**4. Smith Predictor design**

12 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

IAE\_Value = IAE\_Value + (1-output(i))\*int\_T;

**Figure 5.** Closed loop Pressure Control with Pade approximation.

IAE\_Value = IAE\_Value + (1-output(i))\*(-1)\*int\_T ;

The closed loop system model with a PI control was built at SIMULINK as represented at

Applying a step function from 51 bar to 85 bar at the input of the system presented at figure 5, the output is presented at figure 6 for the tuning parameters obtained at the exhaustive

Pressure Response

0 5 10 15 20 25 30

Time(s)

for i=1:Tam, if output(i) < 1

else

 end end

end

figure 5.

search algorithm.

45

**Figure 6.** Step response of the closed loop pressure control system.

80 85 90

Pressure

A design tool very useful to control engineers when it is necessary to design a control system with delay at time response is the Smith Predictor (Ogata, 2009). At the distillation plant both SISO systems are represented by transfer functions with time delays. At this item it is done some considerations about the use of this technique to generate better results for the time response of the system. The control structure of the Smith Predictor is presented at figure 7.

**Figure 7.** Smith Predictor Structure.

In the system presented at figure 7, H(s) represents the pure delay time and F(s) represents the plant transfer function without delay. Analysing as separated parts, it is proposed a controller with input E(s) and output U(s) that has the delay time transfer function H(s) and F(s) modelled in its structure. It is possible to analyse the system proposed and verify that its transfer function C(s)/R(s) is equal to the transfer function of the system presented at figure 8.

**Figure 8.** Equivalent system.

At figure 8 it is possible to verify that G(s) may be designed considering the transfer function F(s) without the time-delay. The transfer function of the complete system has the design specification plus the dead time present at the original plant.
