What Are the Types of Transfer Functions in Control Systems?

TL;DR

Transfer functions in control systems are categorized into types based on the power of 'n' in the open loop transfer function. Type 0 systems have steady state errors of 1/(1+k) for step inputs and infinity for ramp and parabolic inputs. Type 1 systems have zero steady state error for step inputs and 1/k for ramp inputs, while type 2 systems have zero steady state errors for both step and ramp inputs, and 1/k for parabolic inputs.

Transcript

hello friends in this video we are going to study about the types of transfer function and their steady state errors okay so let's start with the topic so what is a type of a system as we know that the open loop transfer function of a system it is given by the equation gs hs equals to k so this is how we represent the open loop transfer function of... Read More

Key Insights

• 🤗 The type of a system is determined by the power of 'n' in the open loop transfer function equation.
• 🔠 Type 0 systems have steady state errors of 1/(1+k) for step inputs, and infinity for ramp and parabolic inputs.
• 🔠 Type 1 systems have zero steady state error for step inputs, 1/k for ramp inputs, and infinity for parabolic inputs.

Questions & Answers

Q: What is the open loop transfer function of a system and how does it determine the type of the system?

The open loop transfer function of a system is represented by gs hs = k, where 'n' in the power of s denotes the type of the system. For example, if n=0, it is a type 0 system.

Q: What is the steady state error for a type 0 system with a step input?

The steady state error for a type 0 system with a step input is 1/(1+k).

Q: What is the steady state error for a type 1 system with a ramp input?

The steady state error for a type 1 system with a ramp input is 1/k.

Q: What is the steady state error for a type 2 system with a parabolic input?

The steady state error for a type 2 system with a parabolic input is 1/k.

Q: How does the power of 'n' in the open loop transfer function affect the steady state error?

The power of 'n' in the open loop transfer function determines the type of the system and directly affects the steady state error. Higher values of 'n' result in lower steady state errors for certain input types.

Summary & Key Takeaways

• The open loop transfer function of a system determines its type, which is denoted by the power of 'n' in the equation gs hs = k.

• For a type 0 system, the steady state error for step, ramp, and parabolic inputs is 1/(1+k), infinity, and infinity, respectively.

• For a type 1 system, the steady state error for step, ramp, and parabolic inputs is 0, 1/k, and infinity, respectively.

• For a type 2 system, the steady state error for step, ramp, and parabolic inputs is 0, 0, and 1/k, respectively.