional, Kp Decrease Increase Small change Decrease Decrease
Integral, Ki Decrease Increase Increase Eliminate Decrease
Derivative, Kd Small change
Decrease Decrease - Increase if Kd small
1.5 Description of Performance Measurement Criteria
A) Settling time
Time required for the process to achieve the stable state and condition, thus stay at that state for certain range.
B) Overshoot
The problem that occur in the process control when the limit was exceeded. Also called as the maximum peak of the response curve
C) Decay Ratio
Depending on damping ratio and number of oscillation in a period of time. The lower the damping ratio, the lower the number of oscillation in a very long period of time, the lower the decay ratio.
D) Number of Oscillation
Number of oscillation is measured as frequency by dividing with the period of time. It shows how much the system behavior is disturbed from its equilibrium condition.
1.6 Objectives Of Experiment
To study the effect of P,I & D value towards the output system by manipulated it with the given value.
2.0 PROCEDURES
LAB 1
Figure 2.1: Block diagram of Lab 1
1. The block diagram was set up based on the process given.
2. The arrangement of the block diagram is connected to one by one which consist of the scope, display, PID controller, transfer function block, and also clock.
3. Every block diagram was then been filled with the information given which is
Set point = 1 PID controller: P = 0.05, I = 0.01, D = 0 Transfer function = 10s s 5 2
Workspace1 = set to be as ‘ARRAY’ and renamed as TIME
The simulation time was set to 600.
4. The process was run and the graph was been plotted by using the command, “plot(TIME,PV)”
5. Step 1 to 3 was repeated twice for P = 0.1 and P = 0.2 and the graph then was plotted as “figure(2),plot(TIME,PV)” for P = 0.1 and “figure(3),plot(TIME,PV)” for P = 0.2.
6. All of the graph then been combined as one figure which consists of 3 different lines.
LAB 2
Figure 2.2: Block diagram of Lab 2
1. Step 1 to 4 in LAB 1 was repeated by using the same value and information given.
2. Step 1 to 3 in LAB 1 was repeated twice by using different I value which is I = 0.005 and I = 0.0155 the graph then was plotted as “figure(2),plot(TIME,PV)” for I = 0.005 and “figure(3),plot(TIME,PV)” for I = 0.015.
LAB 3
Figure 2.3: Block diagram of Lab 3
1. Step 1 to 4 in LAB 1 was repeated by using the same value and information given.
2. Step 1 to 3 in LAB 1 was repeated twice by using different D value which is D = 1 and D = 2 the graph then was plotted as “figure(2),plot(TIME,PV)” for D=1 and
“figure(3),plot(TIME,PV)” for D = 2.
LAB 4
Figure 2.4: Block diagram of Lab 4
1. The block diagram was set up based on the process given.
2. The arrangement of the block diagram is connected to one by one which consist of the scope, display, PID controller, transfer function block, death time and also clock.
3. Every block diagram was then been filled with the information given which is
Set point = 1 PID controller: P = 0.05, I = 0.01, D = 0 Time delay = 5 Transfer function = 10s s 5 2
Workspace1 = set to be as ‘ARRAY’ and renamed as TIME
Workspace = set to be as ‘ARRAY’ and renamed as PV
4. The process was run and the graph was been plotted by using the command, “plot(TIME,PV)”
5. Step 1 to 3 was repeated twice for time delay = 7 and time delay = 9 and the graph then was plotted as “figure(2),plot(TIME,PV)” for time delay = 7 and “figure(3),plot(TIME,PV)” for time
delay = 9.
3.0 RESULTS AND DICUSSION
LAB 1
In lab 1, the objective of the experiment is to study the effect of Proportional. Proportional has a lesser effect on achieving the set point when it is proven in the experiment conducted. In the experiment conducted, the values of proportional used were 0.5, 0.1 and 0.2. As the proportional values increase, the peak values increase too from P=0.05 to P=0.2. Yet, the number of oscillation and the peak values decrease with increasing time. If the proportional gain is too low, the control action may be too small since it had not enough input to response with the larger disturbances. Thus the optimum value of proportional gained are 0.2 which not too low nor too high. As shown in Figure 4.5 below, the lowest damping ratio obtained by manipulating the proportional term compared to manipulating the integral term or derivative term.
0 100 200 300 400 500 600 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 time P V
effect of controller gain
P = 0.05 P = 0.2 p = 0.1
LAB 2
In lab 2, the objective of the experiment is to study the effect of Integral. Integral has a lesser effect on achieving the set point when it is proven in the experiment conducted. In the experiment conducted, the values of integral used were 0.005, 0.01 and 0.015. The changes in the fluctuation are more obvious as the number of oscillation decreased. From this, it can be confirmed that increasing I, will decrease the number of oscillation . In the figure obtained, it can be concluded that integral time takes a longer time to achieve set point compared to P as in the LAB 1. The integral term accelerates the movement of the process towards set point and eliminates the residual steady-state error that occurs with a pure proportional controller. However, since the integral term responds to accumulated errors from the past, it can cause the present value to overshoot the set point value.
0 100 200 300 400 500 600 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Figure 3.2 I = 0.015 I = 0.01 I = 0.005
Effect of Integral time
LAB 3
In lab 3, the objective of the experiment is to study the effect of Derivative. In the experiment conducted, the values of D used were 0, 1, and 2. Based on the graph, the peaks of the graphs decrease as increasing time with decreasing number of oscillation. The derivative of the process error is calculated by determining the slope of the error over time and multiplying this rate of change by the derivative gain K d . From Figure 3.3 below shows that it has more damping ratio as
compared to the Lab 1 and Lab 2.
0 100 200 300 400 500 600 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
effect of derivative time
time P V D = 0 D = 1 D = 2 Figure 4.7 D = 2 D = 1 D = 0
LAB 4
The objective of the experiment was to study the effect of the dead time by changing the time delay with constant PID value. The dead time delays the input by a specified amount of time. The input to this block should be a continuous signal. At the start of simulation, the block outputs parameter until the simulation time exceeds the time delay parameter. The time delay used in this experiment are 5, 6 and 7 respectively. From the Figure 3.4 shown, increasing value of death time will increased the peak value which obtained the maximum peak value when used 9 as the time delay value and the minimum peak value with time delay of 5. The number of oscillation and peak value decrease with increasing the time of simulation for all values of time delay. 0 100 200 300 400 500 600 0 0.5 1 1.5 2 2.5 time P V
lab 4 (effect of dead time)
time delay = 5 time delay = 7 time delay = 9
4.0 CONCLUSIONS AND RECOMMENDATIONS
Conclusions
Based from the experiment done, the PID uses and function has been determined clearly. Each terms plays important roles in order to control the process without any disturbance or occurrence. The basic term which is proportional term is was first used to eliminate the disturbance. Yet, it was insufficient to responses to large disturbance. Thus, the integral term and derivative term was developed as addition to the proportional term. This three terms regulate the process to produce the signal output which are free of disturbance. The death time is the delay time occur
when processing the signal output. This occurrence need to be totally eliminate. increasing value of PID terms with increasing time will increase the response curve or response peak. However, the number of oscillation decreased with increasing time of simulation. The higher value of delay time the higher disturbance occurred in the process.
Recommendations
1. Calculate the PID values first manually in order to get the range of desired PID values.
