Control System’s Coursework Project Overview
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Transcript of Control System’s Coursework Project Overview
CONTROL SYSTEM’S COURSEWORK PROJECT
OVERVIEW
Josh NeighborM.Sc Mechanical EngineeringUniversity of California San Diego
COURSES WITH PROJECTS HIGHLIGHTED:• Linear Systems Theory• Linear Control Design • Optimal Estimation• Robust and Multivariable Control
LINEAR SYSTEMS THEORY
Tasks: Derivation of Linearized Models
Created state space realization using linearized equations of motion, motor dynamics, and known parameters
Model Analysis Stability analysis of open loop system Analysis of controllability and observability of system
Output feedback control design with observer Observer and controller design to stabilize MiP
Mobile Inverted Pendulum (MiP) figures from Figure 17.6 of Dr. Thomas Bewley’s Numerical Rennaisance, First
Edition, 2014
Project: Linear control in state variable form for a mobile inverted pendulum
(pictured)
LINEAR SYSTEMS THEORY
System model (solid line) with Observer (dashed line) for output feedback controlled system: (1) motor torque, (2) Wheel angle and MiP Angle with respect to normal, (3) Change in wheel angle and MiP angle.
Result:• Successfully modeled system
stabilized by output feedback controller
Notes:• The system was also modeled for a
constant disturbance torque (wind)• Controller and Observer poles
placed arbitrarily to be stable and at desired speed (wanted to see system dynamics well). They could have been placed using more robust techniques.
LINEAR SYSTEMS THEORY
System response to a constant disturbance. States include Torque, change in Theta, Theta, Phi and change in Phi. We see both the change
in Phi and Theta converge to zero while Theta and Phi converge to constants.
Result:• Successfully modeled system that
stabilized the MiP under constant disturbance.
Notes:• The system was also modeled for a
constant disturbance torque (wind)• Determined the Observability and
Controllability properties of the system in order to design functional observer and controller.
LINEAR CONTROL DESIGNProject:
Analysis and controller design for a model of the pitch dynamics of an aircraft.
Tasks:• LQR Control Design to minimize cost function• Stability Margin Analysis• Estimator Design for system with noise and subsequent LQG controller design• Loop Transfer Recovery for noisy system
LINEAR CONTROL DESIGN
Bode Plot for LQR Controller. With no noise on the system, the cost function was minimized while
offering an infinite gain margin
Bode Plot for LQG controller after Loop Transfer Recovery. Some gain margin was gained after the
losses due to the noise on the system. Increases in stability come with losses of optimization for the
objective function
OPTIMAL ESTIMATIONProject:
Modeling of a chemical reaction with a nonlinear dependence. Estimate the concentration of the reagent to drive a feedback controller.
Tasks• Analyze observability properties of time-varying, nonlinear system• Create extended and linearized Kalman filters• Evaluate filter performance
OPTIMAL ESTIMATION
Linearized and Extended Kalman Filters performance evaluated by analysis of autocorrelation of the filter error. More uncorrelated error indicates better performance.
ROBUST AND MULTIVARIABLE CONTROLProject:
State feedback control and observer design for a 2DOF helicopter model
Tasks• State feedback and full order design
for given multivariable transfer function
• Pole placement at given poles using Sylvester’s equation
• Decouple systemResult:• Successful pole placement for all poles at -
1• Decoupled system (pictured)
Multivariable transfer function step response for
the decoupled system
ROBUST AND MULTIVARIABLE CONTROLProject:
Design stabilizing feedback controller that aims at minimizing the effect of additive disturbances on the output of the plant, given constrains on control signals and/or uncertainty present in the plant.
Tasks• Verify nominal disturbance rejection
performance• Verify nominal tracking or measurement
noise sensitivity performance• Derive relevant transfer function M11
used for robust stability condition and plot of maximum/structured singular value of M11 to check stability robustness.
Result:• Successfully used loop shaping to meet the
performance specifications.• Minimized the effect of additive disturbances.
Hard Disk Drive dual state actuator: MIMO 2 input, 1 output, 8 state model.
ROBUST AND MULTIVARIABLE CONTROL
M11 was found using the following equation, as it is
used for the robust stability test. We have an additive
uncertainty on one resonant frequency of the system,
so we use the additive uncertainty equation to then
find M11 of our system.
END Please feel free to contact me with any further questions.
Thank you.