Review, PID controller

Сентябрь 15, 2022

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Review, PID controller

Содержание

2. “Live as if you were to die tomorrow. Learn as if you were to live forever.”
3. Steady State Error (ess) Steady-state error is defined as the difference between the input (command) and
4. Steady State Error (ess)
5. Steady State Error (ess)- Multiple inputs
6. Classical Controller- PID Controller
7. Introduction More than half of the industrial controllers in use today utilize PID or modified PID
8. PID Control A closed loop (feedback) control system, generally with Single Input-Single Output (SISO) A portion
9. When PID Control is Used PID control works well on SISO systems of 2nd Order, where
10. Output equation of PID controller in time domain
11. Proportional Control A proportional controller attempts to perform better than the On-off type by applying power
12. Integral Control Time Output
13. Proportional-Integral Control The combination of proportional and integral terms is important to increase the speed of
15. Tips for Designing a PID Controller 1. Obtain an open-loop response and determine what needs to
16. The Characteristics of P, I, and D controllers A proportional controller (Kp) will have the effect
17. Proportional Control By only employing proportional control, a steady state error occurs. Proportional and Integral Control
18. Tips for Designing a PID Controller 1. Obtain an open-loop response and determine what needs to
19. num=1; den=[1 10 20]; step(num,den) Open-Loop Control - Example PID Controller (Conti… )
20. Proportional Control - Example The proportional controller (Kp) reduces the rise time, increases the overshoot, and
21. Kp=300; Kd=10; num=[Kd Kp]; den=[1 10+Kd 20+Kp]; t=0:0.01:2; step(num,den,t) Proportional - Derivative - Example The derivative
22. Proportional - Integral - Example The integral controller (Ki) decreases the rise time, increases both the
23. The Characteristics of P, I, and D controllers PID Controller (Conti… )
24. Figure 4.9 Responses of P, PI, and PID control to (a) step disturbance input (b) step
25. Figure 4.10 Model of a satellite attitude control: (a) basic system; (b) PD control; (c) PID
26. Figure 4.11 Process reaction curve PID Controller
27. Figure 4.11 Process reaction curves (R.C.Dorf et.al and Others)
28. Figure 4.12 Quarter decay ratio PID Controller- Ziegler Method #1
29. TABLE 4.2 PID Controller (Conti… )
30. Figure 4.13 Determination of ultimate gain and period PID Controller- Ziegler Method #2
31. Figure 4.14 Neutrally stable system PID Controller (Conti… )
32. TABLE 4.3 PID Controller (Conti… )
34. Скачать презентацию

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“Live as if you were to die tomorrow. Learn as if

you were to live forever.”
― Mahatma Gandhi

Today’s Quote:

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Steady State Error (ess)
Steady-state error is defined as the difference between

the input (command) and the output of a system in the limit as time goes to infinity (i.e. when the response has reached steady state). The steady-state error will depend on the type of input (step, ramp, etc.) as well as the system type (0, I, or II).

Note: Steady-state error analysis is only useful for stable systems. You should always check the system for stability before performing a steady-state error analysis.

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Steady State Error (ess)

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Steady State Error (ess)- Multiple inputs

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Classical Controller-
PID Controller

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Introduction
More than half of the industrial controllers in use today utilize

PID or modified PID control schemes.
When the mathematical model of the plant is not known and therefore analytical design methods cannot be used, PID controls prove to be most useful.

Design PID control
Know mathematical model ? various design techniques
Plant is complicated, can’t obtain mathematical model ?
experimental approaches to the tuning of PID controllers

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PID Control
A closed loop (feedback) control system, generally with Single Input-Single

Output (SISO)
A portion of the signal being fed back is:
Proportional to the signal (P)
Proportional to integral of the signal (I)
Proportional to the derivative of the signal (D)

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When PID Control is Used
PID control works well on SISO systems

of 2nd Order, where a desired Set Point can be supplied to the system control input
PID control handles step changes well to the Set Point especially when :
Fast Rise Times
Little or No Overshoot
Fast settling Times
Zero Steady State Error
PID controllers are often fine tuned on-site, using established guidelines

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Output equation of PID controller in time domain

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Proportional Control
A proportional controller attempts to perform better than the On-off

type by applying power in proportion to the difference in temperature between the measured and the set-point.
The P-controller usually has steady-state errors (the difference in set point and actual outcome) unless the control gain is large.
As the control gain becomes larger, issues arise with the stability of the feedback loop.

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Integral Control
Time
Output

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Proportional-Integral Control
The combination of proportional and integral terms is important to

increase the speed of the response.
Eliminate the steady state error.

Time

Output

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Tips for Designing a PID Controller
1. Obtain an open-loop response and determine

what needs to be improved
2. Add a proportional control to improve the rise time
3. Add a derivative control to improve the overshoot
4. Add an integral control to eliminate the steady-state error
Adjust each of Kp, Ki, and Kd until you obtain a desired overall response.
Lastly, please keep in mind that you do not need to implement all three controllers (proportional, derivative, and integral) into a single system, if not necessary. For example, if a PI controller gives a good enough response (like the above example), then you don't need to implement derivative controller to the system. Keep the controller as simple as possible.

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The Characteristics of P, I, and D controllers
A proportional controller (Kp)

will have the effect of reducing the rise time and will reduce, but never eliminate, the steady-state error.
An integral control (Ki) will have the effect of eliminating the steady-state error, but it may make the transient response worse.
A derivative control (Kd) will have the effect of increasing the stability of the system, reducing the overshoot, and improving the transient response.

PID Controller (Conti… )

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Proportional Control
By only employing proportional control, a steady state error occurs.
Proportional

and Integral Control
The response becomes more oscillatory and needs longer to settle, the error disappears.
Proportional, Integral and Derivative Control
All design specifications can be reached.

PID Controller (Conti… )

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Tips for Designing a PID Controller
1. Obtain an open-loop response and determine

PID Controller (Conti… )

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num=1;
den=[1 10 20];
step(num,den)
Open-Loop Control - Example
PID Controller (Conti…

)

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Proportional Control - Example
The proportional controller (Kp) reduces the rise time,

increases the overshoot, and reduces the steady-state error.
MATLAB Example

Kp=300;
num=[Kp];
den=[1 10 20+Kp];
t=0:0.01:2;
step(num,den,t)

K=300

K=100

PID Controller (Conti… )

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Kp=300;
Kd=10;
num=[Kd Kp];
den=[1 10+Kd 20+Kp];
t=0:0.01:2;
step(num,den,t)
Proportional - Derivative - Example
The derivative controller (Kd)

reduces both the overshoot and the settling time.
MATLAB Example

Kd=10

Kd=20

PID Controller (Conti… )

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Proportional - Integral - Example
The integral controller (Ki) decreases the rise

time, increases both the overshoot and the settling time, and eliminates the steady-state error
MATLAB Example

Kp=30;
Ki=70;
num=[Kp Ki];
den=[1 10 20+Kp Ki];
t=0:0.01:2;
step(num,den,t)

Ki=70

Ki=100

PID Controller (Conti… )

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The Characteristics of P, I, and D controllers
PID Controller (Conti… )

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Figure 4.9 Responses of P, PI, and PID control to (a)

step disturbance input (b) step reference input

PID Controller (Conti… )

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Figure 4.10 Model of a satellite attitude control: (a) basic system;

(b) PD control; (c) PID control

PID Controller (Conti… )

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Figure 4.11 Process reaction curve
PID Controller

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Figure 4.11 Process reaction curves (R.C.Dorf et.al and Others)

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Figure 4.12 Quarter decay ratio
PID Controller- Ziegler Method #1

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TABLE 4.2
PID Controller (Conti… )

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Figure 4.13 Determination of ultimate gain and period
PID Controller- Ziegler Method

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Figure 4.14 Neutrally stable system
PID Controller (Conti… )

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Review, PID controller

Содержание

“Live as if you were to die tomorrow. Learn as if

Steady State Error (ess)Steady-state error is defined as the difference between

Steady State Error (ess)

Steady State Error (ess)- Multiple inputs

Classical Controller-PID Controller

IntroductionMore than half of the industrial controllers in use today utilize

PID ControlA closed loop (feedback) control system, generally with Single Input-Single

When PID Control is UsedPID control works well on SISO systems

Output equation of PID controller in time domain

Proportional ControlA proportional controller attempts to perform better than the On-off

Integral ControlTimeOutput

Proportional-Integral ControlThe combination of proportional and integral terms is important to

Tips for Designing a PID Controller1. Obtain an open-loop response and determine

The Characteristics of P, I, and D controllersA proportional controller (Kp)

Proportional ControlBy only employing proportional control, a steady state error occurs.Proportional

Tips for Designing a PID Controller1. Obtain an open-loop response and determine

num=1; den=[1 10 20]; step(num,den) Open-Loop Control - ExamplePID Controller (Conti…

Proportional Control - ExampleThe proportional controller (Kp) reduces the rise time,

Kp=300;Kd=10;num=[Kd Kp];den=[1 10+Kd 20+Kp];t=0:0.01:2;step(num,den,t)Proportional - Derivative - ExampleThe derivative controller (Kd)

Proportional - Integral - ExampleThe integral controller (Ki) decreases the rise

The Characteristics of P, I, and D controllersPID Controller (Conti… )

Figure 4.9 Responses of P, PI, and PID control to (a)

Figure 4.10 Model of a satellite attitude control: (a) basic system;

Figure 4.11 Process reaction curvePID Controller

Figure 4.11 Process reaction curves (R.C.Dorf et.al and Others)

Figure 4.12 Quarter decay ratioPID Controller- Ziegler Method #1

TABLE 4.2PID Controller (Conti… )

Figure 4.13 Determination of ultimate gain and periodPID Controller- Ziegler Method

Figure 4.14 Neutrally stable systemPID Controller (Conti… )

TABLE 4.3PID Controller (Conti… )

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Steady State Error (ess)
Steady-state error is defined as the difference between

Classical Controller-
PID Controller

Introduction
More than half of the industrial controllers in use today utilize

PID Control
A closed loop (feedback) control system, generally with Single Input-Single

When PID Control is Used
PID control works well on SISO systems

Proportional Control
A proportional controller attempts to perform better than the On-off

Integral Control
Time
Output

Proportional-Integral Control
The combination of proportional and integral terms is important to

Tips for Designing a PID Controller
1. Obtain an open-loop response and determine

The Characteristics of P, I, and D controllers
A proportional controller (Kp)

Proportional Control
By only employing proportional control, a steady state error occurs.
Proportional

Tips for Designing a PID Controller
1. Obtain an open-loop response and determine

num=1;
den=[1 10 20];
step(num,den)
Open-Loop Control - Example
PID Controller (Conti…

Proportional Control - Example
The proportional controller (Kp) reduces the rise time,

Kp=300;
Kd=10;
num=[Kd Kp];
den=[1 10+Kd 20+Kp];
t=0:0.01:2;
step(num,den,t)
Proportional - Derivative - Example
The derivative controller (Kd)

Proportional - Integral - Example
The integral controller (Ki) decreases the rise

The Characteristics of P, I, and D controllers
PID Controller (Conti… )

Figure 4.11 Process reaction curve
PID Controller

Figure 4.12 Quarter decay ratio
PID Controller- Ziegler Method #1

TABLE 4.2
PID Controller (Conti… )

Figure 4.13 Determination of ultimate gain and period
PID Controller- Ziegler Method

Figure 4.14 Neutrally stable system
PID Controller (Conti… )

TABLE 4.3
PID Controller (Conti… )