#SK2d Sistem Kontrol: Pemodelan dengan fungsi alih

Summary

In this educational lecture, the instructor discusses three types of system modeling: differential equations, transfer functions, and state-space models. Focus is placed on the transfer function model, explaining that it is derived from the Laplace transformation of differential equations. The process involves transforming the system equations, simplifying them, and finding the output-to-input ratio, all with initial conditions set to zero. A practical example using an RC circuit is explored to demonstrate how transfer functions are developed. Emphasis is placed on understanding the importance of initial conditions in these calculations.

Takeaways

• 😀 The video discusses system modeling, focusing on three main types: differential equations, transfer functions, and state space models.
• 😀 The first type, differential equations, was covered in previous lessons and involves analyzing system behavior through equations.
• 😀 Transfer functions are introduced as the second modeling type, defined as the ratio of the Laplace transform of output to input, under initial conditions of zero.
• 😀 The third modeling type is state space, which the presenter states will be the focus in upcoming lessons.
• 😀 To calculate transfer functions, it's crucial to first have the differential equation of the system, then perform a Laplace transform on it.
• 😀 The purpose of studying Laplace transforms is to obtain the transfer function, which is the key to analyzing systems in the Laplace domain.
• 😀 The speaker stresses the importance of initial conditions being zero when using Laplace transforms for calculating transfer functions.
• 😀 A simple example using an RC circuit is presented to demonstrate the process of finding the differential equation and then applying Laplace transforms.
• 😀 Kirchhoff's Voltage Law (KVL) is applied in the example to derive the system's differential equation, which relates the output and input.
• 😀 The final goal is to simplify the equation, find the ratio of the Laplace transforms of output and input, and express it as the transfer function.
• 😀 The presenter emphasizes that when calculating Laplace transforms, initial conditions of zero allow for simplification, making the process smoother.

Q & A

What are the three types of modeling discussed in the lecture?

The three types of modeling discussed are: 1) Differential equations, 2) Transfer function (using Laplace transforms), and 3) State space representation.

What is a transfer function?

A transfer function is the ratio of the Laplace transform of the output to the Laplace transform of the input, assuming all initial conditions are zero.

What is the importance of the condition 'all initial conditions are zero' when defining a transfer function?

The condition that all initial conditions are zero ensures that the transfer function represents a system's response to input without any influence from previous states or energy stored in the system.

How is the transfer function derived from a differential equation?

The transfer function is derived by first formulating the system's differential equation, applying the Laplace transform, and then simplifying the equation to obtain the ratio of the Laplace transforms of the output and input.

What is the purpose of learning Laplace transforms in the context of transfer functions?

Learning Laplace transforms is essential for deriving transfer functions as it helps transform time-domain equations into the frequency domain, making it easier to analyze and manipulate the system's behavior.

What is the first step in deriving a transfer function from a circuit model?

The first step is to determine the differential equation governing the circuit by applying Kirchhoff's voltage law or current law.

How do you apply Kirchhoff’s law to derive a differential equation for an electrical circuit?

Kirchhoff’s voltage law (KVL) is applied by summing the voltages around a loop in the circuit. For each component, the voltage is expressed in terms of current and resistance, and the resulting equation is set equal to zero.

What happens after obtaining the differential equation for the system?

After obtaining the differential equation, you apply the Laplace transform to both sides of the equation to convert it into the s-domain, where the transfer function can be simplified.

Why are the initial conditions discarded during the Laplace transform of a system?

The initial conditions are discarded in the Laplace transform because the focus is on the system's response after a time t=0, with the assumption that the system starts in a zero state (no initial energy or disturbances).

Can the order of the system be determined from the transfer function?

Yes, the order of the system can be determined from the transfer function by examining the highest power of 's' in the denominator, which corresponds to the order of the differential equation.