Transfer Function Derivation from State Model Statement Problem No 2 - Control Systems

TL;DR

Learn how to obtain the transfer function of a system using the state model representation.

Transcript

hello friends in this video we are going to solve a problem on how to determine the transfer function of a system using the state model so let's take a problem so our problem is to obtain the transfer function for this cso system that is single input and single output system and the state variable representation or the state model of the system is ... Read More

Key Insights

• ❓ The transfer function of a system can be determined using the state model representation and the formula C(sI - A)^(-1)B + D.
• 🔙 The matrices A, B, C, and D can be directly obtained from the given state model representation.
• ❓ The (sI - A) matrix is calculated to find its inverse, which is necessary for the transfer function formula.
• ❓ The determinant and adjoint of the (sI - A) matrix are also calculated in the process.
• 😘 The transfer function expression is simplified by multiplying the matrices C, (sI - A)^(-1), B, and adding D.

Questions & Answers

Q: What is the transfer function formula used to determine the system's transfer function?

The transfer function formula used in this video is C(sI - A)^(-1)B + D, where C, A, B, and D are matrices obtained from the state model representation.

Q: How can the matrices A, B, C, and D be calculated from the state model representation?

The matrices A, B, C, and D can be directly obtained from the given state model representation of the system.

Q: What is the purpose of calculating (sI - A) in the process?

Calculating (sI - A) helps to determine the inverse of the matrix, which is required in the transfer function formula C(sI - A)^(-1)B + D.

Q: How is the transfer function obtained from the calculated matrices?

By substituting the calculated matrices C, (sI - A)^(-1), B, and D into the transfer function formula, the transfer function expression can be simplified and obtained.

Summary & Key Takeaways

• The video explains how to determine the transfer function of a single input and single output system using the state model representation.

• The transfer function is obtained by calculating the matrices A, B, C, and D from the state model representation and then using the formula: C(sI - A)^(-1)B + D.

• Calculations are shown step-by-step for obtaining the matrices, finding the inverse of (sI - A), and finally obtaining the transfer function.