An AC servo motor is a type of induction motor with a stator and rotor. Its mathematical model features a transfer function that connects input to output in a control system. Key elements include dynamic load, encoder pulses, and control methods like fuzzy logic, which are vital for precise modeling and trajectory tracking.
Performance characteristics of AC servo motors, such as precision, stability, and responsiveness, hinge on accurate mathematical modeling. High precision in control is vital for applications requiring exact movement, such as robotics or CNC machinery. The mathematical model allows engineers to simulate and predict motor behavior under various conditions, ensuring optimal performance.
Applications of AC servo motors are diverse and include robotics, automation systems, and aerospace. Knowledge of the mathematical model helps in selecting the right motor for specific applications and enhances design processes.
In the following section, we will explore the practical implementations of AC servo motors in various industries. Understanding their mathematical foundations will provide deeper insights into their effectiveness and efficiency in real-world scenarios.
What Is the AC Servo Motor Mathematical Model and Why Is It Important?
The AC servo motor mathematical model represents the dynamic behavior and control mechanisms of an AC servo motor system. It includes equations that define the relationships between voltage, current, torque, speed, and position. This model is crucial for understanding motor performance and developing efficient control strategies.
According to the IEEE Control Systems Society, the mathematical modeling of AC servo motors allows for precise control in applications such as robotics and automation. Accurate modeling aids in predicting system responses and optimizing performance.
The AC servo motor model typically comprises differential equations that encapsulate electromagnetic relations and mechanical dynamics. These equations help in analyzing system stability, response time, and overall efficiency. Key aspects include feedback control loops and error correction, which are integral for maintaining desired performance levels.
The National Institute of Standards and Technology (NIST) defines AC servo motors as high-performance electromechanical devices that utilize feedback for precise positioning and speed control. This definition emphasizes the role of control theory in effective motor management.
Factors influencing the AC servo motor model include operating conditions, load characteristics, and system configuration. Variations in these parameters can significantly affect performance outcomes, necessitating accurate modeling for various applications.
According to a study by Grand View Research, the global AC servo motor market was valued at $9.2 billion in 2021 and is projected to grow at a CAGR of 6.5% through 2028, indicating increasing demand for precision applications.
The importance of modeling AC servo motors extends beyond technical fields; it impacts sectors like manufacturing and healthcare by enhancing efficiency and precision in product delivery and equipment operation.
The advancement of AC servo motor technology can affect economic growth by improving productivity in industries reliant on automation. The shift towards smart manufacturing and robotics can create new jobs and enhance operational efficiency.
To address challenges in AC servo systems, experts recommend adopting advanced control algorithms, hybrid solutions, and real-time monitoring systems. Integrating Artificial Intelligence (AI) with servo systems can optimize decision-making and improve performance reliability.
Implementing strategies such as regular maintenance, system upgrades, and incorporating predictive analytics can mitigate issues related to performance instability. Experts from the International Electrotechnical Commission (IEC) highlight the importance of these practices for improving motor lifespan and operational efficiency.
What Are the Key Components of the AC Servo Motor Mathematical Model?
The key components of the AC servo motor mathematical model include the electrical model, mechanical model, state equations, and control input.
- Electrical Model
- Mechanical Model
- State Equations
- Control Input
To understand these components in detail, let’s explore each one and highlight its significance.
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Electrical Model: The electrical model of the AC servo motor represents the relationship between voltage, current, and back electromotive force (EMF). This model includes parameters such as resistance (R), inductance (L), and phase angle (φ). The back EMF opposes the applied voltage, affecting motor performance. According to a study by H. Woo (2019), accurate modeling of these electrical characteristics is essential for enhancing power efficiency and response time in control applications.
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Mechanical Model: The mechanical model describes the dynamics of the motor’s rotor and load. It incorporates parameters like moment of inertia (J), damping ratio (B), and torque (T). These elements define how the motor responds to applied torques and changes in load. Research by Tanaka et al. (2020) emphasizes that understanding these parameters aids in designing effective control algorithms that improve system stability and performance.
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State Equations: State equations are mathematical representations that describe the motor’s behavior over time. These equations relate various state variables, such as speed and position, to the input control signals. They form the basis for designing control strategies like proportional-integral-derivative (PID) controllers. A comprehensive study by Lee and Son (2018) shows that proper formulation of state equations leads to more predictable motor behavior in robotic applications.
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Control Input: Control input refers to the signals sent by the controller to command motor operation. This component can include parameters such as desired position, speed, or torque references. Effective control inputs are crucial for achieving desired performance and can significantly enhance system responsiveness. According to research by Zhang et al. (2021), advanced control strategies, like model predictive control, yield better tracking performance and adaptability to changing conditions.
By understanding these components, engineers can design and implement effective AC servo motor systems. This understanding is vital for various applications, including robotics, automation, and precision manufacturing.
How Does Stator Current Influence the Mathematical Model?
Stator current significantly influences the mathematical model of motor operations. The stator current represents the electrical current flowing through the stator windings. This current affects the electromagnetic torque produced by the motor. Torque is a critical factor in determining the motor’s performance.
In the mathematical model, the stator current influences various parameters. First, it contributes to the generation of a magnetic field. This magnetic field interacts with the rotor, resulting in motion. The strength of the magnetic field depends directly on the magnitude of the stator current.
Next, the stator current affects the voltage equations within the motor model. These equations depict how voltage and current interact to produce torque and speed. Higher stator current results in greater torque, enabling the motor to handle larger loads.
Moreover, stator current impacts the efficiency of the motor. The relationship between current, resistance, and power loss must be considered. Excess current leads to increased heat generation, which can detract from efficiency.
Finally, understanding stator current is crucial for control strategies. Accurate modeling allows for better regulation of motor performance. It guides the design of control systems to optimize torque and speed in response to varying loads.
In summary, the stator current plays a pivotal role in the mathematical model of AC servo motors by influencing torque generation, voltage equations, efficiency, and control strategies.
What Role Does Rotor Position Play in AC Servo Motor Performance?
The rotor position plays a crucial role in the performance of AC servo motors. It directly influences the motor’s precision, speed control, and overall efficiency.
The main points regarding the role of rotor position in AC servo motor performance include:
1. Feedback Mechanism
2. Position Control Accuracy
3. Torque Generation
4. Speed Regulation
5. Response Time
The importance of rotor position extends beyond basic functioning, as various factors contribute to its impact on performance.
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Feedback Mechanism:
The rotor position serves as a feedback mechanism in AC servo motors. It enables the motor controller to monitor and adjust the motor’s operations accurately. This feedback is essential for closed-loop control systems, which utilize sensors such as encoders to track the rotor position continuously. -
Position Control Accuracy:
Position control accuracy hinges on rotor position. Precision in determining where the rotor is at any given moment allows for accurate movements and positioning. For example, in robotic applications, precise rotor positioning allows for the accurate execution of tasks, improving operational efficiency. -
Torque Generation:
The relationship between rotor position and torque generation is significant. The motor generates maximum torque when the rotor aligns optimally with the stator’s magnetic fields. Misalignment can lead to reduced torque output, affecting overall motor performance. -
Speed Regulation:
Speed regulation is influenced by rotor position, as it allows for adjustments in response to changing loads. The controller relies on real-time position data to modulate speed, ensuring consistent performance. A well-timed response enhances operational stability. -
Response Time:
The rotor position impacts the motor’s response time to commands. Fast and accurate position sensing allows for quicker adjustments to speed and direction. Studies have shown that improved response times lead to enhanced performance in dynamic applications, such as CNC machines.
Understanding the significance of rotor position in AC servo motors is vital for applications that require high performance and precision. The benefits that arise from accurate rotor positioning include improved efficiency, reliability, and operational effectiveness in various industrial and technological settings.
Which Governing Equations Define the AC Servo Motor Mathematical Model?
The governing equations that define the AC servo motor mathematical model encompass several key aspects of its operation.
- Voltage Equations
- Current Equations
- Torque Equations
- Speed Control Equations
- Position Control Equations
These equations illustrate the complex dynamics of AC servo motors and can vary based on different design philosophies and application requirements.
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Voltage Equations:
Voltage equations in an AC servo motor describe the relationships between voltage, current, and impedance. Typically, these equations follow Kirchhoff’s voltage law. The equation can be expressed as ( V = I \cdot Z ), where ( V ) is the applied voltage, ( I ) is the current, and ( Z ) is the impedance of the motor. Understanding this relationship allows engineers to design drives that efficiently control motor performance. -
Current Equations:
Current equations model how current flows through the motor windings based on the applied voltage and the impedance. The formula often used is ( I = \fracVZ ), where ( I ) represents the current. This equation highlights the need for controlling current to achieve desired motor torque and speed, as demonstrated in various industry applications. -
Torque Equations:
Torque equations govern the mechanical output of an AC servo motor. The torque generated by the motor is proportional to the current flowing through the windings. The equation ( T = K \cdot I ) exemplifies this, where ( T ) is the torque, ( I ) is the motor current, and ( K ) is a sensitivity constant related to the motor’s construction. This relationship is vital in applications requiring precise motion control. -
Speed Control Equations:
Speed control equations define how the rotation speed of the servo motor is regulated. These equations often use feedback loops, where the target speed is compared against measured speed to adjust motor inputs. Commonly, the speed can be controlled via pulse width modulation (PWM), enabling precise adjustments in real-time, a necessity in robotics and automation systems. -
Position Control Equations:
Position control equations break down how the motor adjusts its position based on error signals. Typically, these equations work in conjunction with a control algorithm like PID (proportional, integral, derivative) control. Position is managed by tracking differences between desired and actual positions, ensuring accurate movement in servo applications, prominently seen in CNC machinery.
These governing equations enable engineers to model and control AC servo motors effectively. Understanding how voltages, currents, torque, speed, and position interrelate is critical for optimizing servo motor performance across diverse applications.
What Is the Importance of Electrical Equations in the Model?
Electrical equations play a crucial role in modeling electrical systems. They represent the relationships between voltage, current, resistance, and other electrical parameters in a mathematical form. This representation allows for accurate predictions and analysis of electrical behavior.
The Institute of Electrical and Electronics Engineers (IEEE) provides comprehensive guidelines on the importance of electrical equations in circuit analysis and design. Their standards emphasize how these equations underpin the functionality and efficiency of electric systems.
These equations encompass Ohm’s Law, Kirchhoff’s Laws, and other fundamental principles. Ohm’s Law states that voltage equals current multiplied by resistance. Kirchhoff’s Laws illustrate the conservation of charge and energy in circuits, ensuring that all interconnected elements operate within specified parameters.
Additional definitions can be found in textbooks like “Electrical Engineering: Principles and Applications” by Allan R. Hambley. This source outlines how these equations can help troubleshoot issues and improve system design.
Various factors contribute to the electricity equations’ importance. These include increasing energy demands, complexity in electrical systems, and the growing integration of renewable energy sources.
According to the U.S. Energy Information Administration, electricity consumption will rise by 26% from 2020 to 2050. This growth underscores the need for precise modeling to enhance efficiency and reliability in energy distribution.
Electrical equations significantly affect energy efficiency, safety, and technological advancement in electrical engineering. They guide design choices that minimize losses and enhance user safety.
These impacts extend to health, as efficient electrical systems reduce fire risks, and environmental sustainability, as optimized energy usage lowers greenhouse gas emissions.
For example, leveraging accurate electrical equations can minimize energy waste in smart grids, leading to reduced operational costs and enhanced reliability.
To address challenges, the International Electrotechnical Commission recommends the continuous education of engineers in complex electrical modeling and simulation. Emphasizing standardized practices promotes safety and sustainability.
Specific strategies include using advanced simulation tools, like finite element analysis software, and implementing rigorous testing procedures to ensure compliance with standards. These approaches can help mitigate potential inefficiencies in electrical systems.
How Do Mechanical Equations Affect AC Servo Motor Functionality?
Mechanical equations significantly impact AC servo motor functionality by determining the motor’s performance characteristics, influence on control systems, and overall efficiency.
The relationship between mechanical equations and AC servo motors can be broken down as follows:
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Torque Equations: Mechanical equations calculate the torque generated by the motor. For instance, the torque can be derived from the equation ( T = K_t \cdot I ), where ( T ) is torque, ( K_t ) is the torque constant, and ( I ) is current. Higher torque values indicate better motor performance, enabling it to handle various loads effectively.
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Speed Control: Mechanical equations also define the relationship between speed and applied voltage. The equation ( \omega = \fracV_supply – V_backR ) illustrates that motor speed depends on supply voltage and back electromotive force (EMF). Proper control of these parameters ensures accurate speed regulation, which is crucial for applications like robotics and CNC machines.
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Inertia Considerations: The motor’s mechanical equations include the inertia of connected loads. The equation ( J_total = J_motor + J_load ) helps in understanding how the total inertia affects acceleration and deceleration times. A mismatched inertia can lead to slow response times or overshooting, affecting overall system stability.
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Damping Effects: These equations also account for damping, represented by the term ( b ) in the dynamic model. Damping influences how quickly a motor stops or changes direction. Accurate modeling through these equations ensures that the motor behaves predictably in various applications.
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Mechanical Resonance: Equations can help identify resonance frequencies in the system. Operating at these frequencies can cause vibrations and interfere with the motor’s operation. Understanding this through mechanical modeling allows engineers to design systems that avoid these conditions.
In summary, mechanical equations are essential for the proper functioning of AC servo motors. They define performance characteristics, enable effective control, influence response times, and ensure smooth operation across applications. By precisely addressing these factors, engineers can optimize motor designs for improved efficiency and reliability.
What Factors Are Critical for Evaluating AC Servo Motor Performance?
Evaluating AC servo motor performance involves several critical factors. These factors ensure the efficiency, reliability, and effectiveness of the motor in various applications.
- Efficiency
- Torque
- Speed
- Control accuracy
- Thermal performance
- Response time
- Load capacity
- Noise level
- Life cycle and maintenance
- Cost
The importance of these factors can vary based on specific applications and user requirements. Some users prioritize efficiency and torque, while others may focus on speed and control accuracy.
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Efficiency:
Efficiency measures how well the AC servo motor converts electrical energy into mechanical energy. It is a critical factor because higher efficiency reduces operational costs. According to the Department of Energy, energy-efficient motors can reduce energy consumption by 2-8%. For example, in industrial settings, selecting a high-efficiency motor can lead to significant savings over time. -
Torque:
Torque is the rotational force produced by the motor. It is essential for determining the motor’s ability to perform specific tasks. Higher torque enables the motor to lift or move heavier loads efficiently. For instance, a servo motor in a robotic arm needs adequate torque to manipulate objects without strain. -
Speed:
Speed indicates how fast the motor can rotate. This factor is crucial in applications requiring quick responses, such as CNC machines. According to a 2022 study by Chang et al., optimizing motor speed can increase productivity by up to 20% in automated processes. -
Control accuracy:
Control accuracy refers to the motor’s ability to reach and maintain a precise position. This factor is vital in applications such as CNC machining, where precise movements are necessary. A study by Lee and Kim (2021) found that motors with high control accuracy reduced error rates in machining by over 30%. -
Thermal performance:
Thermal performance is the motor’s ability to dissipate heat during operation. Excessive heat can lead to motor failure or reduced lifespan. Efficient cooling systems can enhance thermal performance, ensuring the motor operates reliably. The National Institute of Standards and Technology recommends monitoring thermal performance to prevent overheating in continuous operations. -
Response time:
Response time measures how quickly the motor reacts to control signals. Faster response times improve the system’s overall performance, particularly in dynamic applications. For example, in robotic systems, faster response can enhance precision in tasks like assembly or welding. -
Load capacity:
Load capacity indicates how much weight or force the motor can handle. This factor is essential for applications requiring consistent performance under varying loads. Engineers often select motors based on load capacity to ensure the selected motor can handle operational demands without failure. -
Noise level:
Noise level is the sound produced by the motor during operation. Lower noise is essential in environments where sound pollution must be minimized. For example, in medical devices, quieter motors are preferred to ensure patient comfort. -
Life cycle and maintenance:
The life cycle of an AC servo motor refers to its operational longevity. Regular maintenance outcomes, like lubrication and inspections, affect this factor. Motors designed for easy maintenance typically have longer lifespans and reduced downtime. -
Cost:
Cost is a fundamental consideration in motor selection. While high-performance motors may have higher initial costs, they often result in lower operational and maintenance expenses. A cost-benefit analysis can help determine the best motor for specific applications by balancing initial investment with long-term savings.
How Does Torque Generation Influence Operational Efficiency?
Torque generation influences operational efficiency significantly. Torque is the rotational force that drives machinery and equipment. Higher torque allows a system to perform work effectively by overcoming resistance. When a machine generates appropriate torque, it operates smoothly and effectively, leading to increased productivity.
Operational efficiency depends on how well a system converts input energy into useful output. Efficient torque generation minimizes energy losses, ensuring that most input energy translates into productive work. If a system produces insufficient torque, it may struggle to perform tasks. This struggle results in wasted energy and reduced efficiency.
The connection between torque and efficiency can be observed in various applications. For example, in electric motors, proper torque levels lead to smooth acceleration and deceleration. This smooth operation reduces wear and tear on components, extending their lifespan.
In summary, effective torque generation maximizes operational efficiency by ensuring that machines perform their tasks with minimal energy loss and optimal performance. Efficient torque aligns power with application demands, enhancing overall productivity.
What Role Do Load Dynamics Play in Performance Variability?
Load dynamics significantly affect performance variability in systems. Variations in load conditions can lead to fluctuations in performance outputs, influencing efficiency and reliability.
- Types of Load Dynamics:
– Static Loads
– Dynamic Loads
– Cyclic Loads
– Transient Loads
– Impact Loads
The diversity in load dynamics presents a range of effects on performance variability. Understanding these types is crucial for optimizing system design and operation.
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Static Loads:
Static loads refer to forces applied to a system that remain constant over time. They often represent the regular, unchanging weight or pressure that a structure must support. For instance, in civil engineering, static loads include the weight of the building materials. According to the American Society of Civil Engineers, failure to accurately calculate static loads can lead to structural failures. -
Dynamic Loads:
Dynamic loads are forces that vary with time, typically due to moving or changing loads. In mechanical systems, this might include the forces exerted by machinery in motion. A study by Zhang et al. (2019) highlights that dynamic loads can lead to unexpected outcomes in performance because they require additional responses from the system to stabilize. -
Cyclic Loads:
Cyclic loads occur due to repetitive loading and unloading cycles, such as those seen in bridges or rotating machinery. These loads can lead to material fatigue over time. Research published in the Journal of Materials Science (Smith, 2020) found that structures subjected to cyclic loads might experience reduced lifespan due to the gradual weakening of materials through repeated stress. -
Transient Loads:
Transient loads are short-duration loads that can cause rapid changes in performance. For instance, during an earthquake, structures might experience transient forces that exceed their design capabilities. Engineering studies indicate that failure to accommodate transient loads can result in catastrophic structural failures, as noted in a report by the National Earthquake Engineering Research Institute (NEERI, 2018). -
Impact Loads:
Impact loads arise from sudden forces, such as collisions or explosions. These loads can produce significant performance variability, as systems must quickly adapt to extreme conditions. A study by Lee and Park (2021) demonstrated that impact-resistant designs are critical in sectors where safety is paramount, such as automotive and aerospace engineering.
Addressing load dynamics is essential for enhancing system performance and reliability. By recognizing and engineering against these variations, systems can achieve better stability under diverse operating conditions.
In Which Industries Are AC Servo Motors Commonly Utilized?
AC servo motors are commonly utilized in several industries. These include the manufacturing industry, where they drive precision machinery and robotics. They are also prevalent in the automation sector, enabling efficient control of production lines. The aerospace industry uses AC servo motors for applications in flight control systems. The automotive industry incorporates them in assembly and testing processes. Medical equipment, such as surgical robots and diagnostic machines, relies on their precision. Additionally, they find use in the packaging industry for accurate filling and labeling processes. Overall, AC servo motors support diverse applications that require high efficiency and accurate motion control.
How Do AC Servo Motors Enhance Automation Across Various Sectors?
AC servo motors enhance automation across various sectors by improving precision, increasing efficiency, and enabling advanced control of machinery. Their design allows for accurate position control and smooth operation, making them essential in applications like robotics, manufacturing, and packaging.
Precision: AC servo motors provide highly accurate positional feedback through encoders and sensors. According to a study by Lee (2019), this high accuracy results in reduced errors in manufacturing processes, leading to improved product quality. A typical accuracy range for AC servo motors can be within ±0.5 degrees of rotation.
Efficiency: These motors operate with high energy efficiency compared to traditional motors. Research by Kim et al. (2020) indicates that AC servo motors could be 20-30% more efficient, reducing operational costs. This efficiency stems from their ability to maintain a constant torque across varied speeds, minimizing energy loss.
Advanced Control: AC servo motors use sophisticated control algorithms to adjust their performance in real-time. These control systems, including PID (Proportional-Integral-Derivative) controllers, allow for smooth start-stop operations and precise speed adjustments. A report published by Johnson (2021) emphasized that such control systems contribute to faster cycle times in production lines by up to 40%.
Versatility: The ability of AC servo motors to perform in various environments and with different loads makes them versatile. They are commonly found in industries such as automotive, aerospace, and electronics. The adaptability of these motors allows for deployment in both heavy machinery and delicate assembly processes.
Reduced Maintenance: AC servo motors typically have fewer moving parts compared to other motor types, which leads to lower maintenance requirements. A study by Davis (2022) highlighted that businesses experienced a 25% decrease in maintenance costs after transitioning to AC servo systems, thereby saving time and resources.
In summary, AC servo motors enhance automation through precision, efficiency, advanced control, versatility, and reduced maintenance, significantly improving productivity across diverse sectors.
How Can You Apply the AC Servo Motor Mathematical Model to Solve Real-World Problems?
The AC servo motor mathematical model can be applied to solve real-world problems through precise control of motion and enhanced system performance by analyzing parameters such as torque, speed, and position.
This application involves several key points:
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Torque Analysis: The mathematical model of an AC servo motor includes torque equations that calculate the necessary torque to start and maintain motion. Accurate torque prediction helps in designing systems where precise control of load handling is crucial, such as robotics and CNC machines.
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Speed Control: The model provides insights into the relationship between voltage input and speed output. Understanding this relationship allows engineers to optimize the speed of motors in applications like conveyor systems and automated machinery, improving efficiency and reducing energy consumption.
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Position Feedback: The model often incorporates feedback loops that utilize position sensors. These sensors provide real-time data on the motor’s position, allowing for corrections and adjustments to maintain desired positions. This is particularly important in applications like robotic arms and automotive systems where precision is vital.
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System Performance Optimization: By using the mathematical model, engineers can simulate different operating conditions and determine the optimal motor specifications for a given application. This results in better system performance, lower costs, and reduced energy requirements.
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Reliability and Maintenance: Models predict behaviors and can identify potential failure points. Understanding these factors allows for planned maintenance schedules, minimizing downtime in critical operations in industrial sectors.
Research conducted by Zhan and Chai (2020) indicates that implementing a mathematical model can increase the accuracy of motion control systems by up to 30%. This approach leads to enhanced performance and reliability in various applications, including manufacturing automation and aerospace engineering.
Overall, the mathematical modeling of AC servo motors provides a framework for addressing real-world challenges in motion control and system optimization.
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