# PID Controller

PID (Proportional Integral Derivative) controller

PID (Proportional Integral Derivative Controller) is a controller for determining precision instrumentation system with the characteristics of the feedback on the proficiency level system. PID control component consists of three types: Proportional, Integrative and Derivatives. All three can be used together or individually depending on the response we want to a plant. A controller proportional-integral-derivative (PID controller) is a generic control loop feedback mechanism (controller) widely used in industrial control systems - a PID feedback controller is most commonly used. A PID controller calculates an "error" value as the difference between a measured process variable and a desired setpoint. Controller tries to minimize the error by adjusting the process control inputs.
Within a control system we know of the existence of some kind of control action, such action is proportional control, integral control action and derivative control action. Each control action has a certain keunggulankeunggulan, which have the advantage of proportional control action fast rise time, integral control action has the advantage to minimize the error, and has the advantage of derivative control action to minimize or mitigate error overshot / undershot. For it so that we can produce output with a fast risetime and a small error that we can combine all three of these controls into action PID control action. Proportional Integral controller parameter derivative (PID) is always based on a review of the characteristics in the set (plant). Thus however the complexity of a plant, the plant behavior must be known before terlabih PID parameter search was conducted.

Proportional controller
Have a proportional controller output is proportional or proportional to the magnitude of the error signal (the difference between the desired magnitude with the actual price). In more simple it can be said that a proportional controller output is proportional to the product of the constant input. Changes in the input signal will immediately cause the system directly to output signals of constant pengalinya.
Figure 2.1 shows a block diagram that illustrates the relationship between the amount of settings, the amount of output current with a magnitude proportional controller. Keasalahan signal (error) is the difference between the amount of actual scale settings. This difference will affect the controller, to issue a positive signal (accelerate achievement of price setting) or negative (slowing the achievement of the desired price).
? Figure 2.1 Block diagram proportional controller
proportional controller has two parameters, proportional bands (proportional band) and a proportional constant. Area controllers work effectively mirrored by proportional tape while showing the value of proportional constant amplification factor Kp error signal tehadap
Proportional relationship between the bands (PB) with a proportional constant (Kp) is shown as a percentage by the following equation:
PB = 1/Kp ? 100% (2.1)
Figure 2.2 shows a graph of the relationship between the PB, and the controller output is the input controller error. When the proportional constant increases the higher, proportionately tape showed a smaller decrease, so that the scope of work that will be strengthened more and more narrow. Figure 2.2 Proportional band of a proportional controller depends on the reinforcement.
The characteristics of a proportional controller must be considered when the controller is applied to a system. In experiments, users should pay attention to controller propoisional the following provisions:
1. if the value of Kp is small, only a proportional controller is able to correct minor errors, so it will result in a slow response sisitem.
2. if the value of Kp is increased, the faster the system response shows reach set point and steady state.
3. but if the value of Kp is enlarged so as to achieve berlebiahan prices, will result in an unstable system work, or will the system response berosolasi

B. Integral controller
Integral controller response function produces a system with zero steady state error. If a plant does not have an element integrator (1 / s), a proportional controller will not be able to guarantee the system output with zero steady state error. With integral controller, the system response can be improved, which has a steady state error zero. Integral controller has karaktiristik as an integral. Strongly influenced by changes in output that is proportional to the value of the error signal. The controller output is the sum of the continuous changes in input. If the error signal is not changed, the output will keep the situation as it was before the change in input. Integral controller output signal is a broad field that is formed by the curve driving errors. Output signal will be worth the same as the previous price when the error signal is worth zero. Figure 2.3 shows an example of an error signal that is fed into the controller integral and integral controller output to changes in the error signal. Figure 2.3 Curves error signal e (t) for t in generating zero offense.
Figure 2.4 shows the block diagram of massive offense with a controller with integral output. Figure 2.4 Block diagram of the relationship between the amount of errors with integral controller
The effect of changing the output integral integral constants shown in Figure 2.5. When the error signal is doubled, then the rate of change of controller output value changed to two times that of the original. If the value of the constant integrator turn into larger, relatively small error signal can result in a large output rate. Figure 2.5 Change in output as a result of amplification and error
When used, the integral controller has a number of the following characteristics:
1. controller output requires a certain time interval, so that the integral controller tend to slow response.
2. valuable when zero error signal, the controller output will hold at the previous value.
3. valuable if no error signal at zero, the output will show an increase or decrease substantially affected by the error signal and the value of Ki.
4. valuable integral constant Ki will accelerate the loss of large offset. But the larger the constants Ki will result in increased oscillation of the controller output signal.

C. Derivative controller
Derivative controller output has properties as does a differensial operations. Abrupt changes in the input controller, will result in very large changes quickly. Figure 2.6 shows the block diagram that illustrates the relationship between the output signal controller esalahan. Figure 2.6 Block diagram Derivative controller
Figure 2.7 gives the relationship between the input signal to the controller output signal Derivative. When the input is not changed, the controller output is also unchanged, whereas if the input signal is changed suddenly and ascending (shaped step function), the output signal produces shaped impulse. If the input signal is turned up slowly (ramp function), the output is actually a big step function magnitudnya heavily influenced by the speed up of the ramp function and the differential constant factor.

Figure 2.7 Curves time input-output relationship Derivative controller
Derivative controller characteristics are as follows:
1. This controller can not produce output if there is no change in the input (such as an error signal).
2. if the error signal changes with time, then output the resulting controller depends on the value of Td and the rate of change of the error signal. (Powell, 1994, 184).
3. derivative controller has a character to precede, so that the controller can produce a significant correction before the plants become very big mistake. So the derivative controller can anticipate generating errors, provide corrective action, and tends to increase the stability of the system.
Based on the characteristics of the controller, the controller derivative commonly used to speed up the initial response of a system, but it does not minimize the error in steady state. Derivative controllers only work effectively on a narrow scope, namely the transition period. Hence derivative controller is never used without any other controller of a system (Sutrisno, 1990, 102).

D. PID controller
Any advantages and disadvantages of each controller P, I and D can cover each other by combining all three in parallel to the controller proportional plus integral plus derivative (PID controller). Control elements P, I and D, respectively overall aim to accelerate the reaction of a system, eliminating the offset and result in a large initial change. Figure 2.8 Block diagram of analog PID controller
PID controller output is the sum of the output of a proportional controller, integral controller output. Figure 2.9 shows the relationship. Figure 2.9 The relationship in time between the signal output function with input for PID controller
Characteristics of the PID controller is strongly influenced by the large contribution of the three parameters P, I and D. Setting constants Kp, Ti, and Td will result in protrusion of the properties of each element. One or two of the three constants can be regulated more prominent than others. Prominent constants that will contribute to the effect on overall system responsiveness.