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ADVANCED MOTION CONTROL First and Second Order Motion by Peter Nachtwey

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Pressure/Force OnlyPosition-SpeedPosition-ForcePressure/Force LimitPosition-Pressure Closed Loop Control

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Why Bother Making Another Hydraulic Motion Controller? Connect. Control. Optimize. 32 bits to interface with 32 bit PLCs and PCs. 32 or 64 bit floating point math Motion Control / User Programs off load PLCs. 10/100Mb Full Duplex Ethernet using EtherNet/IP. 2 nd Order Control most important.

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First order vs. Second order control Motors look like first order systems Hydraulic systems look like 2nd order systems Modeled as a Mass between two springs as a representative, effective, simple models.

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Mass and Two Springs

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First and Second Order Response

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First and Second Order Controllers First Order Controllers have a PID and velocity and acceleration feed forward. Second order controllers have a PID with a second derivative and velocity, acceleration and jerk feed forwards.

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Its costly to design hydraulic systems with natural frequencies high enough for higher production rates. Response is limited by ξω n /2 without 2 nd order motion control One answer is to control the system with 2nd order motion controllers quicker accels and decels (under control) than what 1st order systems permit. Lower damping factor & natural frequency, allows greater advantage over 1st order controllers Compensate for mechanical cost in the electronic controls Why 2 nd Order Control?

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3 Challenges implementing a Second order controller Challenge 1. Must have smooth motion profiles where the jerk changes smoothly for the jerk feed forward. Simple motion or target profile generators arent good enough.

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3 Challenges implementing a Second order controller Challenge 2. Using the double derivative gain is problematic. The derivative gain is difficult enough ! quantizing error due to lack of resolution. Sample jitter Noise.

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3 Challenges implementing a Second order controller Challenge 2.

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3 Challenges implementing a Second order controller Challenge 3. How does one tune a second order? Use a 5th order motion profile or target generator. Use model based control. Auto tuning determines the jerk feed forward and second derivative gain.

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Solutions to 2nd order controller implementation problems Use a 5 th order motion profile or target generato r. Use model based control. Use Auto tuning to determine the jerk feed forward and second derivative gain.

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Second Order Motion Profile - Higher Order PID Higher Order Target Generator

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PID w 2 nd derivative gain + FF

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Model Based Control Why Bother?

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Model Based Control The PID and feed forwards use the positions, velocities, and accelerations generated by the model, not the feedback. The feedback continuously updates the model to keep the model from going astray. The advantage is that the PID sees a nearly perfect system virtually free of quantizing errors, sample jitter and noise.

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Model Based Control The result is a smoother output which allows use of higher gains. However, one should ask, Where does the model come from?

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System Identification and Auto Tuning The information needed is in the plots/graphs Need time, control output and actual position or velocity The result is Gain and time constant for a first order model Gain, damping factor and natural frequency second order. Choose the model for the best fit.

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First Order Model

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Second Order Model

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Actual vs. Estimated Velocity

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Actual and Estimated Accelerations

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Estimated State Feedback

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Selecting the Closed Loop Gain. Closed Loop Gains are calculated from the model and the desired bandwidth. Only one parameter to choose – the desired bandwidth. Feed-Forward Gains are calculated from the model only

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Auto Tuning via Tuning Wizard

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Step Response for Different Bandwidths

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Summary Why Bother? Machines can be simpler and less costly to manufacture. Technology allows advances in machine motion control

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Thank You for Your Time and Attention! Questions?

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Hydraulic Design Guide

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ADVANCED MOTION CONTROL First and Second Order Motion by Peter Nachtwey

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Solutions to 2nd order controller implementation problems x(t)=x(0)+v(0)*t+.5*a(0)*t^2+0.1666*j(0)*t^3+c4*t^4+c5*t^5 v(t)=v(0)+a(0)*t+0.5*j(0)*t^2+4*c4^3+c5*t^4 a(t)=a(0)+j(0)*t+12*c4*t^2+20*c5*t^3 j(t)=j(0)+24*c4*t+60*t^2 The fifth order motion profile

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Feedback/Transducer Components of a Motion System Actuator Controller Closed Loop Control Load

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System Identification and Auto Tuning Choosing the model that provides the best fit.

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