Resonant Electromechanical Servomechanism

Summary

In practical servo systems one often encounters cases in which resonances are a significant factor. Examples include robotic systems where the flexing of the arm can lead to a non-negligible system resonance.

If these types of resonance are ignored in the control system design, then the performance can be severely compromised.

The aim of the current laboratory is to investigate the impact of resonance on control system design with particular reference to electromechanical servomechanisms. The laboratory is motivated by the problem of pointing a radio telescope. This type of system has significant structural resonances. The physical system has to contend with wind disturbances and the drive technology is not perfect.

The control system therefore should:

  • Reject wind disturbances
  • Deal with stiction effects in the drive system
  • Reject drift in the analog motor drive circuitry
  • Reject DC offsets in the analog motor drive circuitry
  • Deal with structural resonances

Figure 2.1: Radio Telescope Array at Narrabri in NSW, Australia
Figure 2.1: Radio Telescope Array at Narrabri in NSW, Australia

The Physical Apparatus

Laboratory 1 was concerned with standard electromechanical servomechanisms. This system was somewhat ideal in the sense that no resonances existed. In practice one often encounters cases in which resonances are a significant factor. Examples include robotic systems where the flexing of the arm can lead to a non-negligible system resonance. If these types of resonance are ignored in the control system design, then the performance can be severely compromised. The aim of the current laboratory is to investigate the impact of resonance on control system design with particular reference to electromechanical servomechanisms.

As a motivating example, we refer to the problem of pointing a radio telescope. A photograph of a radio telescope array at Narrabri in NSW Australia is shown in Figure 2.1. Indeed, the current laboratory is loosely based on some of the experience gained when designing the control systems for this set of telescopes.

These telescopes have a 22m fully steerable parabolic antenna dish, The dish and supporting structures weigh over 60 tonne. Six of these units, spread out over 6km are used in combination to form the Australia Telescope Compact Array.

These antennas work together using a technique called “interferometry” which allows the antennas to mimic a much larger antenna. This gives the telescope the ability to see very fine detail.

The antennas are primarily used for deep space radio astronomy. The motion of the earth results in these objects appearing to trace out complex trajectories (including parabolic trajectories) in the sky. The “direction” of these objects are calculated by an astronomical computer and the results are sent to the antenna control system which ensures that the dish points in the desired direction.

In addition to tracking a single object the user may wish to switch rapidly from tracking one object to another. These manoeuvres require high speed and quick settling times.

In order to fulfill the above goals, the servo control system should be designed so as to:

  • Track constant ramps and parabolic trajectories.
  • Provide good transient response.
  • Slew rapidly through large angles and then smoothly enter the position tracking mode.

Typical specifications are:

  • Star tracking rates from 0 to 200arcsec/s with accelerations up to 0.3arcsec/s2.
  • Position errors of the order of 3arcsec.

The physical system has to contend with wind disturbances and the drive technology is not perfect. The control system therefore should:

  • Reject wind disturbances.
  • Deal with stiction effects in the drive system.
  • Reject drift in the analog motor drive circuitry.
  • Reject DC offsets in the analog motor drive circuitry.

Finally, safety considerations are of prime importance, thus:

  • Equipment and personnel safety requirements demand that under no circumstances should the control actions excite structural resonances.
  • The control system must be stable and robust under all operating conditions.
  • The control system must be simple to tune, maintain and to re-tune in case the antenna is assigned different performance goals in the future.

Details of the control hardware are given below:

Mounting

The azimuth position encoder is mounted on the azimuth structure. The position encoder signals are calibrated so that they reflect the true bore sight, corrected for structural alignment, antenna seating misalignment and dish distortions.

  • A 22 bit position encoder was used leading to a resolution of 0.3arcsec.

Drive Assembly

Stiction can be particularly problematic when the tracking trajectory requires very low movement rates. Friction effects, Coulomb as well as stiction in the gears and motor assembly are important since they impact on achievable performance.

The drive system consists of DC servo controllers and high performance DC motors. In practice, two motors are used which work against each other in a torque-share-bias drive arrangement. This is an engineering approach to avoiding backlash problems by keeping the gear teeth in constant contact.

In this laboratory we will simulate a resonant servo using a similar set-up as in laboratory 1 but with the addition of a flexible shaft between the motor and the mechanical load.

The set-up will be as follows:

  • A DC motor will be connected to a mechanical load via a flexible coupling.
  • The field current of the DC motor will be assumed constant and a very high bandwidth armature current control loop will be used to ensure that motor torque can be considered as a control variable. Therefore, it can be safely assumed that the electrical torque exerted by the motor, Te, is simple proportional to the armature voltage. We further assume that the proportionality constant is one for simplicity. Therefore, we consider Te as the control input.
  • Our goal will be to control the angular position of the mechanical load. The control loop should be able to asymptotically track (i.e., track with no steady state error) step and ramp references and to asymptotically compensate step input disturbances.

Prerequisites

The laboratory would be suitable for a first or second course in control. The assumed knowledge includes

  • Frequency response
  • Bode diagrams
  • Root locus
  • Step responses
  • Linear robustness analysis

Learning Objectives

The learning objectives of this virtual laboratory include:

  • Physical modelling
  • Estimation of model parameters
  • Control tuning under robustness constraints
  • Widebandwidth design for a resonant system