Nonlinear Gain Compensation ( 对象非线性增益补偿)

1. Nonlinear Gain Compensation(对象非线性增益补偿) Lei Xie Institute of Industrial Control, Zhejiang University, Hangzhou, P. R. China

2. Problem Discussion for Nonlinearity Gain Compensation (1) which kind of nonlinearity are there in the control loop for a heat exchanger? Give your methods to compensate there nonlinearity. (2) analyze why the PH reactor is one of the most difficulty controlled process & provide improved schemes.

3. Heat Exchanger Process Steady-state Model： Plant Gain: Discussion: How to reduce the nonlinearity of process gain or make the compensated augmented plant become linear.

4. Compensation Method: Nonlinear Valves Equal-percentage valve (等百分比阀或对数阀) Linear valve (线性阀)

5. Characteristics for FC Valves Suppose • Linear valve • Equal-percentage valve How about FO valves ?

6. Compensation Method: Cascade Control Plant Gain:

7. Compensation Method: Ratio Control For controller TC, the augmented controlled plant is nearly linear (why?)

8. Basic pH Control Base Acid Acid flow, % of Base for a strong base-strong acid system Existing problem ?

9. Closed-loop Response for Basic pH Control • Experimental process • pHsp: 6.5↑7.0 at 60 min • F1: 30↓15 L/min at 110 min • pH1: 5↓4.5 at 160 min • pH2: 11↓10.5 at 210 min

10. pH Ratio Cascade Control Base Acid Advantages & Disadvantages ?

11. Closed-loop Response for pH Ratio Cascade Control • Experimental process • pHsp: 6.5↑7.0 at 60 min • F1: 30↓15 L/min at 110 min • pH1: 5↓4.5 at 160 min • pH2: 11↓10.5 at 210 min

12. pH Control with Nonlinear Gain Problem: if the setpoint is not at pH=7.0, which will happen ?

13. Closed-loop Response for Nonlinear pH Control • Experimental process • pHsp: 6.5↑7.0 at 60 min • F1: 30↓15 L/min at 110 min • pH1: 5↓4.5 at 160 min • pH2: 11↓10.5 at 210 min

14. pH Control with Nonlinear Transformation Note: x is nearly proportional to acid flow, F2, which results in a linear augmented plant. Besides, x is corresponding to pH. If pH=7, then x = 0; if pH>7, x > 0; and if pH<7, x < 0.

15. Closed-loop Response for pH Control with Nonlinear Transformation • Experimental process • pHsp: 6.5↑7.0 at 60 min • F1: 30↓15 L/min at 110 min • pH1: 5↓4.5 at 160 min • pH2: 11↓10.5 at 210 min

16. Methods for Compensating Process Nonlinearity • Nonlinear Valves • Cascade Control • Variable Ratio Control • Nonlinear Gain Compensation • Nonlinear Transformation • Identification + Adaptive Control