Auto-Tuning Control Using Ziegler-Nichols
Automatic step testsOne of the earliest auto-tuning controllers still on the market is the 53MC5000 Process Control Station from MicroMod Automation. It uses the Easy-Tune algorithm originally developed at Fischer & Porter (now part of ABB) in the early 1980s. It automatically executes a step test similar to the open-loop Ziegler-Nichols method that forces the controller to make an abrupt change in its control effort while sensor feedback is disabled.
The amount by which the process variable subsequently changes and the time required
for it to reach 63.2% of its final value indicate the steady-state gain and time constant of the process, respectively. If the sensor in the loop happens to be located some distance from the actuator, the process’s response to such a step input may also demonstrate a deadtime between the instant that the step was applied and the instant that the process variable first began to react.
These three model parameters tell the Easy- Tune algorithm everything it needs to know about the behavior of a typical process, allowing it to predict how the process will react to any corrective effort, not just step inputs. That in
turn allows the Easy-Tune algorithm to compute tuning parameters to make the controller compatible with the process.
Closed loop tests
In 1984, Karl Åström and Tore Hägglund of the Lund (Sweden) Institute of Technology
published an improved version of Ziegler and Nichols’ closed-loop tuning method. Like the open-loop method, this technique excites the process to identify its behavior, but without disabling sensor feedback.
The Åström-Hägglund method works by forcing the process variable into a series of
sustained oscillations known as a limit cycle. The controller first applies a step input to the process and holds it at a user-defined value until the process variable passes the setpoint. It then applies a negative step and waits for the process variable to drop back below the setpoint. Repeating this procedure each time the process variable passes the setpoint in either direction forces the process variable to oscillate out of sync with the control effort, but at the same frequency. See the “Relay Test” graphic. The time required to complete a single oscillation is known as the process’s ultimate period (Tu), and the relative amplitude of the two oscillations multiplied by 4/π gives the ultimate gain (Pu). Ziegler and Nichols theorized that these two parameters could be used instead of the steady-state gain, time constant, and deadtime to compute suitable tuning parameters according to their famous tuning equations or tuning rules shown in the equation on the left.
They discovered empirically that these rules generally yield a controller that responds quickly to intentional changes in the setpoint as well as to random disturbances to the process variable. However, a controller thus tuned will also tend to cause overshoot and oscillations in the process variable, so most auto-tuning controllers offer several sets of alternative tuning rules that make the controller less aggressive to varying degrees. An operator typically only has to select the required speed of response (slow, medium, fast), and the controller chooses appropriate rules automatically.
http://www.das.ufsc.br/~aarc/ensino/posgraduacao/DAS6613/Auto-Tuning%20Control%20Using%20Ziegler-Nichols.pdf
REVISITING THE ZIEGLER-NICHOLS TUNING RULES
FOR PI CONTROL — PART II
THE FREQUENCY RESPONSE METHOD
ABSTRACT
This paper presents an analysis of the Ziegler-Nichols frequency response
method for tuning PI controllers, showing that this method has severe
limitations. The limitations can be overcome by a simple modification for
processes where the time delay is not too short. By a major modification it is
possible to obtain new tuning rules that also cover processes that are lag
dominated.
I. INTRODUCTION
II. TEST BATCH AND DESIGN METHOD
2.1 The MIGO design method
2.2 The test batch
2.3 The AMIGOs tuning rules
2.4 Parameterization
III. A FIRST ATTEMPT
3.1 Stable processes
3.2 Integrating processes
3.3 Tuning rules for balanced and
delay-dominated processes
3.4 Summary
IV. ANALYSIS
4.1 Modified tuning procedures
V. THE AMIGOF TUNING RULES
5.1 Other values of Ms
5.2 How to find the frequency ωφ?
5.3 Summary
VI. AN INTERPRETATION OF
THE RESULTS
VII. EXAMPLES
Example 1. LAG DOMINATED DYNAMICS
Example 2. BALANCED LAG AND DELAY
Example 3. DELAY DOMINATED DYNAMICS
VIII. CONCLUSION
http://www.ajc.org.tw/pages/PAPER/6.4PD/AC0604-P469-FR0371.pdf
Automatic step testsOne of the earliest auto-tuning controllers still on the market is the 53MC5000 Process Control Station from MicroMod Automation. It uses the Easy-Tune algorithm originally developed at Fischer & Porter (now part of ABB) in the early 1980s. It automatically executes a step test similar to the open-loop Ziegler-Nichols method that forces the controller to make an abrupt change in its control effort while sensor feedback is disabled.
The amount by which the process variable subsequently changes and the time required
for it to reach 63.2% of its final value indicate the steady-state gain and time constant of the process, respectively. If the sensor in the loop happens to be located some distance from the actuator, the process’s response to such a step input may also demonstrate a deadtime between the instant that the step was applied and the instant that the process variable first began to react.
These three model parameters tell the Easy- Tune algorithm everything it needs to know about the behavior of a typical process, allowing it to predict how the process will react to any corrective effort, not just step inputs. That in
turn allows the Easy-Tune algorithm to compute tuning parameters to make the controller compatible with the process.
Closed loop tests
In 1984, Karl Åström and Tore Hägglund of the Lund (Sweden) Institute of Technology
published an improved version of Ziegler and Nichols’ closed-loop tuning method. Like the open-loop method, this technique excites the process to identify its behavior, but without disabling sensor feedback.
The Åström-Hägglund method works by forcing the process variable into a series of
sustained oscillations known as a limit cycle. The controller first applies a step input to the process and holds it at a user-defined value until the process variable passes the setpoint. It then applies a negative step and waits for the process variable to drop back below the setpoint. Repeating this procedure each time the process variable passes the setpoint in either direction forces the process variable to oscillate out of sync with the control effort, but at the same frequency. See the “Relay Test” graphic. The time required to complete a single oscillation is known as the process’s ultimate period (Tu), and the relative amplitude of the two oscillations multiplied by 4/π gives the ultimate gain (Pu). Ziegler and Nichols theorized that these two parameters could be used instead of the steady-state gain, time constant, and deadtime to compute suitable tuning parameters according to their famous tuning equations or tuning rules shown in the equation on the left.
They discovered empirically that these rules generally yield a controller that responds quickly to intentional changes in the setpoint as well as to random disturbances to the process variable. However, a controller thus tuned will also tend to cause overshoot and oscillations in the process variable, so most auto-tuning controllers offer several sets of alternative tuning rules that make the controller less aggressive to varying degrees. An operator typically only has to select the required speed of response (slow, medium, fast), and the controller chooses appropriate rules automatically.
http://www.das.ufsc.br/~aarc/ensino/posgraduacao/DAS6613/Auto-Tuning%20Control%20Using%20Ziegler-Nichols.pdf
REVISITING THE ZIEGLER-NICHOLS TUNING RULES
FOR PI CONTROL — PART II
THE FREQUENCY RESPONSE METHOD
ABSTRACT
This paper presents an analysis of the Ziegler-Nichols frequency response
method for tuning PI controllers, showing that this method has severe
limitations. The limitations can be overcome by a simple modification for
processes where the time delay is not too short. By a major modification it is
possible to obtain new tuning rules that also cover processes that are lag
dominated.
I. INTRODUCTION
II. TEST BATCH AND DESIGN METHOD
2.1 The MIGO design method
2.2 The test batch
2.3 The AMIGOs tuning rules
2.4 Parameterization
III. A FIRST ATTEMPT
3.1 Stable processes
3.2 Integrating processes
3.3 Tuning rules for balanced and
delay-dominated processes
3.4 Summary
IV. ANALYSIS
4.1 Modified tuning procedures
V. THE AMIGOF TUNING RULES
5.1 Other values of Ms
5.2 How to find the frequency ωφ?
5.3 Summary
VI. AN INTERPRETATION OF
THE RESULTS
VII. EXAMPLES
Example 1. LAG DOMINATED DYNAMICS
Example 2. BALANCED LAG AND DELAY
Example 3. DELAY DOMINATED DYNAMICS
VIII. CONCLUSION
http://www.ajc.org.tw/pages/PAPER/6.4PD/AC0604-P469-FR0371.pdf
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