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**Tuning PID Controller Institute of Industrial Control,**

Zhejiang University, Hangzhou, P. R. China 2013/03/27

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**Last Lecture Selection of Valve Action Action of Feedback Controllers**

Performance Criterion of Process Control Systems Understand Typical Controllers (P, PI and PID)

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**Single-loop PID Control System**

Problem: For an unknown extended controlled process, how to design and tune our PID controller ?

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**Proportional-Integral-Derivative (PID) Controller**

Ideal PID Controller Td is the derivative time. Industrial PID Controller (design and realization ?) The derivative gain Ad = 10.

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Problem Discussion Explain the function of PID controller for a stable controlled process. Analyze the effect of PID parameter changes on control performances How can we realize the industrial PID controller in Simulink ? PID tuning example (See ../PIDControl /PIDLoop.mdl )

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**( discuss the initial condition setting)**

Problem 2-1 For the level controlled process, h2 is selected as its controlled variable, and Qin is the main input of the process. Suppose the sectional area of two tanks are A1 and A2. The rates of outlet flow are assumed to satisfy the following equations: Please obtain the process characteristics by dynamic equations, and build the corresponding SimuLink model. ( discuss the initial condition setting)

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**( load the file temp.mat )**

Problem 2-2 For a heater with electricity, the step response data of outlet temperature can be shown as follows. Please determine its characteristic parameters K, T,τ if the span of temperature transmitter is 0 to 50 ℃. t, min 3 6 9 12 15 18 21 24 27 U, % 60 40 T, ℃ 38.7 38.3 38.8 39.0 38.4 37.0 35.3 33.6 30 33 36 39 42 45 48 51 54 57 32.2 31.0 30.2 29.5 29.0 28.6 28.3 28.0 27.9 27.8 ( load the file temp.mat )

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**Contents Selection of PID Controller Types （PID控制器类型选择）**

Tuning of PID Controller Parameters （控制器参数整定） Flow Control （流量控制） Level Control （液位控制） Reset Windup and Its Prevention （积分饱和与防止） Summary

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**Type Selection of PID Controllers**

*1: For some slow processes with long time constants, the derivative action is suggested to use. However, if there exists strong measurement noises, a first-order or average filter should be added. Controlled Variable Controller Type Temperature / Composition PID*1 Flow / Pressure /Liquid-Level PI Liquid-Level P Please analyze the rule of type selection ?

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PID Tuning Concept

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**Offline Tuning Based on Process Parameters: K, T,τ**

Step 1: switch the controller to manual mode, change the output of controller in step form, and record input/output data of controller. Step 2: obtain process characteristics: K, T,τ, from the step response data. Step 3: set the PID parameters Kc, Ti , Td, and switch the controller to automatic mode. Step 4: increase or decrease the gain Kc until obtaining the satisfactory response.

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**Simulation of Offline Tuning step 1: Step Testing**

See ../PIDControl/PIDLoop.mdl

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**Step 2: Obtain Process Para.**

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**Step 3: Obtain Initial PID Para. (Ziegler-Nichols Method)**

Controller Kc Ti Td P PI PID Note: the above method was developed for

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**Step 3: Obtain Initial PID Para. (Lambda Tuning Method)**

Controller Kc Ti Td P PI T PID τ/2 Initial Value Note: the above method is not limited by the value of

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**Simulation Example #1 K = 1.75 T = 6.5,τ= 3.3 min For PI Controller,**

Z-N tuning: Kc = 1.0, Ti = 11 min Lambda tuning: Kc = 0.56, Ti = 6.5 min

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**Simulation Example #2 K = 1.75 T = 6.5,τ= 6.3 min For PI Controller,**

Z-N tuning: Kc = 0.53, Ti = 20.8 min Lambda tuning: Kc = 0.30, Ti = 6.5 min

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**Procedure of Online Tuning: Ziegler-Nichols Technique**

Step 1: with the controller online (in automatic mode), remove all the reset (Ti = maximum) and derivative (Td = 0) modes. Start with a small Kc value. Step 2: make a small set point or load change and observe the response of CV. Step 3: if the response is not continuously oscillatory, increase Kc, or decrease PB, repeat step 2. Step 4: Repeat step 3 until a continuous oscillatory response is obtained.

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**Example of Online Tuning**

See ../PIDControl/PIDLoop.mdl

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**Online Tuning: Ziegler-Nichols Technique**

The gain that gives these continuous oscillations is the ultimate gain (临界增益), Kcu. The period of the oscillations is called the ultimate period (临界周期), Tu. the ultimate gain and the ultimate period are the characteristics of the process being tuned. The following formulas are then applied: Controller Kc Ti Td P 0.5Kcu PI 0.45Kcu Tu /1.2 PID 0.65Kcu Tu /2 Tu /8

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Online Tuning Result See ../PIDControl/PIDLoop.mdl

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**Limitation of Online Tuning**

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**Auto-tuning Based on Relay Feedback (基于继电反馈的参数自整定)**

Here we suppose the process gain > 0

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**Relay Feedback Example**

The controlled process can be described as The amplitude of relay controller is d = ±2.0

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**Response of Relay Feedback**

Oscillation period TU & amplitude AY（振荡周期与幅度）? See the detailed results: ../ PIDLoopAutoTuning.mdl

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**The Ultimate Gain (临界增益) Kcu Calculation**

经FT变换可知，控制输出的一次谐波幅度为 而对应的控制器临界增益为

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**Online Z-N Tuning Parameters**

Controller Kc Ti Td P 0.5Kcu PI 0.45Kcu Tu /1.2 PID 0.65Kcu Tu /2 Tu /8 If we use a PID controller, then we select the following parameters ……

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**Closed-loop Response of PID Feedback System**

Above auto-tuning method can be applied to other controlled processes ?

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**Characteristics of Flow Loops**

Fast dynamic response Zero dead time, which results in an infinite controller gain in every tuning equation Large measurement noise To decrease the change of control valve, a PI controller is common used with very small proportional action and a large integral action to approximate an integral controller. (Why?)

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**Tuning Example of Flow Loops**

See ../PIDControl/FlowLoop.mdl Please compare the proportional gain with the integral gain

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**Examples of Level Loops**

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**Characteristics of Level Loops**

Very often levels are integrating processes There are two types of possible control objectives when the input flow varies: (1) Tight Level Control; (2) Average Level Control (“液位均匀控制”)

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Tight Level Control The objective is to control the level tightly at set point, and the output flow can be allowed to vary without limitation If a level process happens to be self-regulated, and it is possible to obtain K, T andτ, the above tuning techniques can be used directly If a level process is integrating, a PI controller is common used with large proportional action and a very small integral action

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Average Level Control The objective is to smooth the output flow from the tank, which feeds the downstream unit, the level in the tank must be allowed to “float” between a high and a low level A P controller is common used in Average Level Control with a small proportional gain Tuning: the gain should be set to be as small as possible, as long as the level changes between a high and a low level for the expected flow deviation from the average flow.

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**Example of Level Control**

See ../PIDControl/ LevelLoop.mdl

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**Analysis of Average Level Control Systems**

Dynamic equation of the controlled process: where A is the area of the tank. Suppose

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**Analysis of Average Level Control Systems (cont.)**

For a proportional controller, Gc = －Kc, Please analyze the above models.

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**Examples of Average Level Control Systems**

Please see ../PIDControl/ AverageLevelLoop.mdl

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**Simulation Results of P-type Average Level Control**

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**Please see the following simulation example**

Reset Windup Problem Please see the following simulation example …/PIDControl/PidLoopwithLimit.mdl

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**Simulation Result with Reset Windup in a Single-Loop System**

Discussion: Which difference exists between reset windup and the open or closed status of the control valve completely ?

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**The Principle of Preventing Reset Windup**

Principle: remove the reset or integral action if the control output is beyond the normal operation range.

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**Anti-reset Windup Example**

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**Industrial PID Controller**

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**Summary Selection of PID Controller Types**

Tuning of PID Controller Parameters Tuning of PID Controller for Flow Loops Tight / Average Level Control Reset Windup and Its Prevention

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Problem Discussion For an unknown stable temperature control system, can you determine PID parameters in Offline and Online tuning methods ? Please realize the industrial PID controller in Simulink ? For the fast flow control loop, show me your tuning principle and explain why. For the AVERAGE level control loop, show me your tuning principle and explain why. Explain the existing reason of reset windup and show me your prevention schemes

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Exercise 3.1 A controlled process is shown in the Problem 2-1 (p.34) in Automated Continuous Process Control. calculate its characteristics parameters K, T and τ; decide on the action of the valve and the controller; tune your PID controller.

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Exercise 3.2 假设Relay(继电器法)镇定PID参数时，控制器输出如上图所示，信号周期为Tu, 振幅为d=2。证明经傅立叶变换，控制输出的一次谐波幅度为

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