đồ án chỉnh lưu công suất

đồ án chỉnh lưu công suất

Chapter 1 deals with plant process characterization and the PID control of the plant using

computer simulation software The software being use is LabVIEW The report will also

present an introduction to a plant setup, wiring and proper operation

Theory

There are many situations that require some type of servo-control system This section

reviews the fundamentals of PID controllers

Proportional-Integral-Derivative (PID) Control

PID controllers are commonly used to regulate the time-domain behavior of many

different types of dynamic plants These controllers are extremely popular because they

can usually provide good closed-loop response characteristics, can be tuned using

relatively simple design rules, and are easy to construct using either analog or digital

components Consider the feedback system architecture that is shown in Figure 1.1,

where it can be assumed that the plant is a DC motor whose shaft position must be

accurately regulated

e(t)

Figure 1.1: PID control

The PID controller K(s) is placed in the forward path, so that its output becomes the

voltage applied to the motor’s armature The feedback signal is either an angular shaft

position or velocity, measured by a potentiometer or a tachometer, respectively In the

block diagram, these transducer dynamics are in the feedback path The output position

signal y(t), or velocity signal, is summed with a reference signal r (t), or command signal,

Sensor Dynamics Σ

CHAPTER 1: Plant Process Characterization and PID

to form the error signal e (t) Finally, the error signal is the input to the PID controller

The concept for this closed-loop system is simple The sensor, which is attached to the

motor shaft, provides a voltage that is compared to the reference voltage r (t) at the

summer When this error signal is non-zero, there will be an input to the controller, and

hence some action taken by the DC motor Once the sensor signal is equal to the

reference signal, there is no input to the controller and no voltage applied to the motor,

causing the motor to stop However, this simple explanation does not provide us a with a method whereby the motor position can be brought to an exact position (with absolute

accuracy) and does not tell us how to make the motor perform this positioning task as

quickly as possible

Before examining the input-output relationships and design methods for the PID

controller, it is helpful to review typical characteristics observed for the velocity response

of a DC motor to a step voltage input Different characteristics of the motor response

(steady-state error, peak overshoot, rise time, etc.) are controlled by selection of the three gains that modify the PID controller dynamics This is discussed in detail below The

PID controller is defined by the following relationship between the controller input

e(t) and the controller output v(t) that is applied to the motor armature:

Taking the Laplace transform of this equation gives the transfer function K(s):

This transfer function clearly illustrates the proportional, integral, and derivative gains

dt

t de K d e K t E K t

V( ) P ( ) i ( ) d ( )

0

+

) (

) (

) ( )

S

K K s E

s V s

p + +

=

=

Then, the transfer function can be expressed to easily show that the PID controller leads

to a pole at the origin of the Laplace plane and design freedom over two zeros:

The Vi used for this laboratory contains the capability of varying the control inputs (Kp,

Ki and Kd) It also can make the system an open loop control or close loop control A

close loop control system is a system that can control an output with feedback, thus

giving the system a real time control over the response of the system, as shown in figure

1.2

Figure 1.2: PID controller using LabVIEW (closed loop)

An open loop control system is a system that has no type of real time control for the

plant’s output, due to there being no feedback in the system Figure 1.3 graphical

represents the open loop system

) 1 1

( )

d i d

d

T T

S T

S S

KT s

Figure 1.3: PID controller using LabVIEW (open loop)

The Vi can also vary the damping ratio and natural frequency The damping ratio is

defined as the ratio of the damping of the system over the critic damping, where critical

damping is the point were you have the fastest response without overshoot and ringing

The natural frequency is the frequency of the system or better known as its resonance

frequency When the damping ratio is greater than one, we can see the output with the

slowest response, known as over damping When the damping ration is one, we can see the output with the fastest response without overshooting and ringing, known as critical

damping When the damping ratio is between one and zero, we can see a fast response

with overshooting and ringing, this is called under damping The transfer function of the

system is used as the basic characteristic of the plant, as shown in figure 4 The transfer

function is used to understand the plant in used

Figure 1.4: Transfer function of the plant

Discussion

constant, we acquired our results We observed that this system setup allowed the

response to be conformed to an ideal response without having to vary the transfer

function

For the lab we were first given a graph with the response curve of some unknown transfer function We initially made sure to set the P=1, I=0, and D=0 This was to insure that

there would be no PID control influence upon the response curve Figure 1.5 shows the

open loop response that we were trying to conform our system to

1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.5

y(t) u(t) e(t) r(t)

Figure 1.5: Open loop response

By doing this we could then determine the transfer function of the unknown system

Once the PID variables were set we then varied only the damping ratio number till our

response resembled what is seen in figure 1.5 Graphically we achieved a fairly accurate representation of the unknown curve Our response is shown in figure 1.6

Figure 1.6: Our response

Once this response was displayed on the graph we then considered the transfer function

in figure 1.4 to be the transfer function of the unknown response If you carefully

observe the responses in figures 1.5 and 1.6 you can see that both of there rise time

resemble one another One problem with the results is the fact that the resolution

between the desired response and our response is considerably different This variance

overall amplitude of the response curve had been impeded This result came from the

introduction of the force feedback into the system, also known as closed loop control

Figure 1.7 is a display of the closed loop influence on the response curve

Figure 1.7: Closed loop response

Finally by randomly manipulating the PID variables, of the closed loop system, we

achieved our desired curve Figure 1.6, which is the given response, and figure 1.7,

which is our created response, and is an acceptable representation of one another Again there remains a resolution discrepancies between the two therefore we can not say are

results are 100% accurate, but our results are within acceptable tolerances

1.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.3

y(t) u(t) e(t) r(t)

Figure 1.8: The given response

Figure 1.9: The response

Figure 1.10: RPM Vs Vout of system

Figure 1.11 Vin ramp Vs Vout response

Conclusion

In conclusion we observed that both the transfer function and the PID control could have

a large influence upon the response of the system More specifically the transfer

functions damping ratio can be adjusted so in crease of decrease the response curves rise

RPM vs Vout of system

y = 822.57x + 41.566

0 500 1000 1500 2000 2500 3000

Vout of system

RPM Linear (RPM)

Vin ramp Vs Vout response

y = 0.0899x - 0.0642

y = 0.3415x - 7E-14

-2 0 2 4 6 8 10

12

time sec

OUTPUT INPUT Linear (OUTPUT) Linear (INPUT)

time From our observation was concluded that as the Zn increases the rise time

decreases and as the Zn decreases to one the rise time increase to a point Once in that

critically damped state the PID controls can be used to fine-tune the response The P:

proportional directly multiplies the amplitude to the response, while the integral and

differential work against on another to fine-tune the shape of the curve Over all we

considered the lab to be very informative Our only suggestion is that the lab needs to

address the resolution difference so that we can increase the accuracy of our results