# 0.9 State feedback compensation of a 2dof rectilinear system

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The objective of this lab is to design, simulate, and implement a state feedback compensator for a 2DOF mass-spring system. The controller will be designed and implemented in LabVIEW using the Simulation Module and Control Design Toolkit.

## Objectives

• Design, simulate, and implement a state feedback compensator for a 2DOF mass-spring system.

## Pre-lab

• Derive the equations of motion for the 2DOF rectilinear mass-spring. The plant configuration is shown below. The first andsecond mass carriages are free and the third is clamped. The medium stiffness spring is connecting the first and second carriages, andthe low stiffness spring is connecting the second and third.
• Find a state-space realization of the system.
• Design and simulate a full state feedback compensator to control the position of the second mass carriage. Design yourcompensator to meet the following performance specifications:
• Percent overshoot $\le 10%$
• Settling time $\le 1\mathrm{sec}$
• Zero steady-state error to a step input.

## Lab procedure

• Configure the plant as shown in Fig. 1 above.
• Code your state feedback compensator into the control loop VI.
• Perform a 3000 count step input and determine if you have met the performance specifications.
• Once you have achieved the desired performance, save your plot and turn it in with the rest of your work.

## Post-lab

• Explain how the state feedback gains affect the system's response in terms of its characteristic equation.
• What effect does the compensator have on the zero(s) of the system? If a system has an undesirable zero, how can its effect bereduced using only a state feedback compensator?
• Why is full state feedback compensation often unfeasible especially with higher-order systems?

#### Questions & Answers

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Introduction about quantum dots in nanotechnology
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s.
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