FC 160 - Inferential Smith Controller

The inferential smith controller (ISC) function code provides predictive control on an error signal developed from the process variable and set point inputs measured against an internal model of the process. The ISC controller utilizes a first order dynamic model with deadtime to predict the current value of the process variable based on past values of the control output. The ISC controller function block provides regulatory process control similar to a PID algorithm. However, the ISC controller has the added advantage of effective control for processes with a significant transport delay (deadtime). The ISC controller prevents controller windup by limiting control output to operator specified high and low limits. The ISC controller also prevents windup in cascade configurations with the use of an external reference value.

 

Processes with long deadtimes are difficult to control with PID controllers using traditional tuning methods. The ISC controller algorithm functionally replaces the standard PID controller function. The ISC controller easily deals with process deadtime and tunes with a single tuning parameter.

 

 

 

Outputs:

Blk

Type

Description

N

R

Control output (CO)

 

 

Specifications:

Spec

Tune

Default

Type

Range

Description

S1

N

5

I

Note 1

Block address of process variable

S2

N

5

I

Note 1

Block address of set point

S3

N

5

I

Note 1

Block address of track reference value

S4

N

0

I

Note 1

Block address of track switch signal:

0 = track

1 = release

S5

N

5

I

Note 1

Block address of (cascade) external reference value

S6

N

0

I

0 or 1

External reference flag:

0 = normal

1 = use external reference

S7

Y

1.000

R

Full

Process model gain

S8

Y

0.000

R

0 - 9.2E18

Process model deadtime (in secs)

S9

Y

0.000

R

0 - 9.2E18

Process model lag time constant (in secs)

S10

Y

9.2E18

R

0 - 9.2E18

Controller tuning time constant (in secs)

S11

Y

105.000

R

Full

Control output high limit

S12

Y

-5.000

R

Full

Control output low limit

 

NOTES:

1. Maximum values are:9,998 for the BRC-100, IMMFP11/12 and 31,998 for the HAC

 

 

160.1   Explanation

 

Many processes have open-loop step responses similar to the one shown in Figure 160-1. In an open-loop step test, the controller is in manual and the controller output (CO) increases or decreases in a single step. The process response is the behavior of the process variable (PV) in response to the CO change. In the test, PV and CO are initially at steady-state near the desired operating point (i.e., the values of PV and CO are constant over a reasonable period prior to the CO step change). The value of CO stays constant after the step change, and PV is monitored until it has reached a new constant value.

 

 

 

The ISC controller uses three parameters to characterize the open-loop step process response: S7, process model gain (K); S8, process model deadtime (D); and S9, process model lag time constant (L). Figure 160-1 shows an example of these parameters. In this example, PV is initially at steady-state at 30 degrees Celsius and CO is at ten percent. CO changes from ten percent to 25 percent at time t0. PV starts to move from its initial value at time t1 and reaches a new steady-state temperature of about 70 degrees Celsius. Process model gain is the ratio of the steady-state change in PV to the change in CO, for example,

 

                 

In this example, K is a positive value (i.e., PV increases as CO increases and PV decreases as CO decreases). In other cases, K may be a negative value (i.e., PV increases as CO decreases and PV decreases as CO increases). Process model deadtime is the time of a change in the control output until a change in the process variable. Process model lag time is the time to reach 63 percent of the final value after the response begins.  Inside the ISC controller function code calculations, the algorithm tries to predict the behavior of the real process based on process model parameters S7, S8 and S9. Because these parameters are only approximations of the real process, there will generally be errors in the prediction. A controller tuning parameter (S10), T, takes into account the effects of the prediction error. Smaller values of T would result in more rapid changes in CO; whereas larger values of T would result in slower changes in CO.

 

More specifically, if T is less than L, there is more lead action in the control output; if T is greater than L, there is more lag action in the control output. Control output is limited to high and low limits specified in S11 and S12. Qualitatively, larger values of T should be used if the model representation is poor, or quick and large movements of CO are undesirable. One method for tuning is to initially set T to the sum of the process model deadtime (S8) and the process model lag time constant (S9). Place the controller in auto, perform set point changes and adjust T to get a desirable response. Decrease T if the closed-loop response appears too sluggish. Increase T if the closed-loop response is too oscillatory.  The process model parameters are approximate descriptions of the real process about a single operating point. The model becomes less accurate as operating conditions move away from the initial point. Process model parameters may have to be re-estimated as operating conditions change.

 

The ISC controller should not be used in highly nonlinear processes (example, pH control), or in very fast processes (i.e., processes with dynamics dominated by process gains with negligible deadtime and lag effects). The ISC controller is useful for regulatory control with step-type disturbances (e.g., load disturbances through processes where deadtime is dominant over lag effects). The ISC controller provides bumpless tuning (i.e., CO will not jump as a result of changing the value of S7, S8, S9 or S10). In addition, the ISC controller provides bumpless manual-to-auto transfer.

 

Figure 160-2 shows the use of an external reference signal in a cascade configuration. In this case, the outer loop model refers to the effects of the inner loop PV on the outer loop PV; the inner loop model refers to the effects of the inner loop manipulated variable (example, valve position) on the inner loop PV. The inner loop PV is the external reference signal to the outer loop ISC controller. This prevents controller windup in the outer loop ISC controller should the inner loop saturate. Specification S6 of the outer loop ISC controller must equal one.

 

 

 

160.1.1  Specifications

 

S1 - PV

Block address of process variable (PV).

 

S2 - SP

Block address of set point (SP).

 

S3 - TR

Block address of track reference (TR). The ISC control output (CO) will track the value in this block when the track switch (TS) signal is zero.

 

S4 - TS

Block address of track switch (TS). The ISC control output (CO) will track <S3> when the value of TS is zero.

0 = track

1 = release

 

S5 - C

Block address of the cascade (C) external reference value. When the ISC controller is a control module or outer loop controller in a cascade configuration, the control loop uses the external reference value to prevent controller windup should the I/O module or inner loop controller saturate. Typically, the external reference value is the inner loop process variable. To use the external reference value, S6 of the outer loop ISC controller must equal one.

 

S6

External reference flag. Set the value of S6 to one to use the external reference value defined in S5; otherwise, S6 should

always equal zero.

0 = normal configuration, external reference not used

1 = use external reference

 

S7, S8 and S9

Characterize the response of the process variable to a step change in control output. The ISC controller uses a first-order lag with deadtime approximation of the actual process in its internal calculations. These parameters are the ISC process model parameters. Refer to Figure 160-1 for sample calculations of these parameters.

 

S7 - K

Process model gain (K). K can be positive or negative.

 

S8 - D

Process model deadtime (D).

 

S9 - L

Process model lag time constant (L).

 

S10 - T

ISC controller tuning parameter (T). T must be greater than zero. Without information on model uncertainty, a starting point for tuning T is to set it to the sum of D (S8) and L (S9).

 

For control with an accurate model, this parameter may be set to 30 percent of process lag time, L (S9). For slower controller response, or when the process model is not considered accurate, the value of this parameter can be increased to the process deadtime, D (S8) plus 300 percent of the process lag time, L (S9).

 

S11

High control output limit. This specifies the maximum output of the ISC controller block.

 

S12

Low control output limit. This specifies the minimum output of the ISC controller block.

 

 

160.2  ISC Structure

 

Figure 160-3 shows a block diagram representation of the ISC controller structure. In the diagram, U represents the effects of disturbances on the process. Ue is an estimate of the disturbances and effects of modeling error. The ISC controller uses a first-order with deadtime approximation of the process. If there are no modeling errors (i.e., process model equals process), the process output is:

 

PV(s) = F(s) SP(s) + [1 – F(s)] U(s)

 

where:

 

 

F(s) is the closed-loop response of the system to a set point change, and T is a measure of the closed-loop response speed. The controller is basically a lead/lag feedforward controller with the disturbance estimated by subtracting the model output from the actual measure process value. In real applications, there are always modeling errors and T is a tuning parameter in the lead/lag controller.

 

Control output constraints and process constraints must be considered in any controller design. In the ISC controller algorithm, this is done by constraining the controller output to within high and low limits (S11 and S12), and by taking into account the predicted model output in the controller calculations. If the control output saturates at a control limit, the input to the model will be a constant value (CO = high limit or low limit) and hence the predicted model output also reaches a constant value.

 

The controller sees the saturated predicted model output and prevents the control calculations from growing beyond the control limits (i.e., prevents controller windup). The same reasoning applies to cascade control. When using the ISC controller as the control loop, the inner loop PV is the external reference signal (Figure 160-2) and the input to the process model (Figure 160-3, S6=1). This external reference feedback prevents controller windup should the inner loop saturate.

 

 

 

160.3   Applications

 

Figure 160-4 shows how to use the inferential smith controller with a manual/automatic station (function code 80).