| Summary: | AC induction motor-drive systems are the backbone for numerous industrial
applications, such as aerospace, medical equipment, and nuclear power plants.
The control performance of electric drives is sensitive to several uncontrollable
disturbances from changes in ambient conditions in the form of machine parameter
variations such as: magnetizing inductance (Lm), and rotor resistance (Rr). Such
variations may trigger instability because of mismatch between the reference and
desired conditions. The most common techniques to solve the issue are: (a) gain
adaptation that requires instrumentation to monitor system, (b) nonlinear control
methods, such as sliding mode, feedback linearization, and (c) robust control method,
such as H∞, and μ-analysis to account for motor uncertainties. Despite the prevalence
of PID controllers, a systematic method to tune their parameters to ensure robustness
remains an open problem. In this dissertation, a systematic method to tune PI controllers while factoring
uncertainties is developed. Two major design methods are proposed: (a) based on
Kharitonov’s theorem and (b) based on fractional order controllers. In (a), the
control design problem for AC drives can be cast into as a set of interval polynomials
that can be analyzed via Kharitonov’s theorem. Also proposed a method to solve
the resulting polynomials, which then yield the controller coefficients. In (b), we
show how fractional order controllers (FrOC)-a generalization of PID that consider
fractional values for the integral and derivative coefficients can be designed to achieve
our main objectives. A unique advantage of such controllers is the so-called isodamping
property (constant phase) and robustness. The performance of controllers is
assessed by comparing them with two well established techniques: traditional method
based on gain/phase margin requirements, and symmetric optimum techniques an
industrially popular technique that requires constant gain over a desired bandwidth. While both these techniques use reduced order models, the proposed methods are
advantageous because they can handle the full model of the machine. The simulation
results suggest that the proposed controllers remain robust against the chosen
uncertainties while both traditionally designed controllers succumb to instability. The
work paves a novel way for the design and tuning of robust PID controllers in electric
drives.
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