Introduction A control system is an interconnection of components forming a system configuration that will provide a desired system response. The basis for analysis of a system is the foundation provided by linear system theory [1]. Many type of controllers are available in the industry, the main two types are: on/off and linear control system. Linear control systems use linear negative feedback to produce a control signal mathematically based on other variables, with a view to maintain the controlled process within an acceptable operating range.
The output from a linear control system into the controlled process may be in the form of a directly variable signal [2]. The main devices which are used in linear control system are: proportional controller and proportional with (integral or derivative action) controller or a sum of integral and derivative controller (PID). 1. 1 Proportional (P) control A proportional control system is a type of linear feedback control system which is more complex than an on-off control system, but simpler than a proportional-integral-derivative (PID) control system [3].
In the proportional control algorithm, the controller output is proportional to the error signal, which is the difference between the set point and the process variable. In other words, the output of a proportional controller is the multiplication product of the error signal and the proportional gain. [4] P controller can be mathematically expressed as: (1) Where y: Output of the proportional controller Kp: Proportional gain e(t): Instantaneous process error at time (t). And: e(t)= SP-PV Where: SP is set point and PV is process variable. 1. Proportional-Integral (PI) Control PI controllers are often employed in practice where its combination of P and I controller and are connected in parallel. This type of controller is used to eliminate offset and it shows a maximum overshoot and settling time similar to the P controller but no steady-state error. Mathematically it can be expressed as: (2) Where it includes proportional term with additional to integral term. 1. 3 Proportional-Derivative (PD) Control Proportional-Derivative or PD control combines proportional control and derivative control in parallel.
It has a smaller maximum overshoot due to the faster derivative action. Also in this case a steady-state error is visible, which is smaller than in the case of the P controller. This is because the PD controller generally is tuned to have a larger gain Kc due to the positive phase shift of the derivative action [3]. PD controller mathematically can be expressed as: (3) Where it includes proportional term with additional to derivative term. | 1. 4 Proportional–Integral–Derivative Controller (PID) PID controller is a generic control loop feedback mechanism (controller) widely used as feedback controller.
It calculates an “error” value as the difference between a measured process variable and a desired set point. It’s called three-term control due to present of three terms: the proportional, the integral and derivative terms. [4] PID controller causes the controlled variable to reach its set point more quickly, thus reaching steady state more rapidly. Also the control action is increased with any change in error due to presence of derivative term with addition to the manipulated variable generated by the PI component [4]. PID can be expressed mathematically as: (4) .
Where is includes proportional, integral and derivative terms. In this experiment, ( complete Humod) References: [1]. International Electrotechnical Vocabulary. , Chapter 351:Automatic control. IEC Publication 50. [2] Anderson, Norman A. : Instrumentation for Process Measurement and Control. Radnor, PA: Chilton Book Company [3] Murrill, Paul W. ’ Fundamentals of Process Control Theory’, Research Triangle Park, N. C. , Instrument Society of America, 1981 [4] Carlos A. Smith, Armando B. Corripio, ’Principles and Practice of Automatic Process Control’, Chapter 8, John Wiley & Sons, Inc.
