The block diagram of a position control system is shown below. 1. Rewrite the system into a state...

Question

The block diagram of a position control system is shown below. 1. Rewrite the system into a state space description format shown below, and simulate this continuous plant for a unit step input. y CX AX Bu dt dX ? ? ? (10 marks) 2. Discretise this system into a discrete time system in the format below XXXXXXXXXXy CX k X k X k u k ? ? ? ? ? ? (20 marks) 3. Simulate this discrete time system for a unit step input, and change T to observe the changes in responses. Select a proper sampling interval T for the rest of the assignment. (10 marks) 4. Design a state variable feedback regulator for the system with a pair of complex poles at 0.4? j0.3. Simulate this closed loop system for a unit step input. (30 marks) 5. If the system state variables are not available. Design a dead-beat observer to provide state variables for your regulator. For a unit step input, simulate the complete system with regulator and observer in place and non-zero initial errors in state variables. (30 marks) Please note that marks will be awarded according to the solution presented which includes the presentation of results and reasoning. It is strongly suggested that all of the assignment should be typed. A listing of computer code should be provided for
	
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Assignment 2 
Due date: 9 June 2017 
Value: 10% 
Total marks: 100 
Penalty for late submission: 5% per day 
 
The block diagram of a position control system is shown below.

1. Rewrite the system into a state space description format shown below, and simulate 
this continuous plant for a unit step input. 
dX
? AX?Bu
 XXXXXXXXXXmarks) 
dt
y?CX
2. Discretise this system into a discrete time system in the format below
X (k?1)??X (k)??u(k)
 XXXXXXXXXXmarks) 
y?CX (k)
3. Simulate this discrete time system for a unit step input, and change T to observe the 
changes in responses. Select a proper sampling interval T for the rest of the 
assignment XXXXXXXXXXmarks) 
 
4. Design a state variable feedback regulator for the system with a pair of complex 
poles at 0.4? j0.3. Simulate this closed loop system for a unit step input.  
 XXXXXXXXXXmarks) 
 
5. If the system state variables are not available. Design a dead-beat observer to 
provide state variables for your regulator. For a unit step input, simulate the 
complete system with regulator and observer in place and non-zero initial errors in 
state variables XXXXXXXXXXmarks) 
 
Please note that marks will be awarded according to the solution presented which 
includes the presentation of results and reasoning. It is strongly suggested that all of 
the assignment should be typed. A listing of computer code should be provided for 
verification purpose. 
© University of Southern Queensland

David · Accepted Answer

Assignment 2 

The block diagram of a position control system is shown below.
Solution:
Conversion of continuous system to State space representation yields:
Step Response of the System:
G =[ 0.3616    0.1809 
    1.0101    1.0000] 
H =[   1.0101 
   -0.5970]
Solution: As T decreases , The discrete system looks similar to continuous system.
T= 0.01 will be selected for rest of the assignment as the response is very much identical to the 
continuous response.
Solution:

The block diagram of a position control system is shown below. 1. Rewrite the system into a state space description format shown below, and simulate this continuous plant for a unit step input. y CX...

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