# Chapter 9 PID Tuning Methods.

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Chapter 9 PID Tuning Methods

Overall Course Objectives
Develop the skills necessary to function as an industrial process control engineer. Skills Tuning loops Control loop design Control loop troubleshooting Command of the terminology Fundamental understanding Process dynamics Feedback control

Controller Tuning Involves selection of the proper values of Kc, tI, and tD. Affects control performance. Affects controller reliability Therefore, controller tuning is, in many cases, a compromise between performance and reliability.

Tuning Criteria Specific criteria General criteria Decay ratio
Minimize settling time General criteria Minimize variability Remain stable for the worst disturbance upset (i.e., reliability) Avoid excessive variation in the manipulated variable

Decay Ratio for Non-Symmetric Oscillations

Performance Assessment
Performance statistics (IAE, ISE, etc.) which can be used in simulation studies. Standard deviation from setpoint which is a measure of the variability in the controlled variable. SPC charts which plot product composition analysis along with its upper and lower limits.

Example of an SPC Chart

Classical Tuning Methods
Examples: Cohen and Coon method, Ziegler-Nichols tuning, Cianione and Marlin tuning, and many others. Usually based on having a model of the process (e.g., a FOPDT model) and in most cases in the time that it takes to develop the model, the controller could have been tuned several times over using other techniques. Also, they are based on a preset tuning criterion (e.g., QAD)

Controller Tuning by Pole Placement
Based on model of the process Select the closed-loop dynamic response and calculate the corresponding tuning parameters. Application of pole placement shows that the closed-loop damping factor and time constant are not independent. Therefore, the decay ratio is a reasonable tuning criterion.

Controller Design by Pole Placement
A generalized controller (i.e., not PID) can be derived by using pole placement. Generalized controllers are not generally used in industry because Process models are not usually available PID control is a standard function built into DCSs.

IMC-Based Tuning A process model is required (Table 9.4 contain the PID settings for several types of models based on IMC tuning). Although a process model is required, IMC tuning allows for adjusting the aggressiveness of the controller online using a single tuning parameter, tf.

Controller Reliability
The ability of a controller to remain in stable operation with acceptable performance in the face of the worst disturbances that the controller is expected to handle.

Controller Reliability
Analysis of the closed loop transfer function for a disturbance shows that the type of dynamic response (i.e., decay ratio) is unaffected by the magnitude to the disturbance.

Controller Reliability
We know from industrial experience that certain large magnitude disturbance can cause control loops to become unstable. The explanation of this apparent contradiction is that disturbances can cause significant changes in Kp, tp, and qp which a linear analysis does not consider.

Controller Reliability Example: CSTR with DCA0 Upsets

Controller Reliability
Is determined by the combination of the following factors Process nonlinearity Disturbance type Disturbance magnitude and duration If process nonlinearity is high but disturbance magnitude is low, reliability is good. If disturbance magnitude is high but process nonlinearity is low, reliability is good.

Tuning Criterion Selection

Tuning Criterion Selection

Tuning Criterion Selection Procedure
First, based on overall process objectives, evaluate controller performance for the loop in question. If the control loop should be detuned based on the overall process objectives, the tuning criterion is set. If the control loop should be tuned aggressively based on the overall process objectives, the tuning criterion is selected based on a compromise between performance and reliability.

Selecting the Tuning Criterion based on a Compromise between Performance and Reliability
Select the tuning criterion (typically from critically damped to 1/6 decay ratio) based on the process characteristics: Process nonlinearity Disturbance types and magnitudes

Effect of Tuning Criterion on Control Performance
The more aggressive the control criterion, the better the control performance, but the more likely the controller can go unstable.

For most sensor readings, a filter time constant of 3 to 5 s is more than adequate and does not slow down the closed-loop dynamics. For a noisy sensor, sensor filtering usually slows the closed-loop dynamics. To evaluate compare the filter time constant with the time constants for the acutator, process and sensor.

Recommended Tuning Approach
Select the tuning criterion for the control loop. Apply filtering to the sensor reading Determine if the control system is fast or slow responding. For fast responding, field tune (trail-and-error) For slow responding, apply ATV-based tuning

Field Tuning Approach Turn off integral and derivative action.
Make initial estimate of Kc based on process knowledge. Using setpoint changes, increase Kc until tuning criterion is met

Field Tuning Approach Decrease Kc by 10%.
Make initial estimate of tI (i.e., tI=5tp). Reduce tI until offset is eliminated Check that proper amount of Kc and tI are used.

An Example of Inadequate Integral Action
Oscillations not centered about setpoint and slow offset removal indicate inadequate integral action.

Demonstration: Visual Basic Simulator
Field Tuning Example

ATV Identification and Online Tuning
Perform ATV test and determine ultimate gain and ultimate period. Select tuning method (i.e., ZN or TL settings). Adjust tuning factor, FT, to meet tuning criterion online using setpoint changes or observing process performance: Kc=KcZN/FT tI=tIZN×FT

ATV Test Select h so that process is not unduly upset but an accurate a results. Controller output is switched when ys crosses y0 It usually take 3-4 cycles before standing is established and a and Pu can be measured.

Applying the ATV Results
Calculate Ku from ATV results. ZN settings TL settings

Comparison of ZN and TL Settings
ZN settings are too aggressive in many cases while TL settings tend to be too conservative. TL settings use much less integral action compared to the proportional action than ZN settings. As a result, in certain cases when using TL settings, additional integral action is required to remove offset in a timely fashion.

Much faster than open loop test. As a result, it is less susceptible to disturbances Does not unduly upset the process.

Online Tuning Provides simple one-dimensional tuning which can be applied using setpoint changes or observing controller performance over a period of time.

ATV Test Applied to Composition Mixer

CST Composition Mixer Example
Calculate Ku Calculate ZN settings Apply online tuning

Online Tuning for CST Composition Mixer Example
FT=0.75 FT=0.5

Control Performance for Tuned Controller

Critically Damped Tuning for CST Composition Mixer

Comparison Between 1/6 Decay Ratio and Critically Damped Tuning

Demonstration: Visual Basic Simulator
ATV based tuning

PID Tuning Procedure Tune PI controller using field tuning or ATV identification with online tuning. Increase tD until minimum response time is obtained. Initially set tD=Pu/8. Increase tD and Kc by the same factor until desired response is obtained. Check response to ensure that proper amount of integral action is being used.

Comparison between PI and PID for the Heat Exchanger Model

Comparison of PI and PID
The derivative action allows for larger Kc which in turn results in better disturbance rejection for certain processes.

Demonstration: Visual Basic Simulator
PID Tuning Example

Initial Settings for Level Controllers for P-only Control
Based on critically damped response. FMAX is largest expected change in feed rate. LMAX is the desired level change under feedback control. Useful as initial estimates for slow responding level control systems.

Initial Settings for Level Controllers for PI Control
Ac is cross-sectional area to tank and r is liquid density. FMAX is largest expected change in feed rate. LMAX is the desired level change under feedback control. Useful as initial estimates for slow responding level control systems.

Initial Settings for Level Controllers
Use online tuning adjusting Kc and tI with FT to obtain final tuning. Remember that Kc is expressed as (flow rate/%); therefore, height difference between 0% and 100% is required to calculate tI.

In-Class Example Calculate the initial PI controller settings for a level controller with a critically damped response for a 10 ft diameter tank (i.e., a cylinder placed on its end) with a measured height of 10 ft that normally handles a feed rate of 1000 lb/h. Assume that it is desired to have a maximum level change of 5% for a 20% feed rate change and that the liquid has a density corresponding to that of water.

Control Interval, Dt Dt is usually 0.5 to 1.0 seconds for regulatory loops and 30 to 120 seconds for supervisory loops for DCS’s. In order to adequately approach continuous performance, select the control interval such that: Dt < 0.05(qp+tp) For certain processes, Dt is set by the timing of analyzer updates and the previous formula can be used to assess the effect on control performance

Effect of Control Interval on Control Performance
qp =0.5 When the controller settings for continuous control are used with Dt=0.5, instability results. Results shown here are based on retuning the system for Dt=0.5 resulting in a 60% reduction in Kc.

Overview Controller tuning is many times a compromise between performance and reliability. Reliability is determined by process nonlinearity and the disturbance type and magnitude. The controller tuning criterion should be based on controller reliability and the process objectives.

Overview Classical tuning methods, pole placement and IMC tuning are not recommended because they are based on a preset tuning criterion and they usually require a process model. Tune fast loops should be tuned using field tuning and slow loops using ATV identification with online tuning.