1. Ming-Feng Yeh3-65 5. Grey Control Controller Plant ＋ r e u y － Grey Predictor

2. Ming-Feng Yeh3-66 Grey Prediction Control The control principle of control theory, whether classical or modern, is to control system behavior according to the state sample which has already occurred. The demerits of the afterward manner are Impossible to avert accidents in advance Impossible to control timely Weakly adaptable

3. Ming-Feng Yeh3-67 Essential Idea The essential idea is to control the system behavior in advance with the control strategy obtained from the prediction controller based on GM(1,1) model. Maintain a desired state within reasonably accurate tolerances even though the output is varied. Decision-Making Mechanism Plant Grey Predictor Reference Signal Control Signal Output Signal Predictive Signal ru y

4. Ming-Feng Yeh3-68 GM(1,1) Models x (0) = {x (0) (1), x (0) (2),…, x (0) (n)}, data length = n Whole data GM(1,1) model: data length = n Partial data GM(1,1) model: 4 ≦ data length < n New Information GM(1,1) model: add the newest datum x (0) (n+1) to the original series x (0), i.e., {x (0) (1), x (0) (2),…, x (0) (n), x (0) (n+1)} Equal-dimensional New Information GM(1,1) model: delete the oldest datum and add the newest one, i.e., {x (0) (2), x (0) (3),…, x (0) (n), x (0) (n+1)}

5. Ming-Feng Yeh3-69 Example 5.1 Year 19801981198219831984198519861987 x (0) 33.2730.9343.8863.51127.03138.84141.78156.47 8-dim33.2753.21064.90479.20796.647117.926143.892175.574 7-dim30.9368.42081.83897.876117.066140.013167.460 6-dim43.8891.663105.480121.379139.875160.529 5-dim63.51117.881128.801140.732153.769 4-dim127.03136.498144.331152.635

6. Ming-Feng Yeh3-70 Rolling Prediction x = {x(1), x(2),…, x(n)}, data length = n Step 1: Construct the m-data series x (0) (m<n) from the considered series x. Step 2: Measure the predictive values by the GM(1,1) model built by the m-data series x (0). Step 3: Update the m-data series by deleting the oldest datum and adding the newest one, and then return to Step 2.

7. Ming-Feng Yeh3-71 Example 5.2 Year 19801981198219831984198519861987 x (0) 33.2730.9343.8863.51127.03138.84141.78156.47 80~8333.2730.33443.39962.09288.837127.101181.847260.173 81~8430.9336.48764.569114.264202.206357.831633.232 82~8543.8877.401106.036145.263199.003272.624 83~8663.51128.628135.721143.205151.102 84~87127.03136.810145.459154.656

8. Ming-Feng Yeh3-72 Example 5.3-(1) Data length: m=8 One-step-ahead prediction Error: 6.83%

9. Ming-Feng Yeh3-73 Example 5.3-(2) Data length: m=4 One-step-ahead prediction Error: 2.17%

10. Ming-Feng Yeh3-74 Grey Prediction Control Step 1: Construct the m-data input series from the sensitized signal Step 2: Forecast the p-step-ahead predictive value of y(k) by grey predictor Step 3: Decision-making Step Step 4: Update the m-data input series and then go to Step 2 ControllerPlant ＋ r e u y － Grey Predictor Adjust step-size

11. Ming-Feng Yeh3-75 Example 5.4 Transfer function of plant: Transfer function of controller: Time interval: Sampling interval: 0.05 sec. Reference signal:

12. Ming-Feng Yeh3-76 Example 5.4-(1) Data length: m = 4 Predictive step size =  1 Reference signal  red line With predictor  black line Without predictor  blue line

13. Ming-Feng Yeh3-77 Example 5.4-(2) Data length: m = 4 Predictive step size =  2 Reference signal  red line With predictor  black line Without predictor  blue line

14. Ming-Feng Yeh3-78 Example 5.4-(3) Data length: m = 4 Predictive step size =  1 Reference signal  red line With predictor  black line Without predictor  blue line