Today’s feedback control systems use digital control techniques and observer software control algorithms to achieve the highest accuracies and quickest moves demanded by today’s builders of automated machines. Controlling the behavior of the mechanism or machine loads usually requires the use of a closed-loop control. Closed-loop servo control requires using a measured (feedback) signal that is compared to an input or command signal. The difference in the command versus the feedback signal is the tracking error signal that is carefully managed toward zero during the system operation. The managed or controlled error signal can be velocity, acceleration, position, current, temperature, pressure or combinations of these and other system parameters.
Our focus is the closed-loop servo system used in a myriad of machines, mechanisms, actuators and automation equipment and in most servo systems, the most important parameter to control is position. The latest developments in non-linear control provides the tools to more closely optimize the motion profile and accurately position the application mechanism loads. A typical servo system is composed of a controller/drive, servo motor, display, needed accessories and option boards for special industrial communication protocols (CANopen, Sercos and DeviceNet).
Over the last few years, YET (Yaskawa Eshed Technology Inc.) developed a new non-linear adaptive control technology (NCT) that improves the servo system’s dynamic precision. The NCT observer control algorithms significantly reduces dynamic position error and shortens final setting times. YET’s easy-to-use auto-tuning methods can enable the servo system to quickly reach the highest performance levels in terms of settling times, stability and low vibration performance. This development is the latest in a long process of using closed-loop control of servo systems across a wide range of applications.
TRADITIONAL ANALYSIS TECHNIQUES
All popular servo systems up until the early 1980s were analyzed using linear models. The servo engineer would analyze the servo system using continuous time-data techniques. These linear servo systems, also called analog servo systems, also used mathematical transformations into the continuous frequency domain for ease of analysis. Transfer functions were also used to relate the system output performance to input command. The relationship of the linear system or input R(s) is compared to the output signal C(s).
(1) C(s)/R(s) = G(s)/(1 + G(s) H(s)) Where G(s) represents the plant (motor, drive, load, etc.), H(s) represents the feedback signal.
The notation employed is a LaPlace transfer function that is used in the analysis of linear servo systems. Other traditional analysis techniques using LaPlace transforms would include Nichols charts, Bode plots and Nyquist diagrams. Direct solutions for stability of the servo system in the time domain enlisted root locus or state variable analysis techniques.
KEY SERVO PERFORMANCE PARAMETERS AND STRUCTURE
There are a number of performance parameters that must be established to ensure stable closed-loop servo operation. They include:
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Stability
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Sensitivity
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Disturbance Rejection
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Transient Response
Stability describes how predictably a system follows a move (motion) command. It is the most important performance characteristic of a closed-loop servo system. The main thrust of these many analyses techniques (e.g. Nyquist, Bode, Root-Locus, etc.) is to evaluate the servo system’s stability. The task of the design engineer is to achieve a sufficient margin of stability.
Sensitivity, or more correctly insensitivity, is the system action to certain types of changes or inaccuracies within a servo system. The use of a digital servo system eliminated many of the problems of parameter drift and noise in linear servo systems. The emergence of both non-linear and adaptive control techniques now allow YET’s NCT control to function as a continuously changing servo control system insensitive to almost all system parameter variations.
Disturbances are undesirable inputs to the servo system other than the command input. These disturbance signals usually represent an abrupt change in inertia or friction from the application loads. Tuning the control laws (loop gains) requires a compromise between command response and stability margins. Using feed-forward signals, usually velocity or acceleration, will also attenuate the disturbance signal.
Transient response measures how quickly a system follows the rapidly changing input command. A key measure of system response is system bandwidth. Increasing system bandwidth increases transient response. The most common technique to improve the system’s response time is to increase the system loop gains. Once again, the optimum solution is a compromise between transient response and stability margin.
LINEAR SERVO SYSTEM
A typical brushless PM servo system would be composed of the controller that develops the motion profile command, a series of position commands versus time. These commands are input into the position then velocity loops. The output of these loops is a torque command that drives the brushless PM motors and controls the sequential switching of the windings. A power stage or amplifier drives the motor.
The current loop controls the motor torque levels based on the desired motion profile and the application mechanical loads (inertia, friction, etc.). The position/velocity feedback device develops the feedback signals sent back to various controller elements to complete the closed-loop servo system. Many block diagrams use plant to describe the servo motor and the applications loads. These linear systems were only approximations of the actual servo systems being used.
DIGITAL SYSTEMS COME OF AGE
The arrival of the inexpensive processor, the personal computer (PC) in the 1980s and later the chip computer (microprocessor) furnished the impetus for the use of digital control systems. The digital servo system eliminates a number of major problems the analog servo systems possess. Foremost is analog drift and noise problems. Something as simple as an increase in motor winding resistance due to rising motor temperature is an example of analog drift. Accuracy is often improved dramatically with digital servo systems. Tuning the motor inertial loads to the application loads is simplified. The primary weakness of a digital servo system is increased time delay caused by the sampling delay.
The digital servo system employs new system components and new analysis tools. We live in an analog world. Whenever a digital microprocessor or a digital signal processor (DSP) is used, the analog inputs and outputs must be converted from analog to digital form by analog-to-digital (A/D) converters. Once the control processing is done, the output is converted back to analog signals by a digital-to-analog (D/A) converter. The various arithmetic functions or control laws implemented in hardware in analog systems can be accomplished using stored software programs. This hardware-software trade-off continues today with observer models. Various loop gains can be easily changed as the application loads change over time. Adaptive algorithms can automatically change loop gains as the systems load conditions change.
The “z” transform plays much the same role in describing discrete time signals as the LaPlace “s” transform does for continuous time signals. The digital servo system analysis can be performed by using a set of difference model equations and solving them numerically or modeling the system using z transforms as a transfer function or employing a set of first order coupled difference equations (Luenberger model).
Once again, the system analysis evaluates the system transient response, stability, sensitivity, etc. Much of the analytical processes briefly discussed for state variable analysis under linear servo systems is also directly applicable to digital systems. Filters are devices added to the servo system to reduce noise in the systems. A low- pass filter is often used with derivative control (KD) to reduce noise. Notch filters are also used in many cases to attenuate a narrow band of servo system frequencies for stability reasons.
FEED-FORWARD
Feed-forward techniques are used to improve the linear systems transient response. Velocity feed-forward and/or acceleration feed-forward are common signals placed ahead of the typical position error signal without impacting the servo gains and without agitating the stability margin. The servo systems transient response is significantly improved using feed-forward techniques. Feed-forward signals can reduce position error drastically but suffer from susceptibility to changing machine characteristics. It may have to be retuned several times during machine operation to achieve satisfactory low overshoot and low settling time.
PID CONTROL LAW
PID loop control laws have been in use for more than 40 years, initially in linear control systems and more recently in digital control systems.
The linear continuous and the digital PID control law equations are shown below:
(2) M(s) = (Kp + KDs + KI/s) E(s)
Where Kp = proportional gain
M(s) = input (LaPlace transform)
Kt = integral gain
E(s) = output (LaPlace transform)
KD = derivative gain
(3) M(z) = [Kp + KD ((z-1)Tz)) +(KITZ/Z-1)] E(z)
Where M(z) = input (z transform)
KP = proportional gain
E(z) = output (z transform)
KD = derivative gain
T(z) = sample period
KI = integral gain
Note how similar in structure the PID control for analog servo (s) systems is with respect to digital servo (z) systems. The PID controller algorithm or control law involves three separate parameters; proportional, integral and derivative. The proportional term determines the reaction to the most recent error, the integral term determines the reaction based on the sum of most recent errors. The derivative term determines the system reaction to the rate of change of error. Using PID controllers in motion control systems requires the use of properly scaled velocity or acceleration feed-forward signals in order to achieve a more responsive control system.
PID controllers work best in linear control systems. Performance of PID controllers in non-linear systems is variable and requires special control methods such as fuzzy logic, phase plane or gain scheduling, among others.
NON-LINEAR SYSTEMS
All servo systems used in our physical world are non-linear to a greater or lesser extent. Control design techniques for non-linear servo systems do exist. They can be subdivided into techniques that attempt to treat the system as a linear servo system within a limited operating range. Gain scheduling assumes non-linear time invariant behavior can be predicted (measured or modeled) to reasonable accuracy. Non-linear system behavior includes motor winding inductance effects, load inertia variations, friction, etc.
The YET servo drive uses a new non-linear adaptive servo control scheme. YET’s NCT position control technology simultaneously reduces position error and the system settling error. It uses specially designed adaptive non-linear software control algorithms to provide stable motion and smooth control. The NCT control integrates the position and velocity control loops into one powerful control loop with four branches. The four loops provide PID control functions plus a KIV term that combines both integral and velocity commands in order to respond to the disturbances more quickly and accurately. The IP function represents a special integration and compensation function that is specifically designed to avoid system overshoot when the servo is transitioning from deceleration to final positioning. This control law is responsible for very short setting times.
The G functions are the key to the adaptive non-linear control laws. They adjust their values as a function of the dynamic conditions of the system. The independently variable G functions will significantly increase the control law gain by as much as a factor of 10 times that achieved by conventional servo systems. Both systems’ stability and fast response over a wide speed range are achieved with YET’s NCT non-linear control. Controlling the smoothness of velocity of a servo motor over a long time period at very low speeds (less than 2 rpm) is achievable with the NCT control. A comparison of the servo system’s command velocity versus tracking (position) error shows the NCT technology reduces the tracking error to about 2 percent of the conventional systems’ response over the entire motion profile. The triangular velocity versus time command is the most difficult move to control and is the fastest way for moving from one position to another.
The application involved a THK lead screw with 20-mm pitch with a 2-Kg (4.4-lb) load. It was mechanically coupled to a 200W Yaskawa brushless PM Sigma II servo motor. A 13 bit (8,192 counts per rev) optical encoder was used and a command movement of one turn. The settling error was less than two encoder pulses. The NCT technology can closely control the motion without initiating any system resonances, velocity or position overshoots at final position. It virtually eliminates non-linear hysteresis and deadband effects common between PWM voltage output and the command voltage. Other important features include a number of easy-to-use motor-application load-tuning strategies.
LOOKING AHEAD
The servo control system has come a long way in the past 65 years. Faster throughput and more accurate performance are the two major driving forces in motion control systems. Faster machine throughput allows the user to create more products over time. A more accurate performance currently represented by the YET-NCT technology, provides the user with new opportunities to use more precise and faster responding servo systems. Miniaturization of many industrial and consumer products require more accurate servo-controlled machines, mechanism and actuators. Using more control software with more accurate algorithms and replacing the hardware versions of today’s feedback devices will continue to evolve over the next decade. The next generation of precision machines using servo systems may push adaptation and response to a new level.
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