Sunum İngilizce
Transcript of Sunum İngilizce
Erciyes University
Mechatronics Engineering
Control Systems-II
PID Control Project
Murat Sedat SEVİNDİK
1031120003
Index
1-Abstract
2-Introduction
3.1-Physical Model Of the System
3.2-Mathematical Model of the System
3.3-Control System
4-Control of the System wiht Controllers
5-Simulation Results
6-Conclusion
1-Abstract
We will work to reducing the error which in the systems with various control method.Firstly we convert the mathematical model of the physical model.we find transfer function. We find the system transfer function of obtained from the mathematical model. We will get the transition curve of this transfer function. We will work to set P-PI-PD and PID parameters using rhe transition curve.
2-Introduction
The systems need control effect how to set control value to intented value or control value provide to variable the depending different value and present control error reducing, if possible to reset.
The controllers generate the control effect depending of system’s transfer function.This effect send to last control system part how command signal.
System control shown in Fig 2.1.
Figure 2.1 Control of the Systems
The type of controllers are defined transfer function H(s) that signalize command effect of systems or implementing control type. The controller’s block diagram shown in Fig 2.2.
The controllers can include variable control effect.
This effects are
Proportional effect
Integral effect
Derivative effect.
Figure 2.2 : Block Diagram of the Control Member
3-Description of the System
3.1-Physical Model of the System
Firstly we start explain the components these are in the system.’M’ define the mass.’C’ define the viscous damping characteristic parameter.’K’ define the spring stability characteristic parameter.
Before the solving the system we will assign values to variables for the mathematical model.
M = 10 kg
C1 = C2 = 100 Ns/m
K1 = K2 = 200 N/m
L = 10m
F = Applied the force of rigid links
Θ = Horizontal angle of rigid links
Figure 3.1 Physical Model of the System
3.2-Mathematical Model of the System
After of the defining in physical model we will find the mathematical model of the system.We will find the mathematical model of the system for see response of the system and make laplace transform.This equation will tell us transfer function in laplace domain.
Figure 3.2 Effects of Parts
Fm1=m1∗x Fm2=m2∗x
F c1=c1∗x F c2=c2∗x
F k 1=k 1∗x F k 2=k 2∗x
Firstly we will calculate the moment distribution.But effort distances are equal because of that we can add the forces.This sum give us the moment equality.
Define the forces which clock wise positive force.
∑M A=0
Fm1+Fm2+Fc1+Fc2+Fk 1+Fk 2−F=0
This equation charactarize the moment result. X parameter state movement of vertical
axis.But we need to output that define the Θparameter. Θparameter is horizontal angle of rigid
links.
x= L2∗sinΘ
For the solving the system we are admitted sinΘ~¿Θ and find X parameter.
x= L2∗Θ
x= L2∗Θ
x= L2∗Θ
After the all of the defines we can find the transfer function;
m1∗x+c1∗x+k 1∗x+m2∗x+c2∗x+k2∗x−F=0
F=(m1+m2 ) x+(c¿¿1+c2)∗x+(k1+k 2)∗x ¿
F=(m1+m2 )∗L
2∗Θ+
(c¿¿1+c2)∗L2
∗Θ+(k1+k2)∗L
2∗Θ¿
Laplace transform of equation
F ( s )=(m1+m2 )∗L
2∗Θ ( s )∗s2+
(c¿¿1+c2)∗L2
∗Θ (s )∗s+(k1+k2)∗L
2∗Θ(s)¿
F ( s )=L2∗Θ ( s)∗¿
Θ (s )F (s)
= 2¿¿
3.3-Control System
We will use method of continuous vibration in control system.This method discovering by two researcher Ziegler and Nichols.This method provide determine the temporary P paramater experimental way.I ve D parameters will define ‘0’ value.The first overlap called Kmax which we find the transition curve and the vibration period called Tp.
Proportional Controllers
K=0.5*Kmax
Proportional+Integral Controllers
K=0.45*Kmax
Ti=Tp/1.2
Proportional+Derivative Controllers
K=0.6*Kmax
Td=Tp/8
Proportional +Integral+ Derivative Controllers
K=0.6*Kmax
Ti=Tp/2
Td=Tp/8
4.Control of the System with Controllers
We will design the system in MATLAB Simulink. Find Kmax and prove the all of controllers.
Figure 4.1 Control System of Matlab Simulink
Before the prove all of controllers we must the find Kmax.
We can find Kmax experimantal P parameters define 50000. This time rate first overflow of second overflow is 1/4.We can see in Fig 4.2.
Therefore Kmax=50000 and Tp=0.32.
Figure 4.2 System output(Scope)
Setting the P control parameters;
K=0.5Kmax
K=25000
Setting the PI control parameters;
K=0.45Kmax
K=22500
Ti=Tp/1.2
Ti=0.27
PI Control Parameters
P=22500
I=K/Tı=84375
Setting the PD control parameters;
K=0.6Kmax
K=30000
Td=Tp/8
Td=0.04
PD Control Parameters
P=30000
D=K*Td=1200
Setting the PID control parameters;
K=0.6Kmax
K=30000
Tı=Tp/2
Tı=0.16
Td=Tp/8
Td=0.04
PID Control Parameters
P=30000
I=K/Tı
I=187500
D=K*Td
D=1200
5.Simulation Results
Simulation Results for P Control;
Figure 5.1 P Control Simulation Results
Simulation Results for PI Control;
Figure 5.2 PI Control Simulation Results
Simulation Results for PD Control;
Figure 5.3 PD Control Simulation Results
Simulation Results for PID Control;
Figure 5.4 PID Control Simulation Results
6.Conclusion
Some results stand out when we analyse above case.
P control correct the rise time in the systems. After certain limit, increasing Kp will only increase overshoot.You can see this implication in fig4.2 and fig 5.1.
I control eliminates the steady state error.So steady state error is zero but it provide the slowly control effect and it reduces rise time. You can see this implication in fig5.1 and fig 5.2.
D control decreases the overflow in the systems.Also D control make fastly correction but steady state error isn’t zero. Kd reduces settling time. You can see this implication in fig5.1 and fig 5.3.