Question

Design state-feedback gains to locate the desired closed-loop poles at s=-2.5∓j6, and s=-4. Given the plant transfer function: Gs=14(s+8s)/(2+3s+5)

Answer 1

The question involves designing state-feedback gains to locate desired closed-loop poles for a control system, for which a step-by-step control design process would be used, such as converting the transfer function to state-space and applying pole placement techniques.

Step-by-step explanation:

The student is tasked with designing state-feedback gains to achieve desired pole locations for a system represented by a transfer function in a control engineering problem. The desired closed-loop poles are given as s = -2.5 ± j6 and s = -4. Here, controller design and setting suitable state-feedback gains will ensure the system's behavior matches the specified dynamic characteristics.

To solve this, one would typically:

1. Convert the transfer function to a state-space representation.
2. Determine the system's controllability.
3. Use the Ackermann's formula or pole placement techniques to find the required feedback gains.

However, without the actual state-space equations or further details, we cannot compute the gains directly. This step-by-step approach provides the conceptual roadmap for designing the required control system.

Answer 2

The question is about designing state-feedback gains to achieve specific closed-loop pole locations for a given plant transfer function in control systems engineering. One would convert the transfer function to state-space form and then compute the feedback vector K using pole placement techniques.

Step-by-step explanation:

The question asks about designing state-feedback gains to locate the desired closed-loop poles for a control system. The plant transfer function provided is G(s) = 14(s + 8)/(s^2 + 3s + 5). To achieve the desired pole locations at s = -2.5 ± j6, and s = -4, one needs to apply control theory techniques such as pole placement using state-space representation of the system.

Firstly confirming the state-space model is necessary, which typically includes matrices known as A, B, C, and D that represent the system dynamics. With these matrices, one can use the Ackermann's formula or any other pole placement method to compute the state feedback vector, commonly denoted as K.

Once the state feedback vector K is computed, it can be applied to the system to achieve the desired closed-loop pole locations, ensuring the system's stability and performance as specified.