{"id":712,"date":"2025-10-19T11:03:16","date_gmt":"2025-10-19T09:03:16","guid":{"rendered":"https:\/\/avlos.gr\/wpress\/?p=712"},"modified":"2025-10-19T11:03:16","modified_gmt":"2025-10-19T09:03:16","slug":"pid-controller","status":"publish","type":"post","link":"https:\/\/avlos.gr\/wpress\/en\/pid-controller\/","title":{"rendered":"PID Controller"},"content":{"rendered":"\n

Introduction<\/h2>\n\n\n\n

The PID Controller is a Proportional \u2013 Integral \u2013 Derivative controller or three-term controller. It is a control loop mechanism that uses feedback and is widely used in industrial control systems and in a variety of other applications that require constantly configured control. A PID controller continuously calculates an error value e (t) as the difference between a desired setpoint (SetPoint -SP) and the current value of a measurable process variable (Process Variable PV) and applies a correction based on analog, integral and derivative term (denoted by P, I and D respectively), hence the name.<\/p>\n\n\n\n

In practice, it automatically applies an accurate and responsive correction to a control function. An everyday example is cruise control in a car, where climbing a hill would reduce speed if there was only constant engine power. The controller PID algorithm restores the measured speed to the desired speed with minimal delay and exceedance by increasing the motor output power in a controlled manner.<\/p>\n\n\n\n

Controller operation<\/h2>\n\n\n\n

The feature of the PID controller is the ability to use the three control terms of analog, integral and derivative influence on the controller output to implement accurate and optimal control. The controller block diagram shown below shows the principles of how these terms are created and applied. Displays a PID controller, which continuously calculates an error value e (t) as the difference between a desired setpoint SP = r (t) and a measured process variable PV = y (t) e (t) = r (t) -y (t) and applies a correction based on a proportional, integral and derivative term. The controller tries to minimize the error over time by adjusting a control variable u (t), such as e.g. opening a control valve,to a new value determined by a weighted sum of the control conditions.<\/p>\n\n\n\n

\"PID
PID Controler<\/figcaption><\/figure>\n\n\n\n

How does the PID controller work?<\/h2>\n\n\n\n

The overall output of the PID controller is a combination of the three terms as shown in the figure above, P, I and D<\/p>\n\n\n\n

The term P is proportional to the current value of the error SP\u2212PV = e(t).<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

For example, if the error is large and positive, the control output will be proportionally large and positive, taking into account the gain factor Kp<\/sub>. Only P control (Proportional) is sufficient and a system works well when:<\/p>\n\n\n\n

a. The system is simple and responds quickly.
b. Absolute accuracy in the final result is not required.
c. It is acceptable to have a little error in the steady-state (final state).
d. You have no problem with a constant deviation from the setpoint.
Thus, when only P control operates in a system, there are limitations:<\/p>\n\n\n\n

    \n
  1. Steady-state error:
    a. P control cannot completely eliminate the error.
    b. As you approach the desired value, the error decreases \u2192 so the correction also decreases \u2192 and stops before you reach the setpoint.<\/li>\n\n\n\n
  2. Power limitation:
    a. If you make the proportional coefficient Kp\u200b too large, to \u201cpush\u201d it harder, then:
    a1. The system becomes unstable<\/strong>.
    a2. You may have oscillations or overshoot.<\/strong><\/li>\n\n\n\n
  3. Bad behavior in slow or complex systems:
    a. In systems with inertia (such as thermal or mechanical), P control alone does not have time<\/strong> or is slow to react correctly<\/strong>.<\/li>\n<\/ol>\n\n\n\n

    For example, let’s say you’re controlling a motor to reach a specific speed.
    With P alone<\/strong>, it can get close to the target, but:
    a. It may stop at 98%<\/strong> of the target and never go exactly to 100%.
    b. If you increase Kp, it may oscillate around 100% (overshoot \u2192 undershoot \u2192 overshoot\u2026).<\/p>\n\n\n\n

    Term I takes into account the previous values \u200b\u200bof the SP \u2212 PV error<\/p>\n\n\n\n

    \"Iout\"<\/figure>\n\n\n\n

    and integrates them over time to produce the term I. For example, if there is a residual error SP \u2212 PV after the analog control is applied, the term integral seeks to eliminate the residual error by adding a control result, weight K\u00a0i\u00a0<\/sub>\u00a0, due to the historical cumulative value of the error.\u00a0When the error is eliminated, the term will stop growing.\u00a0This will result in a reduction in the analog result as the error decreases, but this is offset by the increasing overall effect.<\/p>\n\n\n\n

    Term D is the best estimate of the future trend of the SP \u2212 PV error,<\/p>\n\n\n\n

    \"Dout\"<\/figure>\n\n\n\n

    ased on its current rate of change.\u00a0It is sometimes referred to as “prudential control”, as it essentially seeks to reduce the effect of the SP \u2212 PV error by exerting a control influence created by the rate of change of the error.\u00a0The faster the change, the greater the effect of control or damping.\u00a0The role of the constant K\u00a0d\u00a0<\/sub>\u00a0in the calculation of the correction D is important.<\/p>\n\n\n\n

    Application of PID controller in Code<\/h2>\n\n\n\n

    To implement a PID controller in code or an Arduino program, five parameters must be known:<\/p>\n\n\n\n