Table of Contents:
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.
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
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
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,
Gcl , are listed beneath Table 1 and the frequency response for Gcl is listed in Table 3 for comparison with the actual response in Table 2. The Gcl 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
Gcl 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
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
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
A brief review of the Bode Plot Technique for servo analysis is presented in Chapter 6.
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
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
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
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