Understanding Type-2 Systems
Type-2 systems are characterized by having two integrators in their open-loop transfer function. This means they can effectively track inputs that have a degree of polynomial behavior.
Steady State Error Analysis
When analyzing the steady state error for different types of inputs, we consider the following:
- Step Input: For a type-2 system, the steady state error is zero.
- Ramp Input: The steady state error remains zero as well.
- Parabolic Input: This is where the steady state error becomes relevant.
Steady State Error for Parabolic Input
For a parabolic input, which can be represented as a quadratic function, the system's ability to track such inputs can be evaluated using the error constant. Here’s how it works:
- A type-2 system has an infinite velocity error constant, which implies its ability to track linear inputs perfectly.
- However, for a parabolic input, the system will not be able to follow the trajectory perfectly due to its inherent limitations.
- The steady state error in this case is finite, meaning the output will settle at a specific value that is not the desired response but is determined by the characteristics of the system.
Conclusion
Thus, the correct answer to the question regarding the steady state error due to a parabolic input in a type-2 system is:
- a) Finite: This reflects that while the system can handle certain inputs effectively, it will still exhibit some level of error when faced with more complex input profiles like parabolas.