PID principle and application of simulation program (Matlab Simulation and Image Processing Series Issue 3)

PID controller simulator

Overview:

PID controller is a commonly used feedback control algorithm to achieve precise adjustment between system output and desired value. The PID controller simulator is a tool that can simulate and test the performance of the PID controller, and tune and optimize the system.

Input parameters:

• setpoint: expected value or target value
• process_variable: process variable or actual measured value
• Kp: Proportional gain coefficient, used to adjust the response of the controller to the error
• Ki: Integral gain coefficient, used to correct system static error
• Kd: differential gain coefficient, used to suppress system oscillation and fast response

return value:

• output: the output of the PID controller, used to adjust the control signal of the system

working principle:

The PID controller calculates an output based on the current error (the difference between the set point and the actual value), which minimizes the error by adjusting the system control signal. It comprehensively considers the control behavior of three aspects: proportional, integral and differential.

• Proportional: adjust according to the size of the error. The proportional gain coefficient Kp determines the sensitivity of the response, a larger Kp will lead to a faster response but may cause system oscillation.
• Integral: The integral gain coefficient Ki is used to correct the static error of the system, that is, the persistent deviation. It adjusts the output by accumulating historical errors to reduce bias.
• Derivative: The differential gain coefficient Kd is used to suppress the oscillation and fast response of the system. It predicts future trends by taking into account the rate of change of error and adjusts the output accordingly.

The PID controller simulator calculates the output of the PID controller based on the input set and actual values, as well as the given Kp, Ki and Kd parameters. The output can be used to adjust the control signal of the system to achieve the desired control effect.

Notice:

A PID controller simulator is a theoretical tool and requires correct parameter setting for optimal control. In practical applications, real-time adjustment and optimization are also required, and parameters are finely adjusted according to the dynamic characteristics of the system. This involves processes such as system modeling, experimental testing, and closed-loop feedback debugging.

code

After subscribing to the blogger: PID Controller Simulator acquisition

program effect

In order to run the program, users must have MATLAB R2017a or later with Control Systems Toolbox installed. This application requires the definition of the transfer function of the system by defining the coefficients of the numerator and denominator polynomials. In this new version, the system's input delay and feedback transfer functions can also be considered.

It should be noted that before using the program, the user needs to ensure that the required version of MATLAB is installed and that Control Systems Toolbox is installed. In addition, the user needs to provide the coefficients of the system's transfer function polynomial, input delay, and feedback transfer function in order to run the program correctly and obtain the desired results.

PID simulation model construction

PID controller (Proportional-Integral-Derivative Controller) is a classic feedback control algorithm, which is widely used in industrial automation systems. Based on the current error, historical error and error change rate, it adjusts the control signal through three links of proportionality, integration and differentiation to achieve precise control of the system output. In this article, I will elaborate on the principle of PID control and the simulation process.

1. Proportional: Proportional control is adjusted according to the current error, and its output is proportional to the error. The proportional coefficient Kp determines the response degree of the proportional control to the error, and adjusting Kp can change the sensitivity of the system. A larger Kp value will result in a faster response, but may cause oscillation and instability of the system.

2. Integral link (Integral): Integral control is used to correct the static error of the system, that is, the persistent deviation. It adjusts the output by accumulating historical errors to reduce bias. Integral coefficient Ki determines the gain of integral control, too large Ki value may lead to excessive adjustment of system response or overshoot.

3. Derivative: Derivative control predicts future trends by taking into account the rate of change of error and adjusts the output accordingly. Differential control can suppress system oscillation and quick response, reducing overshoot. The differential coefficient Kd determines the gain of the differential control, and an excessively large Kd value may cause the system to be too sensitive to noise and interference.

4. PID controller output calculation formula:
   [
   u(t) = Kp \cdot e(t) + Ki \cdot \int_{0}^{t}e(\tau)d\tau + Kd \cdot \frac{de( t)}{dt}
   ]
   Among them, u(t) is the output of the PID controller, e(t) is the current error, Ki is the integral coefficient, and Kd is the differential coefficient. The above formula includes three links of proportional, integral and differential.

5. Advantages of PID controllers:

• Simple and easy to implement, suitable for most control problems.
• Parameters can be tuned as needed to obtain the desired control performance.
• It has good adaptability to both linear and nonlinear systems.
• It has good stability and robustness.

The simulation process of the PID controller:

1. Determine the system model: First, the mathematical model of the controlled object (Plant) needs to be established. This can be described by a transfer function or state-space model of the system.

2. Setting goals: Determine the expected output of the system, that is, the set point (Setpoint). This represents the target state we want the system to achieve.

3. Select the control strategy: Based on the dynamic characteristics and design requirements of the system, select the PID controller as the control strategy. Determine the parameters Kp, Ki and Kd of the PID controller, and make a preliminary estimate.

4. Set up the simulation environment: In MATLAB, set up the simulation environment by building a model or defining a transfer function. You can use the Simulink toolbox to create a closed-loop control system, including the controlled object, PID controller and feedback link.

5. Run the simulation: In the simulation environment, the setpoint is input into the system and adjusted according to the output of the PID controller. Observing the response of the system, the control effect can be evaluated by plotting the output response curve.

6. Adjustment parameters: According to the actual simulation results, adjust the parameters according to the dynamic characteristics of the system. The best combination of PID parameters can be found using trial and error or advanced auto-tuning algorithms.

7. Evaluate performance: Under different working conditions, evaluate the performance of PID controller, including indicators such as steady-state error, adjustment time, overshoot and oscillation. Optimize PID parameters as needed to achieve better control effect.

8. Real-time implementation: Apply the optimized PID parameters after simulation and debugging to the actual control system in real time, and conduct field tests and feedback.

Summarize:

PID controller is a classic and practical control algorithm applicable to various control problems. Through reasonable selection of PID parameters and simulation debugging, precise control between system output and expected value can be realized. The use of the simulation process can help us better understand the dynamic characteristics of the control system and optimize the performance of the PID controller.