SEE701 Control Systems Engineering Assignment

Reference no: EM132870096

SEE701 Control Systems Engineering - Deakin University

QUESTION 1

Consider the following state-space model

x(t) = Ax(t) + Bu(t)
Y(t) = Cx(t) + Du(t)

where matrices A, B, C, D are as given below:

A=[-3 -2 -0.75 0 0; -3 0 0 0 0; 0 2 0 0 0; 0 0 1 0 0; 0 0 0 2 0]; B=[1;0;0;0;0];
C=[0 0 0 0 2.75]; D=0.
Check the stability of this system and also determine whether this system is controllable.

QUESTION 2

Consider the following state-space model

x?(t) = Ax(t) + Bu(t)
Y(t) = Cx(t) + Du(t)

Where matrices A, B, C, D are as given below:

A=[-10 0; 1 0]; B=[1;2]; C=[0 1]; D=0.

(a) Determine whether the system is controllable.

(b) Assume that the state vector is available for feedback control, design a full state feedback controller so that the closed-loop system achieves a settling time (with a 2% criterion) of a seconds, and an overshoot of about 0.5b%. Use Matlab to simulate and plot the response of the closed-loop system. Include all codes and figures.

QUESTION 3 Consider a system with an open-loop transfer function given by:

G(s) = Y(s)/U(s) = s+1/s²-2

(a) Derive a state-space representation of the system in canonical form.

(b) Check the controllability of the system.

(In your working solution, you must clearly show how the feedback controller is obtained. Also, use Matlab to verify your result).

(d) Use Matlab to simulate and plot the response of the closed-loop system to a unit-step reference input. Make note of the steady-state value of the output of the system. Include all codes and plot from Matlab.

(e) Design a suitable PI controller for the system so that the output tracks a step reference input. Use Matlab to simulate and plot the response of the closed-loop system to a unit-step reference input. Does the output now track the reference unit-step input? Show your full working including all codes and plot from Matlab.

Question 4

Consider the following state-space model

x?(t) = Ax(t) + Bu(t)
Y(t) = Cx(t) + Du(t)

As stated in chapter 3, this system is controllable if and only if the rank of the following Controllability Matrix, CM = [B AB A²B ... A^n-1B], is full.

For this question, you are now required to undertake further reading/research into this topic to fully understand why such the above condition is required. Demonstrate your understanding by providing a concise mathematical proof of this stated condition.

Question 5

This is a research-based question and you are required to investigate and analyse a real-world control system. Particularly, you are required to undertake the following tasks:

• Investigate and analyse a real-world control system of your choice. As a requirement, the system under consideration should be of high-order of at least four state variables (for example, an inverted pendulum control, load frequency control of an interconnected power system, spread of an epidemic disease, mass-spring system etc.);
• Based on your chosen system, derive a state-space model for the system;
• Analyse its stability and controllability;
• Specify the required closed-loop system performance and design a suitable state feedback controller for the system to meet the requirement; (In your design, you may also impose an additional constraint that the steady-state error to the unit-step reference command input is zero, thus a PI controller maybe required, etc); and
• Valide your controller design via extensive Matlab simulations.

Attachment:- Control Systems Engineering.rar

Reference no: EM132870096

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