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controller of PID

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A perfect control scheme has a single input and a single output. The PID controller is an example of this kind of controller. PID is an abbreviation for Proportional, Integral, and Derivative. The error message received in a motor controller is broken and routed via the three-term PID controller. The current error provides an answer on the proportional path; the integral path provides a reaction based on the number of errors; and the derivative path decides the changing rate of the errors. A summation of these three words is performed, and feedback is provided to the system. When there is a constant value of the gain, the terms were correctly chosen, and therefore the output should follow.

Figure 1: Block Diagram of a PID Control System

From the diagram, KP represents the gain constant for the proportional gain, KI represent the integral gain and KD is the gain constant for the derivative gain.

Proportional control mode

This is the driving force in the controller by changing the controller output in proportion to the error. Having a controller gain that is high will lead to a corresponding increase in the amount of proportional control action that is known for an error. If a high controller gain is set, an oscillation on the control loop will start causing the whole system to be unstable. Consequently, when it is set at low controller gain, it will not respond to the disturbances or at the set point changes ((O’Dwyer and Aidan 120).

P=KC * E

P is the proportional gain.

KC is the controller gain

E is the error.

Figure 2: Proportional control action.

Integral control mode

This is an automatic reset mode that overrides the manual reset commands. The integral control mode will automatically decrement or decrement the controller’s output continuously thereby, reducing the error. Over time, the integral action will drive the output from the controller far enough causing the error to be back to zero. The rate at which the error will increment or decrement depends on the magnitude of the error. If it is large, the increment or decrement will be faster but if it is small, they will be slow. If the integral time (TI) is set too short, there will be an oscillation to the control loop making the system to be unstable, if it is set too fast, the system will be sluggish (Papadopoulos and Konstantinos G 59).

I=I previous+ KC *E*TS/TI

I stand for integral control, TS stands for sampling time where the integral which the control algorithms are executed.

Figure 3: Integral control action and an integral-only controller’s equation

Derivative control mode

This response is mostly used in motion control. Using a derivative control response will cause a faster response to the system than the PI controllers alone. The rate of change of the error output is produced by this derivative control mode where a more controlling action is produced when there is a faster rate of action change. The derivative rate is zero when there is no change in the error. The control loop will be unstable if the derivative time is set too long (Visioli and Antonio 325).

D=KC *TD/TS*(E previous-E now)

Figure 4: Derivative control action

For a combined PID system, the general equation becomes:

Figure 5: The Standard (Noninteractive) PID controller algorithm

An accurate control system is required in motor control systems, but they are mostly limited by the dead-zone that is caused by static friction that will require a minimum amount of torque to overcome it.

Work cited

O’Dwyer, Aidan. Handbook of Pi and Pid Controller Tuning Rules. London: Imperial College Press, 2009. Print.

Papadopoulos, Konstantinos G. Pid Controller Tuning Using the Magnitude Optimum Criterion. , 2015. Internet resource.

Visioli, Antonio. Practical Pid Control. London: Springer, 2006. Print.

December 08, 2022
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