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The difference between pi regulator and PID control _ Matlab pi regulator parameter selection _MATLAB inside PI control problem
The PI regulator operates as a linear controller that generates a control deviation based on a given value and the actual output value. It combines the proportional and integral components of the deviation in a linear manner to create a control signal that regulates the target system.
The PID controller adjusts the overall control system based on the PID control principle, ensuring that the actual value of the controlled variable aligns with the desired process requirement. Different control laws are suited to varying production processes, so the appropriate control law must be carefully chosen. Otherwise, the PID controller may fail to deliver the expected control outcomes.
Today, the degree of industrial automation has become a key metric for gauging modernization across various industries. Control theory has evolved through three distinct phases: classical control theory, modern control theory, and intelligent control theory. A prime example of intelligent control is the fuzzy fully automatic washing machine. Control systems can be categorized as either open-loop or closed-loop. A control system comprises a controller, a sensor, a transmitter, an actuator, and input/output interfaces. The controller's output is fed into the controlled system via the output interface and the actuator; the controlled variable is sent back to the controller through the input interface using the sensor and transmitter. Different control systems require different sensors, transmitters, and actuators. For instance, pressure control systems utilize pressure sensors, while electric heating systems employ temperature sensors. Many PID controllers and their devices or intelligent PID controllers (meters) are available today. These products are extensively applied in practical engineering. Various PID controller models exist, and major companies have developed their own versions. Intelligent regulators with parameter self-tuning functions enable automatic adjustment of PID controller parameters through intelligent adjustments or self-corrections and adaptive algorithms. Pressure, temperature, flow, and liquid level controllers using PID control, programmable logic controllers (PLCs) capable of implementing PID functions, and PC systems that can execute PID control are all common examples.
Below the image illustrating the differences between PI regulators and PID control in Matlab, we see a detailed comparison of PI and PID control:
P: Proportional
I: Integral
D: Differential Adjustment
PID regulation involves proportional, integral, and differential adjustments. Its aim is to adjust the output signal to match the setpoint by applying proportional, integral, and differential actions (relative to the input-output deviation).
Mathematical differential equation representation: c(t)=ke(t)+t/tdde(t)/dt+TI/tSe(t)dt (S: integral symbol)
Among these:
k is the proportional coefficient, which determines the system's response strength.
Td is the differential time. A smaller value enhances the differential effect but impacts accuracy.
TI is the integral time. A larger value strengthens the integral effect but slows down the response.
The proportional component determines the system's response intensity.
The differential action serves as an anticipatory control mechanism, eliminating errors before they occur.
The integral action helps eliminate errors but results in a slower response.
PID control is the foundational algorithm in industrial production and electronic design, offering effectiveness. However, in cases where system response speed isn't a priority but precision is critical, PI control—proportional and integral control—is often employed.
Its mathematical expression is: c(t)=ke(t)+TI/tSe(t)dt (S: integral symbol).
Matlab’s PI Regulator Parameter Selection Experience:
(1) Determine the Proportional Coefficient Kp
When determining the proportional coefficient Kp, first remove the integral and derivative terms of the PID, setting TI=0 and Td=0 to create pure proportional adjustment. Set the input to 60%-70% of the system's maximum allowable output. Gradually increase the proportional coefficient Kp from 0 until the system oscillates, then decrease it until oscillation ceases. Record the Kp value at this point, setting the PID's proportional coefficient Kp to 60%-70% of this value.
(2) Determine the Integral Time Constant Ti
After determining the proportional coefficient Kp, set a larger integral time constant Ti, then gradually decrease it until the system oscillates. Subsequently, incrementally increase Ti until oscillation stops. Record the Ti value at this stage and set the PID's integral time constant Ti to 150%-180% of this value.
(3) Determine the Differential Time Constant Td
The differential time constant Td is generally not set, usually at 0. At this point, the PID adjustment converts to PI adjustment. If necessary, set it similarly to the method of determining Kp, taking 30% of its value when not oscillating.
(4) Joint No-Load and Load Adjustment
Fine-tune the PID parameters until the performance requirements are satisfied.
A Small Class of Knowledge: PI Control Problem in MATLAB
(To obtain this PI controller with the download symbol, click the download symbol to display the window below.)
In fact, this is the specific implementation within the PI module; you don’t need to understand the internal workings of the module, just how to set the parameters for the PI module.
How to Use a PI Controller in MATLAB?
Select the PID module in Simulink, then enter 0 for parameter D.