Enhanced Single-Loop Control Strategies (Advanced Control) Cascade Control Time-Delay Compensation Inferential Control Selective and Override Control

Transcription

1 Enhanced Single-Loop Control Strategies (Advanced Control) Cascade Control Time-Delay Compensation Inferential Control Selective and Override Control 1

2 Cascade Control A disadvantage of conventional feedback control is that corrective action for disturbance does not begin until after the controlled variables deviates from the set-point. Example: Furnace temperature control Disturbance: Oil flow rate Cold oil temperature satisfactory response Disturbance: Fuel gas supply pressure (Fuel gas flow) sluggish response Conventional feedback control 2

3 Another Example: Temperature control of tanks in series Enhanced Single-Loop Control Strategies How to improve control performance? Disturbance Feedforward control: disturbances have to be measured and a model is required to calculate the controller output Cascade control: use a secondary measurement and a secondary feedback controller 3

4 Cascade control: a primary control loop (TT1 and TC1) and a secondary control loop (TT2 and TC2) Set-point 4

5 Cascade Control of Exothermic Chemical Reactor 5

6 Cascade Control Distinguishing features: 1. Two FB controllers but only a single control valve (two controlled variables, two sensors, and one manipulated variable). 2. Output signal of the "master" controller is the setpoint for slave" controller. 3. Two FB control loops are "nested" with the "slave" (or "secondary") control loop inside the "master" (or "primary") control loop. Terminology: slave vs. master secondary vs. primary inner vs. outer 6

7 A Furnace Cascade Temperature Control Primary (outer) control loop Master controller Slave controller Secondary (inner) Control loop 7

8 Block Diagram of Cascade Control System Enhanced Single-Loop Control Strategies 1 2 D D : primary loop 2 : secondary loop = hot oil temperature = fuel gas pressure = cold oil temperature (or cold oil flow rate) = supply pressure of gas fuel = measured value of m1 1 = measured value of m2 2 = set point for sp1 1 = set point for sp2 2 (Furnace Example) 8

9 Design Considerations for Cascade Control Enhanced Single-Loop Control Strategies For a cascade control system to function properly, the secondary control loop must response faster than the primary loop. The secondary controller is normally a P or PI controller. The primary controller is usually PI or PID. First, design G c2 for inner loop. (inside-out) G 2 c2g vgp2 1 G G G G sp2 c2 v p2 m2 9

10 Then, design G c1 for outer loop. G 1 p1gd 2 D 1 G G G G G G G G G G 2 c 2 v p2 m2 c1 c 2 v p2 p1 m1 G 1 d1 1 Gc 2G vgp2gm2 D 1 G G G G G G G G G G 1 c 2 v p2 m2 c1 c 2 v p2 p1 m1 (16 5) (16 8) 10

11 Example Consider the block diagram with the following transfer functions: 5 4 Gv Gp1 Gp2 1 s1 4s1 2s1 1 Gd 2 1 Gm Gm Gd 1 3s 1 D 2 step response Primary loop: PI Secondary loop: P D 1 step response Great improvement Slight improvement 11

12 Time Delay Compensation (Smith Predictor) The presence of time delay in a process limits the performance of a conventional feedback control system. A time delay will adversely affects closed-loop stability. Example 16.2 Compare the set-point responses for a second-order process with a time delay and without the delay. The transfer function is Assume G m G 1 G ( s) For 0, K 3.02, 6.5. c For 2, 1.23, K c v p e s 5s 13s 1. Use the following PI controllers. I I (the controller gain must be reduced to meet stability requirements) 12

13 Closed-loop set-point responses The response of the closed-loop system will be sluggish compared to that of the control loop with no time delay. (not only 2 min.) 13

14 Model Block Diagram of Smith Predictor Without time delay G = G * e - E' E 1 sp If the process model is perfect and the disturbance is zero, then 2 E' sp For this ideal case the controller responds to the error signal that would occur if no time delay were present. 14

15 Equivalent Structure for Smith Predictor G = G Assuming there is no model error effective transfer function G ' c G c' P G c E 1 G G* 1 e c G * e - s G G, s the inner loop has the

16 For no model error: * s * s Gc G e GcG e GcG 1 GG e 1 G G 1 G G * s * * sp c c c By contrast, for conventional feedback control * s GcG GcG e G G * s 1 G G e sp c c The Smith predictor has the advantage of eliminating the time delay from the characteristic equation. Unfortunately, this advantage is lost if the process model is inaccurate. (It can still provide improvement if the model parameters are within about 30% of the actual values) 16

17 Closed-loop set-point responses Smith predictor (SP) has the same controller settings with conventional feedback PI controller. ( K ) c SP ( 2 ) PI ( 0 ) I The responses are identical, except for the initial time delay. 17

18 How about the disturbance response? Enhanced Single-Loop Control Strategies The Smith predictor generally is beneficial for handling disturbance. However, under certain conditions, a conventional PI controller can provide better regulatory control than SP. 2 D G d 1 GcG 1 e * 1 G G * s c 18

19 Inferential Control Problem: Controlled variable cannot be measured or has large sampling period. Possible solutions: 1. Control a related variable (e.g., temperature instead of composition). 2. Inferential control: Control is based on an estimate of the controlled variable. The estimate is based on available measurements. Examples: empirical relation, neural network Modern term: soft sensor 19

20 Inferential Control with Fast and Slow Measured Variables Soft sensor block diagram ( Note: X and/or can be used for control ) 20

21 Selective Control & Override Control For every controlled variable, it is very desirable that there be at least one manipulated variable. But for some applications, where: N C > N M N C = number of controlled variables N M = number of manipulated variables N Solution: Use a selective control system or an override. C N M 21

22 Low selector: High selector: Median selector: Selectors Selectors are used to improve the control performance as well as to protect equipment from unsafe operating conditions. The output, Z, is the median of an odd number of inputs (useful when redundant sensors are used to measure a single process variable) 22

23 Example: High Selector Control System Enhanced Single-Loop Control Strategies Control of a reactor hotspot temperature multiple measurements one controller one final control element Determine the hotspot temperature 23

24 Overrides Enhanced Single-Loop Control Strategies An override is a special case of a selective control system One of the inputs is a numerical value, a limit. Used when it is desirable to limit the value of a signal (e.g., a controller output). Temperature control of a heater for safety 24

25 A selective control system to handle a sand/water slurry (regulate the level and exit flow rate) 2 measurements, 2 controllers, 1 final control element FC Keep flow rate above its minimum value 25

26 Block Diagram for the Selective Control Loop faster 26

27 Split-Range Control Multiple final control elements or multiple controllers Reactor temperature control (both heating and cooling are used) 27