PAPER No. 7 SUMMARY
Applying Drive Specifications to Systems Applications:
Part I Speed Regulation
1999 IEEE IAS Annual Meeting
Brian Thomas Boulter
Applied Industrial Control Solutions LLC
4597 E Sprague Rd.
Independence, OH, USA 44131
© ApICS ® LLC 2000
Abstract- This paper provides guidelines for the useful interpretation of AC/DC drive speed performance specifications from a drive systemís application perspective..
The technical climate in todayís drive systems business markets has been inundated by drive vendor claims of ever improving drive performance specifications. The objective of this report is to bring these performance specifications into technical focus, and provide the reader with a basis for correctly interpreting them from a systems/applications perspective. Space constraints only allow for a discussion of speed specifications. Future papers will address performance issues associated with cascaded and "parallel", position, tension, and torque regulation schemes.
It is hoped that the reader will walk away from this presentation with the tools required to sift through a given driveís speed performance specifications, and glean from them those points that are truly of importance to the application in question.
To summarize, most of the time the chief performance limiting mechanism in a system is not the responsiveness of the drive, but the physics of the application and/or the system architecture.
A. Paper Overview
The paper is divided into four sections. The first section is composed of this introduction, the second section defines a set of useful terms, the third section defines the most important drive specifications with respect to speed, and methods of determining these criteria for a given drive. The report conclusions are presented in the fourth section.
II. Some useful definitions
Three definitions that prove useful in understanding drive system speed performance criteria are, control loop bandwidth, per-normal Inertia, and noise sensitivity
Control Loop Bandwidth (Fig. 1): Bandwidth is defined as the frequency at which the closed loop response of the controlled variable is attenuated 3 [db] from the set point. It is also approximated as the point at which the open loop gain of the system is unity and is called the "crossover" frequency. The Bode plot graphically represents the magnitude and phase of the ratio of output to input over a range of input frequencies. Therefore, unity gain of the system at the crossover frequency implies that, at that frequency, the output and the input of the open-loop system are equal in magnitude. And at all frequencies below this frequency , the closed loop has unity gain.
Fig. 1. Bandwidth Definition
Per-Normal Inertia (Fig. 2): Per-normal reflected inertia [sec] is the time in seconds that it takes to accelerate the motor and load inertia from zero speed to motor base speed (Sb) with motor rated torque (tRated) and the given reflected inertia (J).
Fig. 2 Per-Normal Inertia [sec]
Imperial units: (1)
SI units: (2)
Noise Sensitivity (Fig 3.): The concept of noise sensitivity is important when the gain of a control loop is taken into account. This can be easily demonstrated: Assume an application has a speed loop resolution of 1 part in 10,000, and a torque loop resolution of 1 part in 10,000, and the speed feedback is corrupted by 10 counts of system noise. In addition, make the assumption that the proportional gain of the controller has been increased to 1,000, to get more "response" out of the drive. When amplified by the proportional controller gain, the noise will produce 10,000 counts of torque reference noise. Clearly, injecting noise with amplitude equal to the maximum torque capability of the drive will adversely affect the drive train integrity. This noise typically comes from uncontrolled mechanical and electrical sources, such as machine vibration, encoder shaft vibration, and electrical emi. Noise in control systems cannot be avoided, and will limit the maximum possible gain of any control loop. The loop gain must be constrained in such a way that an optimum trade-off between gain/bandwidth and the ability of the system to tolerate noise amplification in the controller is achieved. Frequency compensation schemes can be employed to reduce the sensitivity of the controller to noise amplification.
There are many ways of defining the noise content of a signal. However, to avoid complexity, define per-normal system noise as the ratio of the [rms] noise content found on the feedback signal, to the feedback peak-to-peak maximum value. While this approach is crude, it is an adequate description for use in industrial control systems.
Fig. 3 Per-Normal Noise / Controller Gain Limitation
A graphical representation of noise sensitivity is given above in Fig. 3. In this graph a family of curves is used to define the maximum proportional controller gain for a given loop, as a function of the ratio of the dominant (lowest) system natural frequency to the controller bandwidth, and per-normal system noise. Depending on system natural frequency and the amount of noise in the system, there may exist significant differences in maximum possible controller gains. Each application will be different.
To use this graph the user should have some idea of the system natural frequencies, and the expected loop bandwidths. Note that not all systems are second order, and more than one system natural frequency might exist. If this is the case, choose the lowest (dominant) natural frequency.
A good example of the application of this constraint on loop gain is a drive train with a very low torsional frequency and significant backlash. Such a system will not be able to withstand much noise amplification in shaft torque. Noise is composed of a spectrum of excitation frequencies, some of which will inject energy at the torsional natural frequency of the drive train. If the energy contained in the excitation is high enough to exceed an application dependant threshold, the energy exchanged between the inertia and the drive shaft will grow in magnitude. Determining the noise amplification/energy threshold point at which a system becomes unstable is the subject of much research in the area of non-linear controls, and chaotic system behavior. However, from an industrial control systems perspective, the understanding that a threshold point exists and that exceeding it causes instability is adequate.
How to measure the noise content of your application? Run the drive as a speed regulator, average the current reference with a running average filter, then force the current reference to the averaged value. Measure the speed feedback through a scope with the AC setting (to remove any bias, or drift in the measurement), and then divide the measured noise voltage [rms] by the maximum peak-to-peak voltage. This will yield the PN-noise value.
The four earlier examples illustrate that there are both physical, and technology dependant factors that limit the responsiveness of a speed regulator. Briefly, in systems where there are high inertia, and/or noise sensitivity factors limiting the bandwidth (Fig. 3) the use of a "more responsive" drive will provide no additional benefit. In fact experience has shown that in some of these applications, "low technology" MG sets perform every bit as well (some would say better) than their high bandwidth static drive counterparts.
In applications where the inertia is low enough, and the system natural frequency high enough. The loop gain may be increased to a point where either the sampling time of the speed loop, and/or the bandwidth of the torque loop, limit the responsiveness of the speed loop. The use of faster sampling and/or a "more responsive" AC or DC static drive in these applications will provide measurable benefits.
Some applications require high torque loop bandwidths to fully utilize novel torsional and/or friction compensation schemes. In these applications the need for bandwidth does not arise from a need to improve speed regulation, but rather to compensate for a debilitory physical property associated with the mechanics of the machinery. In other applications terminal voltage slewing can impact the performance of a drive in a given application, (e.g. screw down motors on gauge control systems.) These applications require a unique torque regulator structure, that has zero error to a torque ramp. These issues are discussed at length in [1,2,3].
In the interest of fairness, all drive supply vendors should employ measures of drive performance that allow the purchaser of the drive to compare "apples to apples". The author recomends using the approach shown in this paper, where: 1) Static performance measures are in terms of percent deviation from setpoint [%], and 2) Dynamic performance measures are expressed in terms of bandwidth [rad/sec] (frequency domain method). As an alternate dynamic performance measure, the load shock recovery time (time domain method) may be used.
The conditions under which the expected dynamic response can be achieved should be CLEARLY expressed (i.e. the per-normal inertia, the system noise requirements, and the torsional natural frequency).
Alternately, the drive purchaser may themselves employ the techniques described in this paper to determine if the drive has the response required to meet the requirements of his/her particular application. Employing these analytical techniques will greatly improve the ability of the drive purchaser to make intelligent application-specific decisions about his/her drive speed performance requirements.