24 Questions
What is the relationship between the value of the controlled variable and the position of the final control element in proportional mode?
Continuous linear
What is the output of a proportional controller?
c(t) = Kp e(t)
What happens to the system as the gain of a proportional controller is increased?
It responds faster to changes in set-point but becomes progressively underdamped and eventually unstable
What is the major advantage of integral controllers?
They have the ability to return the controlled variable back to the exact set point following a disturbance
What is the disadvantage of integral control mode?
It responds relatively slowly to an error signal and can initially allow a large deviation
Why is the integral control mode not normally used alone?
Because it can lead to system instability and cyclic operation
What is the transfer function of a proportional controller?
Cp(s) = Kp
What is the purpose of combining integral control mode with another control mode?
To improve the stability and robustness of the system
What is the primary purpose of adding derivative action to a controller?
To reduce initial overshoot
What type of control mode combines proportional, integral, and derivative actions?
Proportional-Integral-Derivative (PID) control
What is the effect of a high error signal rate of change in a PD controller?
The final control element is positioned more quickly
What is the primary limitation of PD control?
It does not eliminate steady-state error
What does the letter 'P' stand for in PID controller?
Proportional
What is the purpose of the integral term in a PID controller?
To eliminate steady-state error
What is the advantage of PID controllers in industrial control systems?
PID controllers are widely applicable to most control systems
What is the main purpose of tuning rules in PID controllers?
To adjust PID controllers on-site
What is the transfer function of a PID controller?
Cpid(s) = Kp + Ki/s + Kd*s
What is the effect of adjusting the damping in a system?
It changes the transient response
What type of control is a combination of Proportional and Integral control?
PI control
What is the relationship between the error signal rate of change and the derivative action?
The derivative action is proportional to the rate of change of the error signal
What is the simplest form of control?
On-Off control
What is the main advantage of Proportional control?
It is simple to implement
What is the main limitation of PID controllers?
They are not optimal in all situations
What is the main characteristic of PID controllers?
They are widely applicable to most control systems
Study Notes
Control Systems
- Proportional control (P) has a continuous linear relationship between the controlled variable and the final control element's position.
- The output of a proportional controller is given by
cp(t) = Kp e(t), whereKpis the proportional gain. - The transfer function of a proportional controller is
Cp(s) = Kp.
Proportional Controllers (P)
- Increasing the gain of a proportional controller results in faster response to set-point changes, but it can lead to underdamped and unstable systems.
Proportional Plus Integral Controllers (PI)
- Integral control is based on the rate of change of the output, which is dependent on the magnitude of the input.
- The major advantage of integral controllers is that they can return the controlled variable to the exact set-point after a disturbance.
- Disadvantages of integral control include slow response to error signals and possible large deviations, leading to system instability.
PID Controllers
- PID stands for Proportional, Integral, and Derivative control.
- PID controllers are widely used in industrial control systems, with over half of the controllers in use today being PID or modified PID controllers.
Four Modes of Controllers
- There are four modes of control: On-Off (Bang Bang), Proportional (P), Proportional plus Integral (PI), and Proportional plus Derivative (PD).
Proportional Plus Derivative Control (PD)
- PD control uses the error signal rate of change to position the final control element, reducing initial overshoot and stabilizing the process sooner.
Proportional Plus Integral Plus Derivative Control (PID)
- The PID controller combines proportional, integral, and derivative control modes to achieve optimal control.
- The output of a PID controller is given by
cpid(t) = Kp e(t) + Ki ∫e(t) dt + Kd (de(t)/dt), whereKp,Ki, andKdare the proportional, integral, and derivative gains, respectively. - The transfer function of a PID controller is
Cpid(s) = (Kp + Ki/s + Kd s) / s.
This quiz covers proportional control mode, where the controlled variable and final control element have a continuous linear relationship. Learn about the proportional control equation and its application.
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