Servo and regulated systems are closed-loop systems whose output precisely follows the input: the regulator wants the output to take on a precise value equal to the fixed input (the setpoint or reference) regardless of the disturbance imposed, while the servo system (follower) wants the output to follow an input setpoint that varies over time and whose evolution is not always known in advance. All servo systems or control systems are represented by block diagrams, which include a comparison, power amplification, and measurement. The system's input time signal and output time signal are linked by a differential equation that is often difficult to express and also difficult to solve. For this reason, the Laplace mathematical transform is crucial, as it allows us to move from a function f(t) where the variable is time “t” to a function F(p) where the variable is the complex Laplace operator “P” depending on the pulse ω.
After applying the Laplace transform to the system's differential equation, the dynamic system can be modeled by a transmittance, otherwise known as a transfer function, which is the ratio between the Laplace transform of its output and that of the input. This is valid when all initial conditions are zero. This function characterizes the dynamics of the system and depends only on its physical characteristics.
To calculate the temporal responses of the system, simply calculate the transmittance of the system, take the Laplace transform of the input signal, and multiply these two quantities. An inverse transform of the output signal gives the desired first-order or second-order time response of the system for different types of input (Dirac, step, ramp, and sinusoidal or harmonic input). The stability of servo systems (first-order and second-order) is analyzed using the Routh and Nyquist criteria. The accuracy and speed of the time responses (index, impulse) are assessed via the characteristics of the systems (first-order and second-order). Frequency analysis is also performed using the Bode diagram, which allows the stability and robustness of the closed loop to be evaluated.
- Enseignant: ammar chakhrit
- Enseignant: Ilheim Derradji