3C1

Case Study: Control System DesignDavid Corrigan 2011

http://www.mee.tcd.ie/̃ sigmedia

A Laser Position Control System

A Laser system is used to shape the hip socket for the appropriate insertion of an artificial hip joint.The system uses a motorised system for controlling the position of the laser using a closed loop controlsystem with a proportional controller. The block diagram for the system is

Figure 1: Block Diagram of the Laser Control System

As this system is to be used in surgery it requires high accuracy for the position and velocityresponses. In order to get the required veloctity response the controller gain, K, must be adjusted sothat the steady state error for a ramp input signal x(t) = At (where A = 1 mm/s) is less than 0.1mm. The system must also be stable. A root locus plot of this system for 0 ≤ K <∞ is shown below.

3C1 Signals and Systems 1 Control Systems

Figure 2: Root Locus of the Laser Control System

1. Determine the value of K that satisfies the steady state error and the stability constraints.

2. Determine the position of the poles when the steady state error constraint is met exactly.

3. Assuming that the system contains a pair of dominant complex poles, find the 2% settling timeand percentage overshoot to a unit step input.

4. If the actual system response to a unit step is shown in Fig 3, measure the percentage overshootand settling time to determine whether it is safe to assume that the system has dominant poles.

3C1 Signals and Systems 2 Control Systems

Figure 3: Step Response of the Laser Control System

Figure 4: Ramp Response of the Laser Control System

3C1 Signals and Systems 3 Control Systems

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