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Control system
Control system
The control system controls the inputs to the system to achieve the desired behavior. In the control system, there should be a clear mathematical relationship between the input and the output.
PID control
PID control
PID control is proposed for this project due to simplicity and robustness. It provides closed-loop response characteristics and can regulate the time domain behavior of different types of plants.
PID stands for Proportional, Integral, and Derivative control. It is a closed-loop feedback control system.
It continuously calculates the error value as the difference between the setpoint variable (Input) and its measured parameters (Feedback). PID corrects the error between the measured position and the desired position by calculating the error and outputting a PWM (Pulse Width Modulated) signal to a microcontroller that can adjust the position accordingly.
Proportional Term
The proportional component depends only on the error value. A proportional constant, Kp, also called proportional gain, is multiplied by the error value and is the proportional component of the output of the controller.
Integral Term
The Integral term sums the error up to the present time. The result is that even a small error term will cause the integral component to increase slowly. The integral response will continuously increase over time unless the error is zero. So, it is used to nullify the steady-state error if present in the system. The integral gain term will be represented by Ki.
Derivative Term
The derivative term is proportional to the rate of change of the error signal. Derivative gain is used to damp the oscillations. Even a system with zero oscillations and with no overshoot is possible by selecting a proper derivative gain (Kd).
Therefore, output from PID controller is a summation of proportional, integral and derivative terms.
The output of the PID controller is the function of PID gains (Kp, Ki and Kd). By changing the PID gains the output of system can be varied according to the given system and type of response required from the system. This is known as tuning of the PID controller.
PID controller applications
PID controller applications
PID control has wide applicability across industries and real-world applications. The most common application is the control of a motor's position and speed. This concept is used in applications such as quadcopters, line-following robots, wall-climbing robots, and many other robotics applications. A car moving up a mountain can be maintained at a constant speed using a PID controller. In addition to motor control, it can also be used for applications such as temperature control of boilers, rooms, furnaces, etc.
Block Diagram of Control System
Block Diagram of Control System
Characteristic Equation
Characteristic Equation
Pole Placement Results
Pole Placement Results
Simulation using ode45 solver
Simulation using ode45 solver
Results for Other States in the System for Sinusoidal Input
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