Design Realization lecture 22

1
Design Realization lecture 22

• John Canny
• 11/6/03

2
Last time

• Some physics
• Bending and stretching
• Construction methods
• Molding
• Welding
• Structural components
• Modular systems

3
This time

• Circuit design critique
• Control principles
• Simulation Matlab/Simulink

4
Feedback Control

• Often we want to move a system in a particular
  way, by controlling a parameter such as
• Position control
• Speed control
• Force control
• Feedback control uses sensor(s) to measure this
  parameter and make corrections.
• Feedback must be applied with care to avoid
  ever-increasing corrections (instability).

5
Feedback Control

• Naively, we want to do something like this

V
Amplifier
Input(voltagerepresentingdesired angle)
Potentiometer on shaft(angle sensor)
Motor
6
Feedback Control

• Any difference between input and measured shaft
  angle will be amplified, moving the motor.
• If the direction is correct, the motor will
  reduce the difference. With high gain, the error
  ? 0.

V
Amplifier
Input
Potentiometer on shaft(angle sensor)
Motor
7
Simulink Models

• Tools like Matlab/Simulink allow us to design and
  test controllers before building them.
• Here is the controller just shown in Simulink

Voltage
angle
8
Feedback Instability

• Problem the amplifier has delay, the motor has
  inertia, keeps moving even after error ? 0.
• If gain is too high, it will overshoot, ring or
  possibly oscillate.

9
PD Stabilizing Controller

• The simplest way to control feedback is with a
  PD (Proportional Derivative) controller.
• A multiple of the derivative of the output is
  subtracted from the amplifier input.

10
PD Stabilization

• Why does derivative feedback stabilize the
  system?
• Derivative feedback simulates a damper.
• Motion in a fluid creates viscous drag (F ? -v).
• Viscous drag quickly robs the system of energy.

11
PID Control

• Sometimes there is a residual error between
  desired and actual output (not for DC motors).
• Computing the integral of the difference signal
  will reduce it to zero in the steady state.

12
PID Tracking Controller

• All three terms P,I,D are computed on the
  difference signal

PID controller
13
Implementing PID Controllers

• Normally, the controller CPU is running at fixed
  discrete time steps.
• Derivates can be computed by differencing
  consecutive samples, integrals by summing
  samples.
• This approach introduces delays and can cause
  problems at high frequency.
• Make sure that amplifiers roll off at high
  frequency use a low-pass amplifier.

14
Discrete lowpass amplifier

• Input is (x1,,xn), output is (y1,,yn)
• yk a yk-1 (1-a)b xk a, b
  constants, a lt 1.
• If x 0, y non-zero, then the amplifier outputs
  a decreasing geometric sequence, which is a
  discrete approximation to exponential decay.
• It simulates a simple RC low-pass circuit.

15
Discrete lowpass amplifier

• The amplifiers DC Gain is b
• Corner frequency ?c (- ln a)/t 2?fcwhere t
  is the discrete step time.

16
Automatic code generation

• There is a companion to Matlab/Simulink called
  real-time workshop (RTW).
• RTW automatically generates C code to run a
  Simulink model. It can handle new user-defined
  blocks (e.g. for sensor input or motor output).
• This code can be compiled and run on the control
  processor.

17
Automatic code generation

• RTW code generation includes scheduling and
  event-handling and allows blocks to run at
  different rates.
• It also allows complicated models that may not
  run correctly with a simple discrete-step
  approximation.