Control Theory and Feedback in Radiotherapy An Introduction

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					                                                                                                                                 Feedback and control in radiotherapy
                          Control Theory and Feedback
                                                                                                                            Uncertainties in the precision of radiotherapy delivery
                                in Radiotherapy                                                                             predicate the use of feedback and control

                                      An Introduction                                                                       Sources of uncertainty
                                                                                                                                   Internal movement (for example,
                                                                                                                                   respiration and bladder filling)
                                       Marcia K. O’Malley, Ph.D.                                                                   Inconsistency in patient orientation
                                                                                                                                   from session to session
                                         Department of Mechanical
                                     Engineering and Materials Science                                                             Changing geometry of tumor
                                              Rice University                                                                      and surrounding soft tissue over
                                               Houston, TX                                                                         the course of treatment

                                                                                                                                                                   http://mesothelioma-treatment-ways.blogspot.com/2007/10/mesothelioma-treatment.html



                                                    AAPM 2008                                                                                                                                                                                             2
                                                    Houston, TX
                                                                         Mechatronics and Haptic Interfaces Lab     AAPM – Houston, TX – July 30, 2008                                                                    Mechatronics and Haptic Interfaces Lab




             Objectives of this presentation                                                                                     Feedback

        Define the terms feedback and control                                                                             The process in which part of                                            System 1
        Represent three basic control system structures                                                                   the output of a system is
                      Feedback                                                                                            returned to its input in order
                      Feedforward                                                                                         to regulate its further output
                      Adaptive                                                                                                                                                                     System 2
        Discuss features and limitations of the three structures
        Match potential control solutions with challenges in
           radiotherapy
                                                                                                                          Feedback = mutual interconnection of two (or more) systems

                                                                                                                          Feedback is ubiquitous in natural and engineered systems


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AAPM – Houston, TX – July 30, 2008                                         Mechatronics and Haptic Interfaces Lab   AAPM – Houston, TX – July 30, 2008                                                                    Mechatronics and Haptic Interfaces Lab
             Control                                                                                                             Sample control systems



                                                                                                                                 reference                           Feedforward
               Ensure stability
                                                                                                                                                                      Controller
                  • System maintains desired
                      operating point (hold steady          Actuate                           Sense
                                                                                                                                                             error    Feedback     input                       output
                      speed)                                Throttle                          Speed
                                                                                                                            reference
                                                                                                                            or ‘set point’                            Controller
                                                                                                                                                                                           PLANT
               Improve performance                                                                                                                      -

                  • System responds rapidly to
                      changes (accelerate to 6 m/sec)                    Compute

               Guarantee robustness
                  • System tolerates perturbations in
                      dynamics (mass, drag, etc)

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             Feedback                                                                                                                Features of feedback

                                                                                                                                reference                    error    Feedback     input                       output
                                     error                    input                        output                                                                                          PLANT
        reference                            Feedback
                                                                       PLANT                                                                                          Controller
                                             Controller                                                                                                 -
                                -


                                                          Sensor
                                                                                                                                             Reactive / Error-driven
        Plant                         System to be controlled                                                                                Automatically compensates for disturbances
        Reference                     Desired value of output (also ‘set point’)                                                             (controller acts on error)
        Controller                    Computes compensatory command to the                                                                   Automatically follows change in desired state (set
                                      plant based on error                                                                                   point can change)
                                                                                                                                             Can improve undesirable properties of system/plant
        Sensor                        (implied)
                                                                                                                                             Can be very simple

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             Performance, Stability, Robustness                                                                                                Two main principles of feedback

                                                                                                                                          Robustness to uncertainty through feedback
                                                                                                                                                      Allows high performance in the presence of uncertainty
                                                                                                                                                      Accurate sensing to compare actual to desired, correction
                                                                                                                                                      through computation and actuation



           Improve performance                                              Ensure robustness
                                                                            (e.g., minimize change in output
                                                                                                                                          Design of dynamics through feedback
           (e.g., response time of a
           first order system)                                              response for variations in input)                                         Allows the dynamics (behavior) of the system to be modified
                                                                                                                                                      Interconnection gives closed loop that modifies natural behavior
                                                                                                                                                      Leverage capability to enhance performance or affect stability
                                       Stabilize a response
                                       (e.g., reduce oscillatory effects)



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             Limitations of Feedback                                                                                                           Summary of closed-loop feedback control

        Reactionary solution that relies on existence and                                                                                 Reactive controller based on error between desired and
          observance of error                                                                                                               actual states
        Disturbances applied to system will generate errors                                                                               Automatically compensates for external disturbances and
        Response will be delayed (disturbance rejection)                                                                                    follows changes in command

        Trade-offs exist between performance and stability                                                                                Significant impact on overall system response

        Effects of delay in the feedback path lead to instabilities                                                                       Used extensively in both natural and artificial systems
                                                                                                                                          Limitations:
                                                                                                                                                      Error must be present before actions taken
                                                                                                                                                      Tradeoff between performance and stability



                                                                                                                         11                                                                                                               12

AAPM – Houston, TX – July 30, 2008                                                       Mechatronics and Haptic Interfaces Lab   AAPM – Houston, TX – July 30, 2008                                      Mechatronics and Haptic Interfaces Lab
             Feedforward control                                                                                                            Pre-requisites for feedforward control

                                         Feedforward      input                             output                                     Effects of disturbance or command input must be
             reference
                                                                           PLANT                                                          predictable
                                          Controller
                                                                                                                                       Effects of feedforward compensation must be faster than
                                                                                                                                          response of plant (otherwise use feedback)
        Control element responds to change in command or
        measured disturbance in a pre-defined way                                                                                      Disturbances must be measureable


        Based on prediction of plant behavior (requires model)
        Can react before error actually occurs
                    Overcome sluggish dynamics and delays
                    Does not jeopardize stability


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             One implementation of feedforward                                                                                              An alternate implementation of FF
                                                       Input needed for                                                                                                                                     External disturbance
       Desired output                                     desired output                                                                                  Inverse model
                                     Inverse model                                          output                                                                                             Sensor
                                                                              PLANT                                                                         of system
                                       of system
                                                                                                                                                                        Input needed to
                                                                                                                                                                        cancel disturbance
                                                                                                                                                                                                              output
                                                                                                                                     Desired output
        Model-based prediction of input                                                                                                                             Σ                        PLANT      Σ

                                                                                                                                       Model based prediction of response to compensate for
        Ideally consists of exact inverse model of the plant
                                                                                                                                        disturbances
        Can compensate for known plant dynamics, delays (before
           you get errors)
                                                                                                                                       Same model used to predict change in the input needed to
        No sensors needed
                                                                                                                                         cancel an external disturbance
        System response must be predictable
                                                                                                                                       Disturbances must be measurable    sensor needed

                                                                                                                      15                                                                                                                       16

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             Implementation of FF requires model                                                                                 Limitations of feedforward control

        Mechanistic (first principles) models                                                                               Model must be accurate and include measurements of all
        Machine learning approaches                                                                                           important inputs/outputs
        Statistical models                                                                                                  Model must be invertible
                                                                                                                            May not generalize to conditions outside of training of the
        Performance of feedforward controllers depends on                                                                     model (neural networks)
        accuracy of the model                                                                                               Will not be accurate if the system changes




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             Combining feedback and feedforward                                                                                  Adaptation

        Feedforward and feedback are often used together                                                                    Long timescale variations in plant behavior make adaptive
                    Feedforward component provides rapid response                                                              control approaches appealing
                    Feedback component fills in the rest of the response accurately,
                    compensating for errors in the model                                                                    Allows for appropriate modifications to control in response
                                                                                                                                to controlled system changes
         reference                           Feedforward
                                              Controller                                                                    Can be pre-defined or result from continuous learning of
                                                                                                                                the controlled system’s properties
        reference                    error    Feedback     input                       output                               Can be used with both feedback and feedforward
                                                                   PLANT
                                -
                                              Controller                                                                        controllers




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             Implementation of adaptive control                                                                                                                   Implementing adaptation

                                                                                                                                                             Adapting the feedback controller
         reference                           Feedforward                                                                                                                 Gain scheduling
                                              Controller                                                                                                                 Continuous tuning

                                     error    Feedback              input                                               output
        reference
                                                                                     PLANT                                                                   Adapting the feedforward controller
                                              Controller
                                -                                                                                                                                        Online training of neural net
                                                                                                                                                                         Optimization of model
                                                                                                                                                                         Reinforcement learning




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             Feedback and control in radiotherapy                                                                                                                 Acknowledgements
        Uncertainties in the precision of therapy delivery predicate                                                                                         Paul Keall
        the use of feedback and control
              Inconsistency in patient orientation
              from session to session                                                                                                                        Robert F. Kirsch, Case Western Reserve University
                • FB – adjust treatment in real                                                                                                                     NAKFI Smart Prosthetics lecture
                  time to accommodate minor
                  fluctuations in positioning
                                                                                                                                                             Richard M. Murray, CalTech
              Internal movement (for example,
                                                                                                                                                                    Online textbook and course notes
              respiration and bladder filling)
                • FF – sense disturbance and
                  compensate                               http://mesothelioma-treatment-ways.blogspot.com/2007/10/mesothelioma-treatment.html


              Changing geometry of tumor over
              the course of treatment
                • Adaptive – change treatment plan
                  slowly (manually or automated)

                                                                                                                                            23                                                                                             24

AAPM – Houston, TX – July 30, 2008                                                                          Mechatronics and Haptic Interfaces Lab   AAPM – Houston, TX – July 30, 2008                    Mechatronics and Haptic Interfaces Lab
             Feedback and control in radiotherapy

        Uncertainties in the precision of therapy delivery predicate
        the use of feedback and control
                Inconsistency in patient orientation
                from session to session
                  • FB – adjust treatment plan in
                    real time to accommodate minor
                    fluctuations in positioning
                Internal movement (for example,
                respiration and bladder filling)
                  • FF – sense disturbance and
                    compensate
                Changing geometry of tumor over
                the course of treatment        http://mesothelioma-treatment-ways.blogspot.com/2007/10/mesothelioma-treatment.html


                  • Adaptive – change treatment plan
                    slowly (manually or automated)
                                                                                                                                25
AAPM – Houston, TX – July 30, 2008                                                              Mechatronics and Haptic Interfaces Lab

				
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