Jane Li - WPIusers.wpi.edu/.../L11-FeedbackControl_note.pdf · •Feedback Systems: An Introduction...
Transcript of Jane Li - WPIusers.wpi.edu/.../L11-FeedbackControl_note.pdf · •Feedback Systems: An Introduction...
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Jane Li
Assistant Professor
Mechanical Engineering Department, Robotic Engineering Program
Worcester Polytechnic Institute
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• (2 pts) How to ensure games for rehabilitation can be played by a wide range of stroke patients?
• (4 pts) Name one assistive strategy which are not found in the multi-joint exoskeletons
• (4 pts) Why is it helpful for LL exoskeleton to provide knee joint stability reinforcement? And how to provide it?
10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 2
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• How to make games playable for a broad range of stroke patients?
• Assume no use of hands
• Simple games should support multiple methods of user input
• Calibrate to the patient’s motion range
• Direct and natural mappings are necessary
10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 3
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• Devices for hip, knee and ankle
• Fundamentally different joint functions
• Assistive strategies unique to single-joint device
• Muscle stiffness control, proportional EMG control
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• Gravity compensation
• Feedforward movement assistance during swing
• Knee joint stability reinforcement during stance
•
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• Prepare for understanding the stability control in teleoperation and haptics
• Dynamic system and feedback control
• Stability of continuous and discrete systems
• This is a vey brief introduction
• ES 3011. CONTROL ENGINEERING I – undergrad
• RBE 502. ROBOT CONTROL – grad
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• Feedback Systems: An Introduction for Scientists and Engineers, 2nd Edition, by KJ Astrom and R. M. Murray
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10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10
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• Causes for unstable systems?
• Determine whether a system is stable or not?
• Design a stability controller?
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• Dynamic system
• A system whose behavior changes over time, often in response to external stimulation or forcing
10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 14
Open-loop Closed-loop
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• Feedback allows a system to be
• Resilient to external disturbances
• Insensitive to variations of internal elements
• Feedback may
• Create dynamic instabilities (oscillations or “runaway”)
• Introduce sensor noise into the system
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• In engineering context
• The use of algorithms and feedback to produce desired system behavior
10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 17
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• Cruise control of vehicle
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10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 21
Past FuturePresent
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• How to model this system?
• Time Domain
• ODE
• State space
• Frequency Domain
• Laplace transform
10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 22
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10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 23
ODE – How to solve?
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• Let be a solution,
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• Two distinct real roots:
• General solution
10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 26
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• Two complex conjugate roots
• Euler formula
10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 27
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• General solution
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• Repeated real root
• General solution
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10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 30
Solutions have negative real parts
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• Let be a solution with initial condition
• A solution is stable if other solutions that start near stay close to
• A solution is asymptotically stable if all the nearby solutions converge to this stable solution for large time
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Solution format?
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10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 33
Over
Under
Critical
All asymptotically stable
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• Lyapunov function
• An energy-like function
• Nonnegative function
• Always decreases along trajectories of the system dynamics
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dynamics matrix Control matrix
sensor matrix Direct term
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Stability Criterion?
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• Any linear system? Choose a new coordinate system
10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 44
Stability Criterion = A’s eigenvalues have negative real parts
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• Stability is a property of system dynamics
• Instability of a continuous system
• Due to the introduction of feedback
• How to determine the stability of a dynamic system?
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• Shared virtual object
• PD controller for position coherency
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• For the above systems
• Derive dynamic equations
• Derive state space representation
• m = 1, b=0.4, K=5000 N/m, choose a set of b(s) for stability and instability
• No network delay (Td = 0)
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