Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Autotuning

  • Tore HägglundEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_113-1
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Abstract

Autotuning, or automatic tuning, means that the controller is tuned automatically. Autotuning is normally applied to PID controllers, but the technique can also be used to initialize more advanced controllers. The main approaches to autotuning are based on step response analysis or frequency response analysis obtained using relay feedback. Autotuning has been well received in industry, and today most distributed control systems have some kind of autotuning technique.

Keywords

Relay Feedback Step Response Analysis Automatic Tuning Distributed Control System Gain Scheduling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Background

In the late 1970s and early 1980s, there was a quite rapid change of controller implementation in process control. The analog controllers were replaced by computer-based controllers and distributed control systems. The functionality of the new controllers was often more or less a copy of the old analog equipment, but new functions that utilized the computer implementation were gradually introduced. One of the first functions of this type was autotuning. Autotuning is a method to tune the controllers, normally PID controllers, automatically.

What Is Autotuning?

A PID controller in its basic form has the structure
$$\displaystyle\begin{array}{rcl} u(t) = K{\biggl (e(t) + \frac{1} {T_{i}}\,\displaystyle\int \limits _{0}^{t}e(\tau )d\tau + T_{ d}\, \frac{d} {dt}e(t)\biggr )},& & \\ \end{array}$$
where u is the controller output and e = y sp  − y is the control error, where y sp is the setpoint and y is the process output. There are three parameters in the controller, gain K, integral time T i , and derivative time T d . These parameters have to be set by the user. Their values are dependent of the process dynamics and the specifications of the control loop.

A process control plant may have thousands of control loops, which means that maintaining high-performance controller tuning can be very time consuming. This was the main reason why procedures for automatic tuning were installed so rapidly in the computer-based controllers.

When a controller is to be tuned, the following steps are normally performed by the user:
  1. 1.

    To determine the process dynamics, a minor disturbance is injected by changing the control signal.

     
  2. 2.

    By studying the response in the process output, the process dynamics can be determined, i.e., a process model is derived.

     
  3. 3.

    The controller parameters are finally determined based on the process model and the specifications.

     

Autotuning means simply that these three steps are performed automatically. Instead of having a human to perform these tasks, they are performed automatically on demand from the user. Ideally, the autotuning should be fully automatic, which means that no information about the process dynamics is required from the user.

Automatic tuning can be performed in many ways. The process disturbance can take different forms, e.g., in the form of step changes or some kind of oscillatory excitation. The model obtained can be more or less accurate. There are also many ways to tune the controller based on the process model.

Here, we will discuss two main approaches for autotuning, namely, those that are based on step response analysis and those that are based on frequency response analysis.

Methods Based on Step Response Analysis

Most methods for automatic tuning of PID controllers are based on step response analysis. When the operator wishes to tune the controller, an open-loop step response experiment is performed. A process model is then obtained from the step response, and controller parameters are determined. This is usually done using simple formulas or look-up tables.

The most common process model used for PID controller tuning based on step response experiments is the first-order plus dead-time model
$$G(s) = \frac{K_{p}} {1 + sT}{e}^{-sL}$$
where K p is the static gain, T is the apparent time constant, and L is the apparent dead time. These three parameters can be obtained from a step response experiment according to Fig. 1.
Fig. 1

Determination of K p , L, and T from a step response experiment

Static gain K p is given by the ratio between the steady-state change in process output and the magnitude of the control signal step, \(K_{p} = \Delta y/\Delta u\). Dead-time L is determined from the time elapsed from the step change to the intersection of the largest slope of the process output with the level of the process output before the step change. Finally, time constant T is the time when the process output has reached 63 % of its final value, subtracted by L.

The greatest difficulty in carrying out tuning automatically is in selecting the amplitude of the step. The user naturally wants the disturbance to be as small as possible so that the process is not disturbed more than necessary. On the other hand, it is easier to determine the process model if the disturbance is large. The result of this dilemma is usually that the user has to decide how large the step in the control signal should be. Another problem is to determine when the step response has reached its final value.

Methods Based on Frequency Response Analysis

Frequency-domain characteristics of the process can be obtained by adding sinusoidals to the control signal, but without knowing the frequency response of the process, the interesting frequency range and acceptable amplitudes are not known. A method that automatically provides a relevant frequency response can be determined from experiments with relay feedback according to Fig. 2. Notice that there is a switch that selects either relay feedback or ordinary PID feedback. When it is desired to tune the system, the PID function is disconnected and the system is connected to relay feedback control. Relay feedback control is the same as on/off control, but where the on and off levels are carefully chosen and not 0 and 100 %. The relay feedback makes the control loop oscillate. The period and the amplitude of the oscillation is determined when steady-state oscillation is obtained. This gives the ultimate period and the ultimate gain. The parameters of a PID controller can then be determined from these values. The PID controller is then automatically switched in again, and the control is executed with the new PID parameters.
Fig. 2

The relay autotuner. In the tuning mode the process is connected to relay feedback

For large classes of processes, relay feedback gives an oscillation with period close to the ultimate frequency ω u , as shown in Fig. 3, where the control signal is a square wave and the process output is close to a sinusoid. The gain of the transfer function at this frequency is also easy to obtain from amplitude measurements.
Fig. 3

Process output y and control signal u during relay feedback

Describing function analysis can be used to determine the process characteristics. The describing function of a relay with hysteresis is
$$N(a) = \frac{4d} {\pi a} \left (\sqrt{1 -{ \left ( \frac{\epsilon } {a}\right )}^{2}} - i\, \frac{\epsilon } {a}\right )$$
where d is the relay amplitude, ε the relay hysteresis, and a the amplitude of the input signal. The negative inverse of this describing function is a straight line parallel to the real axis; see Fig. 4. The oscillation corresponds to the point where the negative inverse describing function crosses the Nyquist curve of the process, i.e., where
$$G(i\omega ) = - \frac{1} {N(a)}$$
Since N(a) is known, G() can be determined from the amplitude a and the frequency ω of the oscillation.
Fig. 4

The negative inverse describing function of a relay with hysteresis − 1 ∕ N(a) and a Nyquist curve G()

Notice that the relay experiment is easily automated. There is often an initialization phase where the noise level in the process output is determined during a short period of time. The noise level is used to determine the relay hysteresis and a desired oscillation amplitude in the process output. After this initialization phase, the relay function is introduced. Since the amplitude of the oscillation is proportional to the relay output, it is easy to control it by adjusting the relay output.

Different Adaptive Techniques

In the late 1970s, at the same time as autotuning procedures were developed and implemented in industrial controllers, there was a large academic interest in adaptive control. These two concepts are often mixed up with each other. Autotuning is sometimes called tuning on demand. An identification experiment is performed, controller parameters are determined, and the controller is then run with fixed parameters. An adaptive controller is, however, a controller where the controller parameters are adjusted online based on information from routine data. Automatic tuning and adaptive control have, however, one thing in common, namely, that they are methods to adapt the controller parameters to the actual process dynamics. Therefore, they are both called adaptive techniques.

There is a third adaptive technique, namely, gain scheduling. Gain scheduling is a system where controller parameters are changed depending on measured operating conditions. The scheduling variable can, for instance, be the measurement signal, controller output, or an external signal. For historical reasons the word gain scheduling is used even if other parameters like integral time or derivative time are changed. Gain scheduling is a very effective way of controlling systems whose dynamics change with the operating conditions. Automatic tuning has made it possible to generate gain schedules automatically.

Although research on adaptive techniques has almost exclusively focused on adaptation, experience has shown that autotuning and gain scheduling have much wider industrial applicability. Figure 5 illustrates the appropriate use of the different techniques.
Fig. 5

When to use different adaptive techniques

Controller performance is the first issue to consider. If requirements are modest, a controller with constant parameters and conservative tuning can be used. Other solutions should be considered when higher performance is required.

If the process dynamics are constant, a controller with constant parameters should be used. The parameters of the controller can be obtained by autotuning.

If the process dynamics or the character of the disturbances are changing, it is useful to compensate for these changes by changing the controller. If the variations can be predicted from measured signals, gain scheduling should be used since it is simpler and gives superior and more robust performance than continuous adaptation. Typical examples are variations caused by nonlinearities in the control loop. Autotuning can be used to build up the gain schedules automatically.

There are also cases where the variations in process dynamics are not predictable. Typical examples are changes due to unmeasurable variations in raw material, wear, fouling, etc. These variations cannot be handled by gain scheduling but must be dealt with by adaptation. An autotuning procedure is often used to initialize the adaptive controller. It is then sometimes called pre-tuning or initial tuning.

To summarize, autotuning is a key component in all adaptive techniques and a prerequisite for their use in practice.

Industrial Products

Commercial PID controllers with adaptive techniques have been available since the beginning of the late 1970s, both in single-station controllers and in distributed control systems.

Two important, but distinct, applications of PID autotuners are temperature controllers and process controllers. Temperature controllers are primarily designed for temperature control, whereas process controllers are supposed to work for a wide range of control loops in the process industry such as flow, pressure, level, temperature, and concentration control loops. Automatic tuning is easier to implement in temperature controllers, since most temperature control loops have several common features. This is the main reason why automatic tuning was introduced more rapidly in these controllers.

Since the processes that are controlled with process controllers may have large differences in their dynamics, tuning becomes more difficult compared to the pure temperature control loops.

Automatic tuning can also be performed by external devices which are connected to the control loop during the tuning phase. Since these devices are supposed to work together with controllers from different manufacturers, they must be provided with quite a lot of information about the controller structure and parameterization in order to provide appropriate controller parameters. Such information includes signal ranges, controller structure (series or parallel form), sampling rate, filter time constants, and units of the different controller parameters (gain or proportional band, minutes or seconds, time or repeats/time).

Summary and Future Directions

Most of the autotuning methods that are available in industrial products today were developed about 30 years ago, when computer-based controllers started to appear. These autotuners are often based on simple models and simple tuning rules. With the computer power available today, and the increased knowledge about PID controller design, there is a potential for improving the autotuners, and more efficient autotuners will probably appear in industrial products quite soon.

Cross-References

Bibliography

  1. Åström KJ, Hägglund T (1995) PID controllers: theory, design, and tuning. ISA – The Instrumentation, Systems, and Automation Society, Research Triangle ParkGoogle Scholar
  2. Åström KJ, Hägglund T (2005) Advanced PID control. ISA – The Instrumentation, Systems, and Automation Society, Research Triangle ParkGoogle Scholar
  3. Vilanova R, Visioli A (eds) (2012) PID control in the third millennium. Springer, DordrechtGoogle Scholar
  4. Visioli A (2006) Practical PID control. Springer, LondonGoogle Scholar
  5. Yu C-C (2006) Autotuning of PID controllers – a relay feedback approach. Springer, LondonGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Lund UniversityLundSweden