Distributed Laboratories: Control System Experiments with LabVIEW and the LEGO NXT Platform Greg Droge, Dr. Bonnie Heck Ferri, Jill Auerbach

Outline Motivation and Background Experimental Setup Control Projects – Velocity Control – Position Control Assessment

Motivation and Background Control Theory can be a highly abstract subject Distributed Laboratories: – Experiments can be done in various locations such as homes, classrooms, and dorm rooms – Labs utilize inexpensive equipment – Well-suited for inclusion into lecture-based classes to be done at the desks in the class room or to be taken home as a project New pedagogical model: more complete integration of theory and laboratory experience Goal: Introduce lab experience into early courses through Distributed Laboratories

Motivation and Background Distributed Lab Features – Fully support or demonstrate a fundamental principle that is hard to understand from theory alone – Experiments should not require faculty to change their standard evaluation methods – Should contain supplemental material including a tutorial Logistical Considerations – Each experimental module should be made as accessible as possible to as wide a range of instructors as possible – Designed primarily for faculty who do not have resources for high-end experiments – Must be easy for students to use

Experimental Setup NXT and motor – Includes encoder for position measurement – Only integer arithmetic Experimental Block Diagram – Velocity Control: – Position Control: Reference Filtered Derivative Motor Sensor Controller Position + - Velocity Reference Motor Sensor Controller Position + -

Experimental Setup LABVIEW NXT Toolkit – NXT toolkit free with access to LABVIEW – Students can use floating point arithmetic since the conversion to integer arithmetic is done automatically at a lower level of abstraction – Program controlled with graphical user interfaces

Experimental Setup LABVIEW is based on data-flow: similar to Control Theory block diagrams Reference Filtered Derivative Motor Sensor Controller Position + - Velocity

Velocity Control Fundamental concepts – PID Control – Zeigler-Nichols tuning rules – Steady-state error – Sinusoidal tracking – System performance with different controllers – Frequency response – Controller bandwidth – Resonance – System identification

Velocity Control (In-Class Component) In-Class Component: Zeigler-Nichols tuning rules (performed in 50 minutes) Students given proportional gain which is stable with large steady state error

Students follow rules for Zeigler-Nichols PID tuning – Bring system to steady state oscillation – Use rules for PID gains Velocity Control (In-Class Component)

Velocity Control (At-Home Component) System modeling using sinusoid inputs with different frequencies – Students measure output amplitudes and phase differences – Done using the plotting tools in LABVIEW Open Loop Transfer Function: Example magnitude and phase plots: From Velocity Filter Open LoopPI Control

Position Control Fundamental Concepts – Time domain specifications – System identification – Lead control – Root locus – Discretization – Difference equation implementation – Robustness

Position Control Procedure – Modify motor velocity controller to replace velocity feedback with motor position feedback Step-by-step instructions allow the students to become familiar with LABVIEW dataflow – Obtain model from step response Given closed loop step response, students can determine open- loop system parameters Students can compare results obtained from Velocity experiment

Position Control Procedure – Design lead compensator to achieve a settling time of about.3 seconds (Requires implementing digital control in LABVIEW) – Plot frequency response of closed loop system and compare with expected results

Assessment Data collected from six classes Two assessment tools were used 1.Concepts Inventory Pre and post tests administered to assess students understanding 2.Surveys: administered before students took class and one semester afterward Students were surveyed on their perceived understanding of different topics Requiring students to use Bode plots and root locus in the experiment forced them to understand the concepts on a much deeper level

Assessment (Concepts Inventory) Systems and Controls Concepts Inventory Test % correct comparison / experimental & control classes Concept Inventory Questions Directly Related to Lab Brief Description of Question% correct experimental N=30 % correct control N=28 difference Q A: identify a difference equation corresponding to a transfer function 63.0%57.1%+5.9 Q B: select the z-domain pole-zero plots corresponding to a discretized system 11.1%10.7%+.4 Q C: determine the transfer function of a digital filter corresponding to a discrete time system 63.0%46.4%+16.6 Q D: identify the purpose of a PD controller 74.1%57.1%+17.0 Q E: identify the purpose of a PI controller 81.5%53.6%+27.9

Assessment (Concepts Inventory) Systems and Controls Concepts Inventory Test % change pre- post- tests / experimental & control classes Concept Inventory Questions Directly Related to Lab Questions% change experimental % change control QA: identify a difference equation corresponding to a transfer function +28.6%+17.1% Q B: select the z-domain pole-zero plots corresponding to a discretized system +11.1%-2.6% Q C: determine the transfer function of a digital filter corresponding to a discrete time system +41.1%+16.4% Q D: identify the purpose of a PD controller +58.5%+43.8% Q E: identify the purpose of a PI controller +69.0%+36.9%

Assessment (Follow-up Survey) Students who took follow-up systems and control class – Control:21% – Experimental: 33% Students who said their interest in applications of control engineering had increased – Control:29% – Experimental: 62%

Assessment (Follow-up Survey) Follow-Up Survey for System and Controls Students from Previous Semester Percentage of Students That Rated “Solid Understanding” for 11 Topics Covered in the Course ControlExperimental Implementation of digital filters29%48% Transient response of 1st and 2nd order systems7167 Steady state response of systems71 Root locus methods3652 Frequency response methods4348 Routh-Hurwitz stability criterion*3638 Nyquist stability criterion*3610 PID controllers2943 Lead and lag controllers3638 Discretization of continuous-time systems1462 Discrete time control systems1443

Conclusion Distributed experiments that are integrated into lecture-based courses have a large potential for improving student learning of theoretical material The LabVIEW interface allows the experiment to be abstracted to the point of letting the students see the structure of the system through the graphical programming The position control experiment requires students to modify the code in such a way that they gain practical experience in the implementation of a control system Web support was designed with the goal of lowering the threshold for instructors to adopt these experiments