The concept of bandwidth isn’t just something that communications engineers need to worry about. Bandwidth is also a fundamental concept in industrial servo systems. The speed at which a servo system responds to commands is determined by the servo bandwidth.
For motion control systems requiring high accuracy and responsiveness, this is vital information to know.
In this article, we’ll discuss the concept of servo bandwidth, the technical aspects, and the role it plays in modern control engineering.
What Is Servo Bandwidth?
Servo bandwidth measures how fast a servo system can accurately follow a changing input.
The term “tracking” refers to how well a servo system follows a desired input signal. If a system is tracking properly, its output closely matches the input in both amplitude and phase, meaning the system accurately follows commanded movements or positions.
There are two key technical definitions relevant to servo bandwidth:
- Tracking Performance (90% Amplitude): A system is considered to be tracking if its output reaches at least 90% of the input amplitude, meaning less than 10% error. This is a practical measure of how well the system follows signals in real-world use.
- Bandwidth Limit (-3 dB Point, 70.7% Amplitude): A more formal bandwidth definition is the frequency where the closed-loop response drops by -3 dB, reducing output amplitude to 70.7% of the input. At this point, power to the load is halved, marking where high-frequency tracking starts to degrade.
- Bandwidth depends on loop gain, which comes from the combined response of the plant, sensor, motor, drive, and controller. These elements determine how quickly and accurately the system reacts to input changes.
What is Servo Bandwidth in Simple Terms?
Let’s use an analogy.
Imagine driving a car between traffic cones on a test track. The faster the cones come (higher frequency), the quicker you need to steer to avoid the cones. If your car accurately avoids every cone, your steering response is tight and has a high bandwidth. But if your steering wheel is a little bit loose, there is a delay, the steering response becomes sluggish, and you start hitting cones: this is low bandwidth, meaning the system can’t keep up.
Now, think of amplitude as how sharply you turn the wheel.
At 90% amplitude, you’re still accurately avoiding the cones (less than 10% error).
At the -3 dB point (70.7% amplitude), your response weakens—you’re understeering and struggling to keep up.
A servo system works the same way: higher bandwidth means better, faster tracking of input changes.
What is The Importance of Bandwidth in Servo Systems?
Below we will discuss the importance and the influence of bandwidth on system performance, focusing on frequency response, control loop gains, and the implications of high bandwidth.
Frequency Response and Stability
In servo systems, bandwidth is a key aspect of frequency response, and the two concepts are closely related. Frequency response describes how well a system can follow input signals across a range of frequencies, while bandwidth specifically refers to the upper limit of that frequency range where the system can still respond accurately.
By analyzing amplitude and phase response, we can determine how responsive and stable the system is across different frequency ranges.
Factors Affecting Servo Bandwidth
Servo bandwidth is influenced by several factors. Mechanical characteristics like inertia, friction, and gear ratio affect response speed, with higher inertia or friction reducing bandwidth.
Motor specifications (AC vs. DC), power, and torque impact performance. AC motors are more efficient, while DC motors have lower bandwidth potential. Control system design, including feedback mechanisms (encoders, resolvers) and controllers (PID or digital), affects precision.
How is Servo Bandwidth Related to Control Loops in a Servo System?
Servo bandwidth is intimately connected to the control loops in a servo system, including current, velocity, and position loops.
Each loop is responsible for specific functions that contribute to the overall performance, stability, and responsiveness of the system.
The bandwidth of these loops dictates the speed and precision with which the system can adapt to command changes and external disturbances.
- Control Loop Hierarchy: Servo systems often use a cascade of control loops, where each loop (current, velocity, and position) focuses on a particular aspect of servo control. The bandwidth of each loop varies based on its role in the hierarchy. The current control loop, being the innermost, has the highest bandwidth to enable rapid and precise responses. Next is the velocity control loop, followed by the position control loop, which has the lowest bandwidth.
- Speed and Precision of Response: The bandwidth of a control loop directly influences how quickly and accurately it can respond to changes in its designated command (current, velocity, or position). A higher bandwidth allows the control loop to react more swiftly to input changes, enhancing system performance.
- Stability and Performance of the System: The interplay between the bandwidths of these control loops is crucial for maintaining system stability and achieving optimal performance. Each loop must be finely tuned to handle its specific demands without causing instability in other parts of the system.
- Collaborative Operation: These loops function in a coordinated manner, building on the performance of the previous loop. The rapid response of the current control loop supports the velocity control loop in managing motor speed effectively, which then enables the position control loop to control the motor’s position accurately.
Now, let’s get into a bit more detail on the three main types of control loops: current, velocity, and position.
Cascaded Control Loops
Cascaded control loops in servo systems consist of nested loops, each controlling a specific parameter with its own bandwidth. These loops work together to manage current, velocity, and position, ensuring accurate and stable control. Each loop is optimized for its specific task, from rapid current adjustments to precise positioning.
Current Loop
The current loop controls the motor’s torque by regulating current.
High bandwidth enables quick adjustments to meet changing current demands, ensuring the motor generates precise torque for fast responses to inputs and disturbances.
- Function: Manages the current supplied to the motor to ensure accurate torque production.
- Importance: Rapid current adjustments are crucial for maintaining torque accuracy and swiftly responding to command changes and disturbances.
- Bandwidth: Generally the highest among the control loops to facilitate quick and precise current control.
Velocity Loop
The velocity loop, situated in the middle of the cascaded control structure, features a moderate bandwidth. It ensures the motor adheres to the commanded velocity profile accurately. This loop adjusts the torque produced by the current loop to maintain the desired speed.
- Function: The velocity loop regulates motor speed to follow the given velocity command, ensuring the motor runs smoothly and efficiently.
- Importance: It is crucial for smooth and accurate speed control, compensating for load disturbances and inertia to maintain consistent performance.
- Bandwidth: The bandwidth here is lower than that of the current loop but high enough to handle dynamic speed changes without causing instability. This balance is essential to maintain desired performance while avoiding oscillations.
Position Loop
The position loop is the outermost loop with the lowest bandwidth. It controls precise motor or load positioning. It uses input from the velocity loop to adjust the motor position, ensuring the load’s final position is accurate and consistent with the input command.
- Function: The position loop manages the motor or load position to match the commanded position, ensuring accuracy and consistency.
- Importance: It provides precise positioning, correcting positional errors to achieve the desired outcome, essential for applications requiring high positional accuracy.
- Bandwidth: This loop’s bandwidth is the lowest among the control loops, adequate for controlling slower and less frequent positional changes compared to current and velocity adjustments.
How Is Servo Bandwidth Measured?
Servo bandwidth is typically measured in Hertz (Hz) or radians per second (rad/sec).
Measuring servo bandwidth involves several techniques to determine the system’s frequency response and ability to track input commands accurately – sinusoidal input test, bode plot analysis, and closed-loop transfer function analysis
Measurement of Servo Bandwidth
Standard servo systems have bandwidths below 15 Hz, with larger systems around 1–2 Hz. Direct-drive systems have pushed bandwidths up to 50 Hz. Torque motors and high-sensitivity sensors, introduced in the 1970s, improve accuracy and reduce backlash, benefiting applications like missiles and satellites.
Here are several methods for measuring servo bandwidth:
Sinusoidal Input Test
- Test Procedure: Apply a low-frequency sinusoidal signal, then increase frequency gradually.
- Data Collection: Record output amplitude and compare it to input.
- Bandwidth Determination: Identify the frequency where output drops to 70.7% of input amplitude (-3 dB).
- Test Benefits: Provides an intuitive way to measure frequency response and performance.
Bode Plot Analysis
- Test Procedure: Apply a range of frequencies and record amplitude and phase responses.
- Data Collection: Identify the -3 dB point where output is 70.7% of input amplitude.
- Bandwidth Determination: Assess phase margin for stability.
- Test Benefits: Offers detailed insights into system response, helping identify stability issues.
Closed-Loop Transfer Function
- Test Procedure: Analyze the input-output relationship of the closed-loop system in the frequency domain.
- Data Collection: Measure or model the system’s response to determine bandwidth.
- Bandwidth Determination: Identify the -3 dB point for bandwidth measurement.
- Test Benefits: Provides an accurate measure of system dynamics and stability.
Now that we know what servo bandwidth and its function is it’s time to discuss how it is connected to motor sizing and power dissipation in a servo system.
What is the Relationship Between Bandwidth, Motor Sizing, and Power Dissipation?
Servo bandwidth, motor size, and power dissipation are closely linked. Higher bandwidth demands faster motor response, leading to greater accelerations and increased power dissipation, which challenges thermal management.
Balancing these factors ensures optimal servo performance and longevity.
Bandwidth and Loop Gain
A critical aspect of adjusting servo bandwidth is managing the loop gain of the control system.
Higher bandwidth requires higher loop gain, but this comes with trade-offs related to system stability.
Achieving higher servo bandwidth involves increasing the loop gain of the control system.
Higher loop gain results in greater system responsiveness but requires careful tuning to avoid instability.
Stability Constraints
The maximum achievable bandwidth is limited by stability factors such as phase margin and gain margin.
Phase margin ensures stability at the desired bandwidth frequency, while gain margin prevents oscillations when the phase reaches -180 degrees.
- Phase Margin: This measures how far the system is from instability in terms of phase lag, ensuring that the system can handle changes in the control signal without becoming unstable. A sufficient phase margin is crucial for stable operation, especially at higher bandwidths.
- Gain Margin: This margin indicates how much gain can be increased before the system becomes unstable. Adequate gain margin is essential to prevent oscillations and ensure stable performance.
Power Dissipation
Higher bandwidth demands faster accelerations from the motor, increasing forces and power dissipation, which presents thermal challenges.
- Increased Forces: Higher bandwidth requires the motor to exert greater forces for faster responses. This results in higher current consumption and more heat dissipation as the motor constantly adjusts to input changes. The more frequently the motor accelerates or decelerates, the more energy is lost as heat.
- Thermal Limits: The motor’s thermal capacity limits the achievable bandwidth. Excessive heat from faster responses can lead to thermal runaway, worsening inefficiency and overheating if not properly cooled. Adequate cooling is essential to prevent this and maintain stable performance.
Motor Sizing
Motor sizing is influenced not only by load requirements but also by the need to manage power dissipation and thermal capacity. Motors with higher thermal capacity (indicated by higher Km values) can handle the heat generated during high bandwidth operations without overheating.
- Thermal Capacity: Motors designed with higher thermal capacities can dissipate more heat, allowing for higher bandwidth operations.
- Sizing Considerations: Proper motor sizing involves selecting motors that can handle the thermal load imposed by higher bandwidths, ensuring reliable and efficient performance.
If the motor is too large, it reduces bandwidth and efficiency. If it’s too small, it can cause excessive power dissipation and risk failure. An undersized motor runs at maximum current, generating excess heat that stresses the windings, potentially leading to thermal overload and reduced motor life.
What is a High Bandwidth Servo System?
A high bandwidth servo system is designed to respond quickly to changes in input commands and disturbances.
This responsiveness is achieved by having a high-frequency response in the control loops, especially in the current, velocity, and position loops.
Key characteristics that define a high bandwidth servo system include;
- High Responsiveness: A high bandwidth servo system can swiftly adjust to changes in input commands, ensuring precise control over position, velocity, and torque. This quick adaptation is crucial for applications requiring rapid and accurate movements.
- Fast Settling Time: These systems reduce the time needed to reach the desired position or speed, enhancing overall performance. Faster settling times mean that the system can quickly stabilize after a command change, improving efficiency.
- Effective Disturbance Rejection: High bandwidth servo systems can handle high-frequency disturbances, maintaining stability and accuracy even under varying load conditions. This capability ensures consistent performance despite external disturbances.
- Increased Power Dissipation: Higher bandwidth necessitates greater motor forces and accelerations, which lead to increased thermal loads and power dissipation. Managing this heat is essential to prevent overheating and maintain system reliability.
What is a Low Bandwidth Servo System?
A low bandwidth servo system is tailored for applications where rapid response to input changes and disturbances is less critical. In these systems, control gains are set to lower values, resulting in a reduced frequency response.
This makes them suitable for applications that require stable and steady control rather than fast and dynamic performance. Some key factors to look out for include:
- Lower Responsiveness: Low bandwidth servo systems are slower to adjust to changes in input commands. This slower response can be beneficial in applications where minimizing overshoot and oscillations is important.
- Longer Settling Time: These systems take more time to reach the desired position or speed, which is acceptable in scenarios where high-speed performance is not a priority. This characteristic is suitable for applications where precision is more important than speed.
- Limited Disturbance Rejection: Low bandwidth systems are less effective at handling high-frequency disturbances. However, they are adequate for applications with relatively stable and predictable load conditions.
- Reduced Power Dissipation: Lower bandwidth results in lower motor forces and accelerations, reducing thermal loads and power dissipation. This characteristic makes low bandwidth systems more energy-efficient and easier to manage thermally.
How to Choose Between High and Low Bandwidth?
Choosing the right bandwidth for a servo system involves evaluating several factors that affect performance, stability, and thermal management.
Below are the key considerations to help you decide between high and low bandwidth for your application.
Application Requirements
- Speed and Precision: For applications that need rapid response and high precision, such as robotics, CNC machining, and semiconductor manufacturing, high bandwidth is required. These systems must respond quickly to control signals and maintain precise movements.
- Stability and Smoothness: Low bandwidth is better suited for applications where smooth and stable operation is more important than speed, such as conveyor systems and material handling. These applications benefit from slower, more controlled movements.
Load Characteristics
- Dynamic Loads: High bandwidth systems are ideal for applications with rapidly changing loads. They can adjust quickly to maintain control accuracy and stability, ensuring performance isn’t compromised by sudden changes.
- Stable Loads: For applications with consistent and predictable loads, low bandwidth is sufficient. These systems can control the load effectively without the need for rapid adjustments, making them more stable and easier to manage.
Disturbance Rejection
- High-Frequency Disturbances: High bandwidth systems excel at rejecting high-frequency disturbances. This ability helps maintain accuracy and stability in environments with frequent or unpredictable changes.
- Low-Frequency Disturbances: Low bandwidth systems are adequate in environments with minimal high-frequency disturbances. They provide stable control without the need for rapid responses, suitable for more predictable settings.
Thermal Management
- Power Dissipation: High bandwidth systems generate more heat due to increased motor forces and accelerations. Proper cooling and thermal management solutions are necessary to prevent overheating and maintain performance.
- Thermal Constraints: If thermal management is a concern, low bandwidth systems might be preferable. They produce less heat, reducing the need for extensive cooling solutions and making them easier to manage thermally.
System Stability
- Phase and Gain Margins: High bandwidth systems require careful tuning of control gains to maintain stability. Ensuring adequate phase and gain margins is essential to prevent oscillations and instability.
- Simplicity and Robustness: Low bandwidth systems are generally easier to tune and maintain. They offer robust performance with less risk of instability, making them suitable for applications where simplicity is valued.
Cost and Complexity
- High Bandwidth Systems: These systems are typically more complex and expensive. They require advanced control algorithms, high-performance motors, and cooling systems to manage the increased thermal loads.
- Low Bandwidth Systems: Low bandwidth systems are simpler and more cost-effective. They are suitable for budget-conscious applications where high-speed performance is not essential, providing reliable control at a lower cost.
Conclusion
Optimizing the speed of your servo bandwidth isn’t a hard task, you just need to enhance and adjust the system setup, loop gains, and feedback loops.
To get the highest performance of a servo system, ensure it has the highest bandwidth and highest control loop gains. Also, by ensuring proper calibration, using high-quality components, and minimizing noise, you can achieve significant improvements in system performance.
