458.308 Process Control & Design

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458.308 Process Control & Design

Jong Min Lee

School of Chemical and Biological Engineering

Lecture 10: Enhancements to Basic Feedback Control

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Objective

• To learn popular control strategies that add on to the basic feedback control

- Feedback control does not take corrective action until after a deviation in the controlled variable occurs.

- Feedback control does not provide predictive control action to compensate for the eﬀects of known or measurable

disturbances.

- ···

• Relevant Chapters: 15, 16

• Topics

- Feedforward control

- Cascade control

- Time delay compensation

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Feedforward Control

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Complementary Nature of Feedforward and Feedback Control

• In practice, feedforward control is combined with feedback control. Feedforward control

- Enables early compensation to a sensed disturbance (important for processes with delays or slow dynamics).

- Sensitive to model error

- Disturbance must be “sensed”.

• Feedback control

- Continuously correct for error due to other unmeasured disturbances and model/plant mismatch.

• The two controllers can be designed independently and put together.

-

No adverse interaction between the two. (Eq. 15-28).

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Feedforward Controller Design Based on Steady-State Model

Immediately change the MV value when changes in DVs are sensed Use steady-state mass, energy, momentum balances

Ex) Distillation Column

CV: x and y, MV: D

Measured disturbances: F, z Steady-state mass balances:

F

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= D + B F z = Dy + Bx

The feedforward control law is given by D = F(z x_sp)

y_sp x_sp

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Feedforward Controller Design Based on Dynamic Model

Y (s)

D(s) = G_d + G_tG_fG_vG_p 1 + G_cG_vG_pG_m

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Ideal FFC: G_f = G_d G_tG_vG_p

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However, with model error, in general. G_d + G_tG_fG_vG_p 6= 0

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If we make the simplifying assumption that the disturbance measurement and control valve have no dynamics:

G_f = G_d(s) G_p(s)

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(7)

Examples

1st-order process and disturbance transfer functions G_p(s) = K_p

⌧_ps + 1, G_d(s) = K_d

⌧_ds + 1

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G_f =

✓K_d K_p

◆ ⌧_ps + 1

⌧_ds + 1

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A lead-lag controller: a typical form of most feedforward controllers

FOPTD process and disturbance transfer functions G_p(s) = K_pe ^✓^p^s

⌧_ps + 1 , G_d(s) = K_de ^✓^d^s

⌧_ds + 1

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is required for the controller to be realizable

: we cannot have perfect feedforward control, even if the

✓_d ✓_p

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✓_d < ✓_p

G_f =

✓K_d K_p

◆ ⌧_ps + 1

⌧_ds + 1e ^(✓^d ^✓^p^)s

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(8)

Examples

Process higher order than disturbance transfer function

G_p(s) = 2

(15s + 1)(3s + 1), G_d(s) = 1.5 5s + 1

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G_f = 0.75(15s + 1)(3s + 1) 5s + 1

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•

The controller is not physically realizable.

•

We could simply add a first-order filter, like 1/(s + 1), to make the feedforward controller second order over second order.

•

The simplest thing to do is to make the numerator term first order. Most likely , we would use 18s + 1 to approximate the numerator to arrive at the lead-lag controller

G_f = 0.7518s + 1 5s + 1

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Examples

Process has inverse response, disturbance does not

•

The controller has a RHP pole and is therefore unstable.

•

In this case, we would neglect the dynamic part and use only a static feedforward controller like

G_p(s) = 9s + 1

(15s + 1)(3s + 1), G_d(s) = 1.5 5s + 1

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G_f = 1.5 (15s + 1)(3s + 1) ( 9s + 1)(5s + 1)

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G_f(s) = K_f = K_d K_p

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Cascade Control

Disturbance: fuel gas header pressure (upstream of the valve)

Problems with the control valve:

stiction or hysteresis

•

This control scheme also concerns “disturbance rejection.”: practical problem

•

Involves the use of multiple output measurements and a single manipulated input.

-

Note: FF control: disturbance measurement

•

Objective: To improve the response of the most important (primary) output to a disturbance.

(11)

Cascade Control

• Why?

-

Reject disturbance in the slave loop before it aﬀects the main process variable

-

“Linearize” the slave process

-

Improve the dynamics of the slave process

• Tips for Implementation

-

Slave process should be at least 3 times as fast as the master process in terms of response time.

-

I-mode in the slave controller is seldom necessary. P-mode suﬃces in most cases.

‣ Small oﬀsets in the slave loop can be compensated by the master loop.

-

The most common cascade-control loop involves a flow controller as the inner loop. This type of loop easily rejects disturbances in fluid stream pressure, either upstream or downstream of the valve.

-

The inner loop should be tuned before the outer loop. After inner loop is tuned, and closed, the outer loop should be tuned using knowledge of the dynamics of the inner loop.

(12)

Time Delay Compensation

• Delays introduce “phase lag.”

-

The larger the delay, the faster phase angle drops with frequency.

• Large delays make PID tuning very diﬃcult.

-

Severely limits the size of gain one can use (Bode stability criterion).

-

Ziegler-Nichols or Cohen-Coon tuning rules advise that they be used only when θ/τ < 1.0.

-

In IMC tuning rules, delays are approximated. The approximation gets worse with larger delays and hence necessitate a use of a larger τc.

(13)

Comments

• With a Smith predictor, the delay is eﬀectively outside the loop.

• Even though Smith predictor simplifies tuning, it does not remove the delay from the response (physically impossible). There is no

“prediction” made by the Smith predictor.

• It requires implementation of a delay within the control system (hard for analog control, relatively easy for digital control).

• In reality, the model will not be perfect. The performance is known to be sensitive to model error, especially the delay parameter .

• One could use the IMC rule to design Gc and then adjust the time constant τ

c

to adjust sensitivity for model error.

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