Control objective ; To keep the tank temperature at the desired value by adjusting the rate of heat input from the heater. 8. Feedback Controllers. 8.1 Stirred-Tank Heater Example. Basic components in the feedback control loop Process being controlled(stirred tank).
Control objective ; To keep the tank temperature at the desired value by adjusting the rate of heat input from the heater.8. Feedback Controllers
8.1 Stirred-Tank Heater Example
Figure 8.1. Schematic diagram for a stirred-tank control system.
8.2 Controller Implementation Using PC
Figure 8.2. Typical equipment for process control using computer.
8.3.1 Historical Perspectives
250 B.C ; Greeks, water level controller
Their mode of operation was very similar to that of the level regulator in the modern flush toilet.
1788 ; James Watt, fly-ball governor
It played a key role in the development of stream power.
1930s ; PID controller became commercially available
The first theoretical papers on process control were published.
1940s ; Pneumatic PID controller
1950s ; Electronic PID controller
Late 1950 ~ 1960s ; The first computer control applications
Figure 8.3. Flow control system.
Figure 8.4. Schematic diagram of a feedback controller.
Where and denote the set point(the desired process output) and process out put. Constants are called proportional gain, integral time and derivative time, respectively.
18.104.22.168 Structure of PID Controllers.
22.214.171.124 Roles of Three Parts
1. Transfer function.
2. Advantage : immediate corrective action.
3. Disadvantage : steady-state error(offset).
4. Usage : when the steady-state error is tolerable( ex. level control which wants to prevent the system from overflowing or drying), proportional-only controller is attractive because of its simplicity seldom used only.
To remove the steady-state error(offset), the integral control action should be included in the feedback controller.
For usual process(i.e., open-loop stable processes), the control output should be nonzero to keep the process output in a nonzero set point.
PD(or P) controller output is always zero at steady-state if the error is zero(i.e., ).
Not immediate corrective action.
Practically PI controller is used.
Reduce the stability of the system.
Solution ; proper tuning of the controller or including derivative control action which tends to counteract the destabilizing effects.
Reset windup( or integral windup).
Figure 8.5. Reset windup during a set-point change.
2. Advantage : This part enhance the robustness of the PID controller by considering abrupt change of the error.
Figure 8.6. Extrapolation using the derivative of the error
3. Disadvantage : If the process measurement is noisy, this term will change widely and amplify the noise unless the measurement is filtered.
Electronic or pneumatic device that provides ideal derivative action cannot be built(is physically unrealizable). Commercial controllers approximate the ideal behavior as follows.
where is a small number, typically between 0.05 and 0.2.
126.96.36.199 Ideal PID Controller.
1. Transfer function.
where and denote the on and off values, respectively.
Not versatile and ineffective.
Continuous cycling of the controlled variable and excess
wear on the final control element.
Noncritical industrial applications.
Figure 8.7. Typical process response with feedback control.
C is the deviation from the initial steady-state.
less sluggish process response.
undesirable degree of oscillation or even unstable response.
best control result.
Figure 8.8. Process response with proportional control.
more conservative(sluggish) process response.
too long time to reach to the set point after load upset or set-point change occurs.
Figure 8.9. PI control: (a) effect of integral time (b) effect of controller gain.
Figure 8.10. PID control: effect of derivative time.
improved response by reducing the maximum deviation, response time and the degree of oscillation.
measurement noise tends to be amplified and the response may be oscillatory.