Processes

Structure of discussion

Basic process control

• • • • • • • • • •

• Controllers

• Processes • • • • •

Measurement devices Actuators Integration issues Empirical model building PID controller tuning

Process characterisation and examples Pure gain process Pure delay process First order process First order plus deadtime process Dealing with higher order systems Integrating (non self regulating) processes Inverse response process Linear and nonlinear responses Conclusions

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1. Process characterisation • A plant may be thought of as being made up of a series of processes. • A good understanding of these processes is required to design a control system for the plant. • In an existing installation, the plant operators can be a valuable source of information. • Existing controls and measurements are identified on the P&ID. Reference: Process Control Special Short Course 2006 - Fisher-Rosemount Systems 3

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Process definition A process is an arbitrary equipment configuration that acts on inputs to produce outputs. • Controlled variable: process output which is to be maintained at a desired value (setpoint or command signal), by adjustment of a process input. • Manipulated variable: process input which is adjusted to maintain the controlled variable at setpoint. • Disturbance: a process input (other than the manipulated variable) which affects the controlled variable. • Constraint: process output which must be maintained within an operating range. 4

Process example – lime mud filter

Process example – flow in pipe

Response to change in pump speed

Response to change in valve position

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Characterising process static and dynamic responses • The static response (or gain) of a process and the dynamic process response may be described by how the process output responds to a step change in process input. • All other process inputs should be kept at a constant during this test, so that they have no impact on the output of interest. • In an operating plant, it may be necessary to repeat the step test to get consistent results, since not all inputs to the process can be maintained constant and often process noise is present.

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2. Pure gain processes • When the process output tracks the process input except for a change in signal amplitude, the process is known as a pure gain. • For a step change in process input, the process gain is defined as the change in process output divided by the change in process input. 7

G m (s) = K m 8

3. Pure delay process

Pure gain process – example

• When the process output tracks the process input except for a delay in the output signal, the process is known as a pure delay or deadtime process. • For a step change in the process input, process deadtime or time delay is defined as the time from the change in input, to the first effect of the change is seen on the process output.

• An example of a pure gain process is the “jack shaft” used in some boiler combustion control systems. • The gain is determined by the length of the lever arms attached to the jack shaft. 9

Pure delay process - examples • Examples of pure delay processes are a conveyer belt, a pipeline and a paper machine. • Delay is a result of “transport time” and will vary with the speed of the belt or the flow rate through the pipe, for example.

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G m (s) = K m e −sτm

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4. First order process • When the rate at which the process output changes is proportional to the difference between the current output and the final value associated with the current input, the process is known as a first order process. • For a step change in the process input, the time taken for the output to reach 63% of its final change in value is known as the time constant.

G m (s) =

Km 1 + sTm

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First order process - example

5. First order plus deadtime process • Most processes in industry may be approximated as a first order plus deadtime process. • A first order plus deadtime process exhibits the combined characteristics of a first order process and a deadtime process.

• A tank, with outlet flow determined by the tank level, and an outlet flow restriction caused by the orifice. • The level will settle at a value which results in an outlet flow that matches the inlet flow.

G m (s) =

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•

K m e − sτ m 1 + sTm

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6. Dealing with higher order systems …

First order plus deadtime process – Steam heater, pilot examples

• The dynamic response of a process may be as a result of many components working together e.g. I/P transducer, valve actuator, heat transport. • The net process response of such systems may be approximated, in many cases, as a first order plus deadtime model.

scale heating and ventilation system. • The process lag is caused by the heating process. • The deadtime is caused by the transport delay.

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G p (s) =

Kp

(1 + sTp1 )(1 + sTp 2 )(1 + sTp3 )

G m (s) =

K m e − sτ m 1 + sTm

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7. Integrating (non self regulating) processes • When a process output changes without bound when the process input is changed by a step, the process is known as a non-self regulating or integrating process. • The rate of change (slope) of the process output is proportional to the change in the process input and is known as the integrating gain.

G m (s) =

K m e − sτ m s

• Tank level, where output flow is determined by a gear pump. • If the inlet flow does not match the outlet flow, then the level will continue to change until the tank overflows or runs dry. 17

8. Inverse response process • For a small number of processes, the initial change in the process output to a step change in the process input will be in the opposite direction to the final output change. • Processes exhibiting this K (1 − sT )e −sτ characteristic are said to G m (s) = m (1 + sTm 2 ) m1 have an inverse response. • Example: level in a tank to a rapid increase in heat input.

Example of integrating process

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9. Linear and nonlinear responses If the process output response depends on the amplitude or direction of the process input, the process is said to be non-linear. A process is said to be linear if it meets the following conditions:

m

Saturation of the final control element (valve fully open or fully closed) is one source of non-linearity. 19

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Some formative feedback …

Process non-linearity Most processes may be approximated as linear over a small operating range. Over a wide range of operation, processes may exhibit non-linearity. A common cause of nonlinearity is a change in process gain with operating point, reflecting the interaction of the valve with the process. An example of the static input-output characteristics of a dryer shows this nonlinearity. 21

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10. Conclusions • Processes may be modelled by a number of different transfer functions. • Process models are useful for controller design. • Many processes can be modelled in first order lag plus deadtime (FOPDT) form. • Models for processes may be developed either empirically or from first principles. • A standard experimental approach is desirable for development of repeatable empirical process models. 23

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