How can I avoid initial negative response to a step signal?

When designing the control of an LTI system,is it possible to avoid a situation like the one showed in the picture? That is, is it possible to avoid that the respost is initially with respect to the steady state value? In a case like this, what is the overshoot?

Answer 1

[Hornett]

When designing the control of a Linear Time-Invariant (LTI) system, it is indeed possible to influence the transient response characteristics, such as overshoot and initial deviation from the steady-state value. However, without seeing the specific picture you mentioned, I can provide some general guidance on how to address these issues in control system design.Avoiding Initial Deviation from Steady-State

1. Proper Controller Design: Use controllers such as PID (Proportional-Integral-Derivative) to adjust the system's response. Tuning the PID parameters appropriately can help manage the transient response.
2. Feedforward Control: Incorporate feedforward control to anticipate changes and adjust the control input accordingly, minimizing initial deviations.
3. State Feedback: Implement state feedback control to directly influence the system's state, improving the response.
4. Pre-filter Design: Use a pre-filter to shape the reference input, ensuring the system tracks the desired trajectory more closely from the start.
5. Initial Condition Handling: Set initial conditions that align with the desired steady-state values to minimize initial deviations.

Understanding Overshoot

• Overshoot is defined as the amount by which a system exceeds its final steady-state value during its transient response. It is typically expressed as a percentage of the steady-state value.
• Calculating Overshoot: If ( M_p ) is the maximum peak value of the response and ( M_f ) is the steady-state value, the overshoot percentage ( OS ) can be calculated as: [ OS = \left(\frac{M_p - M_f}{M_f}\right) \times 100% ]