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The software consists of 8 programs used to aid the design of servomechanisms. The programs employ closed form solutions with very little iteration, therefore the computations are quick and very accurate. This is especially important for transfer functions that contain very small damping ratios.

Several worked out examples are provided; This makes learning how to use the programs much easier. These examples represent the majority of practical feedback control problems.

Example 1 is used in each program, except Hydrostatic Transmissions & Rotary Hydraulic Motors, to illustrate how each is used. This example is an actual swashplate position control used to control the displacement of a variable displacement pump used in a hydrostatic transmission.

This software is believed to be the only software available that determines the drive train transfer functions for practical servo drives. The examples show how to achieve very high immunity to disturbances by elliminating many of the lags in the drive train by cancelling them with leads in the servoamplifier compensation networks. This technique is especially beneficial when there is a low spring rate in the structure between the motor and the load inertia, because there are more lags at low to moderate frequencies in the drive train transfer function. Chapter 11 in the manual shows how to design these compensators, using high frequency operational amplifiers or digital amplifiers.

These programs provide an analytical method of design. The programs typically used for servo design require a “trial & error” or “cut & try” method which requires more engineering time and the resulting servo performance is usually inferior to that obtained by an analytical approach. Simulation programs are very useful, however. See “Simulations” below. GoToTop

Drive Train Transfer Functions:

The drive train consists of a motor, a maximum of 2 speed convertors, a maximumum of 3 inertias or masses, and a maximum of 1 spring located between the motor and load or between the load and a fixed or movable point. This is illustrated by pictures and block diagrams in Chapter 1. The motor may be an AC or DC electric motor, a linear or rotary hydraulic motor, or a hydrostatic transmission.

In most drives there is one dominant spring that has a spring rate much lower then any other springs or structural compliances in the system. This spring rate can be measured by locking the end near the load and by applying a force or torque at the other end. The spring rate is the torque or force divided by the displacement. If the torque or force and displacement are measured at the motor, then the torque or force at the spring is multiplied by the product of the speed reduction ratio and the convertor efficiency and the spring displacement is divided by the speed reduction ratio.

If all springs are ignored, except for the dominant spring, then a satisfactory servo design can generally be achieved with relatively little effort. The stiffer springs may result in resonant frequencies well beyond the frequency bandwidth of the servo closed loop and thus have negligible effect on stability and performance.

The drive train transfer functions, Gu and Gpt are found in Chapter 1, Drive Train Program. For Example 1, the servo drives a load consisting of an inertia and a spring located between the inertia and the frame. The motor is a hydraulic cylinder controlled by a two stage servo valve. The linear motion of the motor is converted to angular motion at the load by the linkage shown in Figure 1-7. The conversion ratio of the linkage is radius, R, in./ rad. or lb.in./ lb. There are actually two sets of cylinders, links, and springs but only one set is shown to simplify the illustration of the principle of operation.

Block diagrams are shown in Figure 1-8. The servovalve is mounted on the pump. The input parameters are shown in Table 1-1. The results of the run are listed in Appendix 1-A. Tables 1 and 2 list both inputs and computed outputs. Table 3 lists the transfer functions of the drive train. GoToTop

Frequency Response:

The drive train transfer functions and the servovalve transfer function are then used in the Frequency Response Program of Chapter 2 to synthesize the servoamplifier and its compensation characteristics, using Bode Plot techniques. Example 1 employs conventional servo compensation consisting of a lead to cancel the lowest frequency lag in the servovalve and a lag that occurs at a frequency 1 decade greater.

The input parameters and options are shown in Tables 2-1 and 2-2, respectively. The results of the run are listed in Appendix 2-A. Table 1 lists the transfer function inputs. Table 2 lists the requested frequency responses. Parameters for the approximate closed loop transfer function,

G_cl , are listed beneath Table 1 and the frequency response for G_cl is listed in Table 3 for comparison with the actual response in Table 2. The G_cl transfer function, based on the above information, is shown below Table 3.The frequency response curves for Example 1 are shown in Figure 2-2. GoToTop

Transient Response:

G_cl is used in the Transient Response Program of Chapter 3 to determine the transient response to a step change in command of 16 degrees. The input parameters and options are shown in Tables 3-1 and 3-2, respectively. The results of the run are listed in Appendix 3-A. Table 1 lists the input parameters and Table 2 lists the variables vs time. The transient Response curve is shown in Figure 3-1. The transient response program accounts for slewing, but not other non-linearities. GoToTop

Steady State Errors:

The servo steady state errors are found in Chapter 4. The input parameers are listed in Table 4-1 and the results are listed in Appendix 4-A. GoToTop

Hydrostatic Transmissions and Rotary Hydraulic Motors:

Chapter 5 describes this program which finds the small signal characteristics of radial piston, rotary hydraulic motors and hydrostatic transmissions, which contain the above type of motor controlled by a variable displacement pump, as shown in the diagrams of Figure 5-1. These motors and transmissions are non-linear, unlike electric DC and brushless AC servomotors. The program finds the small signal torque gain, damping factor, and the time contant, for hydrostatic transmissions and the volumetric efficiency, hydromechanical efficiency, and the small signal flow resistance for rotary hydraulic motors at any desired operating point. The operating point is determined by user specified, steady state motor torque and velocity or load torque or force and velocity, along with the speed conversion ratio and efficiency. The program also finds several other variables of interest at each operating point. This information is useful in the design of the system, such as sizing the heat exchanger to remove the power loss and prevent excessive temperature.

Example 13, a hydrostatic transmission used to drive a winch, is employed to illustrate how the program is used. The input parameters for Example 13 are listed in Table 5-2 and the analysis options are listed in Table 5-3. The results for Example 13 are listed in Appendix 5-A. These results are then used in the Drive Train Program. GoToTop

Tutorial:

A brief review of the Bode Plot Technique for servo analysis is presented in Chapter 6.

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Curve Plotting Procedure:

Instructions for plotting frequency response and transient response curves, both displayed on the screen and printed, are given in Chapter 7. Several curves in each plot may be given different colors to help distinguish them from one another. See Figures 2-A1 and 3-A1. GoToTop

Electric Motor Drive with Current, Velocity, & Position Control Loops:

Chapter 8 describes a drive train with a brushless AC motor used to drive a winch where the cable acts as a spring between the drum and the load. There are 3 servo loops that control motor current, velocity, and position. The frequency responses are found for each loop. The transient response to command and disturbance inputs are found for the velocity and position loops. The transient responses are verified by non-linear simulations. The position vs time curves are in close agreement due to the high loop gain.

Appendices A and B show how to produce good performance using conventional analog or digital compensation in the velocity loop, only. The servo of Appendix B contains a spring between the load and a fixed or movable point. GoToTop

Pump Displacement Control Servo for a Hydrostatic Transmission:

Chapter 9 describes a pair of spring loaded hydraulic cylinders controlled by a 2 stage servovalve that control the displacement of the pump in the hydrostatic transmission of Example 13. Special servo compensation is used in the servoamplifier to cancel out some of the lags in the drive train. The frequency and transient responses to small & large commands are determined. Appendix 9-A contains an analysis where typical, conventional servo compensation is used. This results in a bandwidth that is less than that of the Hemmer design, described above, by a factor of 22.6. Appendix 9-B contains an analysis where conventional PID digital servo compensation is used to demonstrate its application in a hydraulic drive. GoToTop

Tension Control of a Winch with a Hydrostatic Transmission Drive:

Chapter 10 describes a winch driven by a hydrostatic transmission where the cable tension is controlled. Example 13 is used in chapters 5, 9, and 10 to illustrate the servo design techniques.

Special servo compensation is used in the servoamplifier to cancel out some of the lags in the drive train. The frequency and transient responses to small & large commands are determined. The transient responses to motion disturbances are also found. The transient responses are verified by non-linear simulations, which show close agreement in spite of the non-linear relationships. This is believed to be caused by the large amount of negative feedback used in the two servos.

Appendix 10-A contains an analysis where typical, conventional servo compensation is used in the servos controlling pump displacement and cable tension. This results in a bandwidth that is less than that of the Hemmer design, described above, by a factor of 366. The Hemmer compensation enables the amplifier gain to be raised by a factor of 40 over that of the conventional design.

The Hemmer compensated system exhibits considerably smaller errors for a given velocity disturbance or, conversely, it can tolerate considerably faster disturbances for a given allowable error by factors of 43 and 40, respectively.

Appendix 10-B investigates the effect of adding position control to reduce position disturbance errors. Position control reduces the velocity or position disturbance error by a factor of 2.1 for Hemmer Compensation and 1.105 for Conventional Compensation. Hemmer Compensation reduces the peak error by a factor of 76 when position control is added. GoToTop

Servoamplifier & Compensation Design:

At present, most commercially available digital servoamplifiers, a.k.a. servocontrollers provide one PID function, with an integrator and one or two first order leads or one second order lead or one first order lead without integration, one low pass filter with one first order lag, and one notch filter for servo compensation. The compensation is typically tuned by means of a trial and error technique. The number of PID networks provided is probably limited to one because it would be virtually impossible to tune more than two leads by trial and error. “Off the shelf” servocontrollers generally provide feed-forward compensation, which reduces the following error for commands, but doesn't reduce errors caused by disturbances.

Chapter 11 shows how to design servoamplifiers with the desired compensation for any number of desired leads, using video frequency operational amplifiers. It also can be used to compute PID gains, when applicable.

Note: Only the pump displacement controllers of Chapters 9, 10, 14, and 16 and the web tension controllers of Chapters 10 and 13 employ analog servoamplifiers, including compensation, because their best performance requires more than two leads. The remaining examples and Appendix B of chapter 9 in the manual can employ digital servocontrollers. GoToTop

Simulations :

Steady state and transient responses may be determined in the presense of non-linear characteristics, such as hysteresis, deadband, and saturation using a simulation program as described in Chapter 12.

The simulations may be compared to the performance predicted by by the Hemmer Transient Response program, which only include saturation and time delays for non-linear effects. The simulations can also plot several variables of interest vs time. The Hemmer Transient Response program only plots the controlled variable and its first and second derivatives vs time. GoToTop

Web Tension Control using an Electric Motor Drive

Chapter 13 describes a tension control servo where a plastic film is wound around a reel which is driven by a brush type DC electric motor. PID constants are determined for the conventional compensation. All three drive train lags are cancelled using Hemmer Compensation, but only two of the lags are cancelled using Conventional Compensation. The transient response to a velocity disturbance is found using the Hemmer programs and also by simulations. The curves are in good agreement. The transient tension error for Conventional Compensation exceeds that for Hemmer Compensation by a factor of 12.3 for an empty reel and 17.8 for a full reel. This technique can also be used for tactile control in robots. GoToTop

Velocity Control of a winch with a Hydrostatic Transmission Drive

Chapter 14 describes a winch driven by a hydrostatic transmission, where the cable velocity is controlled. Special servo compensation is used in the servoamplifier to cancel out the 2 lags in the drive train for both Hemmer Compensation and for Conventional Compensation in the outer loop. The required integration with two leads can be handled by a PID network.

The frequency responses to small commands are determined. The transient responses to motion disturbances are also found. The transient responses are verified by non-linear simulations, which show close agreement in spite of the non-linear relationships. This is believed to be caused by the large amount of negative feedback used in the servos.

The performance using the Hemmer Compensated swashplate position controller is superior to that using the Conventional Compensated swashplate position controller because it enables the gain of the outer loop to be raised by a factor of 6.66. The following error for Conventional Compensation is greater than that of the Hemmer Compensated servo by a factor of 6.66. The peak error following a 6,000 b. step disturbance for the full reel is 0.94 in./sec with Hemmer Compensation and 4.53 in./sec. with Conventional Compensation, as found by the simulations, a ratio of 4.82. If the PID network were tuned by trial & error techniques, instead of using the computed gain values, the errors would tend to be greater.

A command filter is used to prevent saturation and its attendant integrator reset windup, thus avoiding a 49% overshoot. It also cuts the response time in half from 0.8 to 0.4 sec. for a 32 in./sec. speed change. GoToTop

Routh’s Stability Criterion

Chapter 15 describes a program that determines the stability of a servo using Routh’s Stability Criterion. This is occasionally used when there are very small damping ratios or there are several unity gain crossover frequencies of the loop transfer function, when other methods, such as root locus, are not sufficiently accurate. It also provides a means for finding the gain margin. GoToTop

Hoist with a Hydrostatic Transmission Drive & Velocity & Position Control Loops:

Chapter 16 describes a drive train with a hydrostatic transmission used to drive a hoist where the cable acts as a spring between the drum and the load. There are 2 servo loops that control velocity and position. The frequency responses are found for each loop. The transient response to command and disturbance inputs are found for both velocity and position control using a simulation program that accounts for non-linearities. This hoist can raise or lower loads of 100 to 11,000 lb. distances up to 100 feet at speeds up to 32 in./sec. with excellent control of speed and position using conventional servo compensation, except for the pump displacement controller. The system is very robust since it can tolorate a wide range of conditions, including a spring rate that varies from 950 to 31,667 lb./in. GoToTop

Elevation Servo for a Robot

Chapter 17 describes a position control servo used for one degree of freedom in a robot used in a vacuum chamber to produce thin film circuits. It is called the elevation servo.

The robot is located in the center of the vacuum chamber. It has an arm with 2 degrees of freedom, rotation and elevation. The moton is controlled by 2 servomechanisms which were designed using the servo design software sold by the Hemmer Engineering Corp.

The robot is used to move substrate and mask pallets between the storage rack and the deposition station and to load the source crucibles with fresh material. Each servo is driven by a 5 watt, 2 phase AC servomotor with a gearhead having speed reductions of 20 and 80, for the elevation and rotation servos, respectively.

The input and early stages of each analog servoamplifier are DC to facilitate the implimentation of the desired servo compensation characteristics, integration plus 1 lead for the elevation servo. These are followed by a polarity sensitive modulator that converts the DC signal to a 60 hz amplitude modulated AC output signal to the AC power amplifier, which supplies the control winding of the servomotor.

The gearhead output shaft is connected to a baseplate feedthrough with a crank inside a metal bellows that seals it off from the vacuum. This is connected to a drive drum for a wire rope inside the vacuum chamber. The wire rope is connected to the load via a driven drum for the rotation servo and through sheaves inside the hollow central column for the elevation servo. It is noted that oil and grease cannot be allowed inside the vacuum chamber because they would contaminate the thin films; unlubricated ball bearings are used extensively to reduce friction acting on moving parts.

The robot motion is shown in a movie that can be accessed from this website

by clicking Robot Video.WMV in the lower right corner of the Contact & Download page.

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