Get control with PID

Phil Black - PII Editor 26/09/2011

221 11 minutes read

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Every industrial and manufacturing process needs accurate control. Tasks such as production, distribution and treatment processes all need tight control. PID controllers are ideal for this and with the right parameters and tuning, can achieve accurate control of virtually any industrial process.

In the past, control techniques for industrial process have relied on either mechanical or solid state electronic technology, with pneumatics being used to activate devices such as valves. More recently, advances in computerised control technology have brought an enormous variety in the way processes can be monitored and controlled. Complex algorithms can be incorporated that not only react to changes in process conditions, but also increasingly predict them as well, enabling corrective action to be taken automatically.

Control systems vary in their capabilities and can be designed to suit the three main types of production. Discrete processes are where discrete items are being produced and handled. . Batch processes are widely used in food and beverage, pharmaceutical and rubber processing applications such as tyre manufacture, while continuous processes, as their name suggests, are those which produce a continuous stream of products over a continuous period of time.

Control systems are classified into two main types, open-loop or closed-loop. Open loop controllers are also known as ‘non-feedback controllers’, as they do not use data from the process to change their output or vary the process. This also means they are unable to compensate for any disturbances in process conditions and are best suited to processes with a stable set of operating conditions, such as those that might exist in many types of discrete processing applications, for example.

For a more accurate or more adaptive control, a closed-loop system is needed, where the output of the system is fed back to the inputs of the controller.

Closed loop control systems

Modern control theory is based on feedback, that is, signals from a process that can be used to control it more effectively. A closed-loop controller uses feedback to control the states or outputs of a system or process. The term ‘closed-loop’ comes from the information path in the system – process inputs to a system have an effect on the process outputs, which is measured with sensors and processed by the controller. The result – the control signal – is used as an input to the process, closing the loop.

Essentially, a sensor measures the output of the system and feeds it back to be compared against a reference value. The controller takes the difference between the output and the reference value and uses it to change the inputs to the system to help compensate for the difference.

Closed-loop controllers offer several key advantages over open-loop controllers, which include their ability to adapt to changing conditions, and stabilise unstable processes.

Introducing PID control

The PID controller is probably the most widely-used type of feedback controller. PID stands for Proportional-Integral-Derivative, referring to the three terms operating on the error signal to produce a control signal.

The proportional term makes a change to the output 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.

A high proportional gain gives a large change in the output for a given change in the error. Too high a proportional gain and the system can become unstable, while too small a gain will produce a small output response to a large input error, resulting in a less responsive or less sensitive controller. The proportional term should form the bulk of the output change.

The integral term outputs a signal that is proportional to both the magnitude of the error and its duration. The integral term accelerates the movement of the process towards set point and eliminates the steady-state error produced by using a pure proportional controller. However, because it responds to accumulated errors, the integral term can cause the present value to overshoot the setpoint value.

The derivative term slows the rate of change of the controller output and is used to reduce the magnitude of the overshoot produced by the integral component. However, it also slows the transient response of the controller. Differentiation also amplifies noise, making this term highly sensitive to noise in the error term, with the possibility that the process can become unstable.

Autotuning

Almost every modern controller will include an autotuning function. This function effectively enables an operator to automatically tune a controller to a process even where they have little or no knowledge of that process.

When the autotuner is first started, the controller switches out the normal PID algorithm and replaces it with a non-linear function which will cause the controller to step up and down a prescribed parameter range until it establishes a consistent control range for the process.

The information created by the autotune about the process is then used to calculate the PID settings for the application.

Autotuning has several key advantages, one of the major ones being that no detailed knowledge of the process is required. The tuning process is executed under tight feedback control and the tuning time is short compared to the closed loop response time. Auto tuning also automatically detects processes where the use of Derivative is not appropriate.

Gain scheduling

For linear processes, where the process characteristics do not change significantly with time or load conditions, using the autotuner to set fixed PID or PI parameters will probably be sufficient to ensure effective control.

However, in the case of non-linear processes, being limited to a single set of fixed parameters can become problematic, as they must be set for the worst case in order to find the best overall response. This means that the controller must be given a very low gain to prevent it causing instability problems when the process is at its highest gain. The result is very sluggish control when the controller is operating where the process gain is at its lowest.

Gain scheduling overcomes these problems by enabling users to opt for more than one set of control parameters. The method uses two feedback loops, where the inner loop is comprised of the process and the controller while the ‘outer loop’ adjusts the controller parameters based on the operating conditions.

Compared to other adaption techniques, gain scheduling may seem relatively simple. However, its ability to respond to rapid changes in operating conditions has made it a popular choice and it has been shown to produce significant improvements in the control of a process.

Gain scheduling brings a number of key advantages. As well as improving the control of non-linear processes, it also eliminates the need to have PID settings detuned to the worst case to avoid instability. Gain scheduling is based on a measurable variable that correlates well with the process dynamics. Three independent sets of PID parameters can be defined and the reference signal can be any analog signal. Two dedicated limits can be programmed in engineering units for ease of use, while the system is capable of responding to rapid changes in operating conditions.

Adaptive control

Gain scheduling is well-suited to the control of non-linear processes which behave in a predictable way and where the characteristics can be correlated to a variable that can be easily measured. However, this is not the case for processes which are subject either to rapid and/or unpredictable changes. In such processes, the solution is to have an adaptive control function.

An adaptive controller works by creating a mathematical model of the process which is then used to estimate the optimum controller settings for the process. This model is continually updated by using data gained from comparing the performance of the model against real-life operating conditions.

This approach is used by the ABB ControlMaster – running the autotuner will help provide both good initial PID values and also a number of other parameters required for the proper operation of the adaptive algorithm.

In the first stage of the process, the control output and the process variable signals are put through a narrow band pass filter. This allows only signal data at a specific frequency to pass through, with any parts of the signal that have a higher or lower frequency being blocked. This prevents unwanted high frequency process noise and low frequency load disturbances that could otherwise distort the process model. The centre frequency of the filter is linked to the process dynamics and is one of the areas identified and set by the auto tuner.

After the signals have been filtered, a mathematical process known as ‘least squares estimation’ is applied to update the coefficients of the mathematical model. Using this information, the adaptive algorithm then calculates the appropriate PID settings that will provide the optimum control of the model, with the controller settings then being modified accordingly.

As the adaptive controller uses the same process dynamics as the autotuner, the user has the option of using PI control only or to calculate controller settings suitable for processes where the deadtime is relatively long.

Adaptive control can also be combined with gain scheduling to deliver benefits for processes which are non-linear but which vary with time or other conditions. Here, the adaptive algorithm automatically builds individual internal models for each segment of the gain scheduler. Using these, the controller automatically updates the appropriate set of PID parameters depending on where in the process curve it is operating.

Summarising the benefits, adaptive control helps control processes with changing dynamics. It is fully integrated with the autotuner to automatically provide initial process knowledge and creates and updates an internal model of the process it is trying to control. It also filters the control output and the process variable signals so that unwanted information from noise and local disturbances are removed. Signals are analysed in a least-squares estimator, with the resulting information used to update the process model and the technique works out the PID settings that would work best with the internal model.

Deadtime compensation

‘Deadtime’ occurs where the variable being measured does not respond to a step change in the controller output for a certain period of time. It commonly occurs in applications where material is being transported via a pipeline or on a conveyor. An example is a pH dosing process. The dosing pump is often located some distance upstream from the sensor, resulting in a delay between the controller increasing the dose and the resulting effect being seen at the sensor. The time it takes for the dose to travel down the pipeline creates an effective deadtime.

To address this, a formula has been devised called the controllability ratio, defined as the ratio of the process deadtime divided by the deadtime plus the dominant time constant. Its purpose is to ascertain how easily a particular process can be controlled.

Small values of the ratio are easy to control. However, as the deadtime becomes more significant compared to the time constant – that is, as the periods of deadtime get longer – the ratio gets larger, making the process increasingly difficult to control with just a simple PID algorithm.

To overcome this, some form of predictive control is needed. The classic solution is known as a ‘Smith Predictor’. This is a deadtime compensating controller which makes a prediction based on the controller output and an internal simulation of the process.

Yet, this approach has a number of disadvantages, the biggest of which is its complexity. To obtain the process model needed for the algorithm, a systematic identification process is needed which needs at least the process gain, time constant and the deadtime all to be specified. Combined with the PI algorithm, operators may find themselves having to tune a total of five parameters. Furthermore, unlike standard PID control, the Smith Predictor cannot be easily manually tuned by trial and error.

Predictive PI (pPI) control – overcoming the Smith Predictor complexity

To overcome these drawbacks, the new ABB ControlMaster range employs a deadtime compensation controller which is much simpler to use.

Called Predictive PI (pPI) control, it shares the same structure as the Smith Predictor, yet differs by having two process model parameters that are determined automatically based simply on the Proportional and Integral values. This means that, as for a standard PID controller, there are just three parameters that need to be tuned, namely the proportional term, the integral term and an estimate of the process deadtime.

PI response vs pPI

A key benefit of predictive PI control is its ability to greatly reduce the impact of deadtime compared to standard PI control. With PI control, where a step change is made to the control setpoint, the control output will slowly increase. As the deadtime is exceeded, the process variable will also start to slowly respond. Although the control is reasonable, the response will tend to be very sluggish.

Because the pPI controller can predict what will happen, it is able to raise the control output much more quickly without the problems of overshoot or instability. Once the deadtime has elapsed, the process variable then approaches the setpoint much more quickly.

Much simpler to use than a Smith Predictor, it uses the same structure, but needs no process model to be specified, as it creates its own process model from gain, integral time and deadtime. This method is ideal where the deadtime is more than double the dominant time constant and it can also be manually tuned using a simple step response test.

Feedforward control

One of the inherent drawbacks of feedback control is that corrective action cannot be taken until the output deviates from the setpoint.

A practical example is that of a dosing control installation. If the flow rate of the solution being treated changes, then the dose amount also needs to be changed accordingly.

If only feedback control is used, the controller will only realise that something has changed once the solution reaches the pH sensor. Any action by the controller to adjust the dosing output will therefore be too late to have any immediate effect on the solution currently being measured.

This situation can be resolved by measuring the flow rate upstream from the dosing pump and using this information as a feedforward signal to help achieve an output proportional to the fluid flow rate. By enabling the dosing rate to immediately track any changes in flow rate, the possibility of potentially expensive or even dangerous over or under dosing is eliminated.

The diagram highlights the simple principle of feedforward control. Here, the feedforward signal, in this case the flow rate, is scaled by a gain factor and then added to the normal PID output. The gain itself can either be set at a fixed value by the user or adjusted dynamically using the ABB ControlMaster’s adaptive feedforward function.

Using adaptive gain confers a number of benefits. Firstly, it eliminates the need to manually calculate the required gain, reducing both the time and complexity of set up and removing the chance of human error. Secondly, it ensures that good control is maintained irrespective of any disturbances to the system, either due to time; any changes in the properties of the solution being treated; or any other potential reasons.

Other key advantages of feedforward control are that it offers a highly effective way of compensating for measurable disturbances before they can affect the process variable. As such, it can often help deliver significant improvements in control quality. Another advantage is that it helps speed up response times and eliminate delays associated with feedback control.

PID controllers are a standard way of controlling processes, but the individual elements have their drawbacks when not supported by other techniques, particularly when dealing with unusual circumstances or when a significant response lag exists within the feedback loop. Methods such as pPI and feedforward can cut the effect of these situations.

Choosing the right type of control for your process is crucial to ensuring the best levels of accuracy, product quality and cost effectiveness.

By Martin Binney – Product Manager – ABB Limited

ABB Limited, St. Neots, Cambridgeshire
Can be contacted on:-
Tel: 0870 600 6122 ref ‘controllers’. E-mail moreinstrumentation@gb.abb.com
Web: www.abb.com