LAB CHE239 PROPORTIONAL, INTEGRAL AND DERIVATIVE TUNING PDF

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UNIVERSITI TEKNOLOGI MARAFACULTY OF CHEMICAL ENGINEERINGPROCESS CONTROL & INSTRUMENTATION (CHE 239)LAB 1: PROPORTIONAL INTEGRAL AND DERIVATIVE TUNINGNo Title Allocated Marks (%) Marks 1 Abstract/Summary 5 2 Introduction -Theory & Aims/Objective 10 3 Methodology/Procedure 10 4 Data/result/Cal...

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UNIVERSITI TEKNOLOGI MARA FACULTY OF CHEMICAL ENGINEERING PROCESS CONTROL & INSTRUMENTATION (CHE 239) LAB 1: PROPORTIONAL INTEGRAL AND DERIVATIVE TUNING

STUDENT’S NAME (ID)

: 1) 2) 3) 4)

GROUP NO EXPERIMENT DATE SUBMITTED SEMESTER LECTURER

:2 : 1 (PID TUNING) : :4 :

No

Title

1

Abstract/Summary

5

2

Introduction -Theory & Aims/Objective

10

3

Methodology/Procedure

10

4

Data/result/Calculation/Graphs

25

5

Discussion

25

6

Conclusion & Recommendation

20

7

Reference

5

Total Checked by: ___________________ Date:

Allocated Marks (%)

100

Marks

Abstract The main purpose of this experiment are to understand the idea of a process control system and to carry out a flow process control test to determine the P, I, and D behaviour patterns. This experiment also to introduce open loops and closed loops.

Introduction A proportional–integral–derivative controller (PID controller or three-term controller) is a feedback-based control loop mechanism that is widely used in industrial control systems and other applications that require continuously modulated control. A PID controller continuously calculates an error value, such as display style, as the difference between a desired set point (SP) and a measured process variable (PV), and applies a correction based on proportional, integral, and derivative terms (denoted P, I, and D, respectively), thus the name. In practise, it applies an accurate and responsive correction to a control function automatically. A common example is a car's cruise control, which reduces speed when ascending a hill if only constant engine power is applied. The PID algorithm in the controller restores the measured speed to the desired speed with minimal delay and overshoot by increasing the engine's power output. Since the PID controller algorithm involves three distinct constant parameters, it is sometimes referred to as three-term control: the proportional, integral, and derivative values, denoted P, I, and D. Simply put, these values can be translated into time: P is determined by the current error, while I is determined by the accumulation of previous errors, and D is a prediction of future errors based on the current rate of change. The weighted sum of these three actions is used to control the process via a control element, such as the position of a control valve, a damper, or the power supplied to a heating element. A PID controller has traditionally been thought to be the most useful controller in the absence of knowledge of the underlying process. The controller can provide control action designed for specific process requirements by fine-tuning the three parameters in the PID controller algorithm. The controller's response can be described in terms of the controller's responsiveness to an error, the degree to which the controller overshoots the set point, and the degree of system oscillation. However, we must note that using the PID algorithm for control does not guarantee optimal system control or system stability. Some applications may only require one or two actions to provide adequate system control. Setting the other parameters to zero accomplishes this. In the absence of the respective control actions, a PID controller will be referred to as a PI, PD, P, or I controller. Since derivative action is sensitive to measurement noise, PI controllers are fairly common, whereas the absence of an integral term may prevent the system from reaching its target value due to the control action.

A PID loop can be tuned in a variety of ways. The most effective methods generally involve the creation of some type of process model, followed by the selection of P, I, and D based on the dynamic model parameters. Manual tuning methods can take a long time, especially for systems with long loop times. The method chosen will be influenced by whether or not the loop can be taken down for tuning and the system's response time. If the system can be taken offline, the best tuning method frequently entails subjecting the system to a step change in input, measuring the output as a function of time, and using this response to determine the control parameters. For this experiment on PID Tuning, we use three kind of method which is Ziegler–Nichol’s (Z-N) tuning method, Cohen-Coon’s (C-C) tuning method and Takahashi’s tuning method.

Theory A feedback controller is programmed to produce an output that causes some corrective effort to be applied to a process in order to drive a measurable process variable towards a desired value known as the setpoint. The controller affects the process with an actuator and measures the results with a sensor. Almost all feedback controllers calculate their output by measuring the difference between the setpoint and a measurement of the process variable. Errors occur when an operator changes the setpoint on purpose or when a process load accidentally changes a process variable. A proportional integral derivative or PID controller perform much the same function as a thermostat but with a more elaborate algorithm for determining its output. The idea of tuning the controller is to weight the sum of the proportional, integral, and derivative terms so as to produce a controller output that steadily drives the process variable in the direction required to eliminate the error. It considers the current error value, the integral of the error over a recent time interval, and the current derivative of the error signal to determine not only how much correction to apply, but also for how long. As shown in the equation, these three quantities are multiplied by a tuning constant and added together to produce the current controller output CO(t). In this equation, P represents the proportional tuning constant, I represents the integral tuning constant, D represents the derivative tuning constant, and e(t) represents the difference between the setpoint P(t) and the process variable PV(t) at time t. If the current error is large, has been present for a long time, or is changing rapidly, the controller will attempt to make a large

correction by generating a large output. In contrast, if the process variable has matched the setpoint for a long enough period of time, the controller will leave well enough alone. The process stability of the PID loop depends on the proportional, integral, and derived constants used. The proportional term produces an output value that is proportional to the current error value. The proportional response can be adjusted by multiplying the error by a constant Kp, called the proportional gain constant. The proportional term is given by;

A high proportional gain causes a large change in output for a small change in error. The system may become unstable if the proportional gain is set too high. A small gain, on the other hand, results in a small output response to a large input error and a less responsive or sensitive controller. When responding to system disturbances, if the proportional gain is too low, the control action may be too small. According to tuning theory and industrial practise, the proportional term should contribute the majority of the output change. For integral, the integral term's contribution is proportional to both the magnitude and duration of the error. In a PID controller, the integral is the sum of the instantaneous error over time, giving the accumulated offset that should have been corrected previously. After that, the accumulated error is multiplied by the integral gain (Ki) and added to the controller output. The integral term is given by;

The integral term accelerates the process's movement toward the setpoint and eliminates the residual steady-state error that occurs with a pure proportional controller. However, because the integral term responds to past errors, it can cause the present value to exceed the setpoint value. For derivative, the process error's derivative is calculated by determining the slope of the error over time and multiplying this rate of change by the derivative gain Kd. The derivative gain, Kd, is the magnitude of the derivative term's contribution to the overall control action. The derivative term is defined as;

Derivative action predicts system behaviour, which improves system settling time and stability. Because an ideal derivative is not causal, PID controller implementations include additional low-pass filtering for the derivative term to limit high-frequency gain and noise.

These techniques extract the most important process dynamics information, such as process dead time (Td) and response rate (RR). This information is then applied in matching rules such as Ziegler Nichols, Takahashi, and Cohen-Coon to estimate the controller's optimal P, I, and D. Process dead time (Td) and response rate (RR) are calculated by drawing a tangent to the response curve's steepest point. A process's delay time (Td) is a period of lagging. Tc is the amount of time it takes for a process to stay constant. These are significant parameters. Better overall process control and greater productivity can be gained as a result of improved loop performance. To estimate the reaction rate, RR, using the method 1 which is tangent method, the PV, MV, and time value must be determined using a graph using the formula:

∆PV = PVf − PVi

∆MV = MVf − MVi

For Response Rate, (RR); 𝑅𝑅 =

∆𝑃𝑉⁄ ∆𝑡 ∆𝑀𝑉

To find time constant Tc, used the formula;

TC = (

63.2 × Output(constant)) − Td 100

Then, plot it on the y axis, make a horizontal line until the line touch the output graph. After that, make a vertical line until it touches the x axis where Tc value can be determined using the formula above.

Besides that, To estimate the reaction rate, RR, Td, and Tc, we can also use the second method which is reformulated tangent method using the formula:

For Response Rate, (RR); RR =

tanθ a ∆MV b

For Dead Time, (Td); 𝑇𝑑 (𝑡𝑖𝑚𝑒) = 𝑇𝑑 (𝑙𝑒𝑛𝑔𝑡ℎ) × 𝑏 Or

𝑏 1 1 𝑇𝑑 (𝑡𝑖𝑚𝑒) = (𝑃𝑉𝑓 − 𝑃𝑉𝑖 ) [ − ] 𝑎 𝑡𝑎𝑏 𝛽 𝑡𝑎𝑛𝜃

For Time constant, (Tc); 𝑇𝑐 (𝑡𝑖𝑚𝑒) = 𝑇𝐶 (𝑙𝑒𝑛𝑔𝑡ℎ) × 𝑏 Or

𝑏 1 ] 𝑇𝑐 (𝑡𝑖𝑚𝑒) = (𝑃𝑉𝑓 − 𝑃𝑉𝑖 ) [ 𝑎 𝑡𝑎𝑛𝜃

Objective 1.

To understand how process control is actually work.

2.

To get basic understanding for how feedback control can be used to modify the behaviour of a dynamic system.

3.

To find the Td, Tc, and RR value using tangent method, and reformulate tangent method.

4.

To perform the correct method in order to do open loop test and closed loop test.

5.

To calculate either the response is linear, slightly non-linear, or roughly non-linear.

6.

To understand find P, PI and PID value is by using Ziegler Nichol’s, Takashi, and Cohen-Coon’s method.

Procedure 1.

Graph are plotted in excel based on the given data and the graph plotted is shown in Figure 1

2.

Based on the graph plotted in Figure 1 we can calculate the RR, td , and tc value

3.

With the excel file given, open the PID simulator

4.

In the PID simulator, enter the gain, time constant, and delay time computed in (2).

5.

Enter value P and set values I and D to 0. The values of P,I, and D can be determined using the tuning procedures in Table 1.

6.

Capture the response obtained.

7.

Repeat step (3) two time with different value P by using different tuning rule as in (5).

8.

From step (3) until step (6), choose the best value of P and key in step 7.

9.

Key in value P and value I and set value D equal to 0. The value of P,I and D value can be calculated based on tuning rules given in Table 1

10. Capture the response obtained. 11. Repeat step 7 two time with different value I by using different tuning rule as in (9). 12. From 7-9, choose the best value I and key in in step (11). 13. Key in value P and value I and any value D. The value of P,I and D value can be calculated based on tuning rules given in Table 1 14. Capture the response obtained. 15. Repeat step 11 two time with different value D by using different tuning rule as in (13).

126.7580868 132.7580868 138.7580868 144.7580868 150

96.75808676 102.7580868 108.7580868 114.7580868 120.7580868 126.7580868 132.7580868 138.7580868 144.7580868 150

PV vs Time

114.7580868 120.7580868

120

102.7580868 108.7580868

78.758 84.75808676 90.75808676

∆ 𝑷𝑽

96.75808676

Time

84.75808676 90.75808676

54.758 60.758 66.758 72.758

∆𝒕

42.758 48.758

Tc

42.75808676 48.75808676

66.75808676

100

10.005 10.124

36.75808676

72.75808676 78.75808676

80

Td

∆ 𝑴𝑽

10.00001317 10

12.873 18.758 24.758 30.758 36.758

54.75808676 60.75808676

60

9.999940165 10.00001317

12.87349915 18.75808676 24.75808676 30.75808676

40

9.998 10 10

9.999552339

10.00495027 10.12363049

20

0

12

10

8

6

4

2

0

0 6 9.838

9.837523163 9.998487938

Time

FIGURE 1 - A step input (bottom) and the associated step response curve (top)

0 6

10.00020306

Data, Result and Calculation

PV(%)

MV

CALCULATION 𝑹𝑹 = (∆𝑷𝑽/𝑻𝑪 )/∆𝑀𝑉

∆𝑃𝑉 = 56.92

𝑅𝑅 = (56.92/23 .127)/10

∆𝑀𝑉 = 10

𝑇𝐶 = 36.000 − 12 .873

𝑇𝐶 = 23.127𝑠

𝑇𝑑 = 12.873 − 10.000

𝑇𝑑 = 2.873𝑠

𝑅𝑅 = 0.2461

𝜇 = 𝑇𝑑 /𝑇𝑐

𝜇 = 2.873/23.127 𝜇 = 0.1242

PID SIMULATOR Ziegler-Nicholes: Setling criteria – QAD; Performance tests – Set point & disturbance. Mode P

P

I

D

𝑃 = 100(0. 2461)(2.873)

𝐼=0

𝐷=0

𝑃 = 100 𝑅𝑅 𝑇𝑑

𝑃 = 70.7045 PI

PID

𝑃 = 111.1 𝑅𝑅 𝑇𝑑

𝐼 = 3.33 𝑇𝑑

𝑃 = 111.1(0.2461)(2.873) 𝐼 = 3.33(2.873) 𝑃 = 78.5527

𝐼 = 9.5671

𝑃 = 83.3(0.2461 )(2.873)

𝐼 = 2(2.873)

𝑃 = 83.3 𝑅𝑅 𝑇𝑑 𝑃 = 58.8969

𝐼 = 2 𝑇𝑑

𝐼 = 5.746

𝐷=0 𝐷 = 0.5 𝑇𝑑

𝐷 = 0.5 (2.873)

𝐷 = 1.4365

Takahashi: Setling criteria – minimum control area; Performance tests – disturbance Mode P

P

I

D

𝑃 = 110(0. 2461)(2.873)

𝐼=0

𝐷=0

𝑃 = 110 𝑅𝑅 𝑇𝑑

𝑃 = 77.7750 PI

𝑃 = 110 𝑅𝑅 𝑇𝑑

𝑃 = 110(0. 2461)(2.873)

𝐼 = 3.3(2.873)

𝑃 = 77 𝑅𝑅 𝑇𝑑

𝐼 = 2.2 𝑇𝑑

𝑃 = 77.7750 PID

𝐼 = 3.3 𝑇𝑑

𝑃 = 77(0.2461 )(2.873) 𝑃 = 54.4425

𝐷=0

𝐼 = 9.4809

𝐷 = 0.45 𝑇𝑑

𝐼 = 2.2(2.873)

𝐷 = 0.45 (2.873)

𝐼 = 6.3206

𝐷 = 1.2929

Cohen-Coon: Setling criteria – QAD; Performance tests – disturbance Mode P

P

100 𝜇 𝑅𝑅 𝑇𝑑 1+ 3 100 𝑃= (0.2461)(2.873) 0.1242 1+ 3

𝐼=0

𝐷=0

𝜇 100 1 + 11 𝜇 𝑅𝑅 𝑇𝑑 ]𝑇 𝐼 = 3.33 [ 1+ 11𝜇 𝑑 11 1+ 5 100 𝑃= (0.2461)(2.873) 0.1242 0.1242 1 + 11 1+ 11 ] (2.873) = 3.33 [ 11(0.1242) 1+ 𝑃 = 69.9151 5 𝑃=

𝐼 = 7.5304

PID

D

𝑃=

𝑃 = 67.8937

PI

I

𝐷=0

100 5 𝜇 𝜇 1 +3𝜇 1 + 𝑅𝑅 𝑇𝑑 𝐼 = 3.33 [1 + ] 𝑇𝑑 5 100 5 𝑃= 0.1242 (0.2461)(2.873) 0.1242 1+ 1+ 5 ] (2.873) = 3.33 [ 5 3(0.1242) 1 + 𝑃 = 68.9908 5 𝑃=

𝐼 = 9.1248

ZIEGLER-NICHOLES:

A) P CONTROLLER

0.37 𝑇𝑑 𝜇 1+5 0.37(2.873 ) 𝐷= 0.1242 1+ 5

𝐷=

𝐷 = 1.0372

B) PI CONTROLLER

C) PID CONTROLLER

TAKAHASHI: A) P CONTROLLER

B) PI CONTROLLER

C) PID CONTOLLER

COHEN-COON: A) P CONTROLLER

B) PI CONTROLLER

C) PID CONTROLLER

Appendices Group 2...