Nonlinear model predictive low-level control
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Date
2022
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Abstract
This dissertation focuses on the development, formalization, and systematic evaluation of a
novel nonlinear model predictive control (MPC) concept with derivative-free optimization.
Motivated by a real industrial application, namely the position control of a directional control
valve, this control concept enables straightforward implementation from scratch, robust
numerical optimization with a deterministic upper computation time bound, intuitive controller
design, and offers extensions to ensure recursive feasibility and asymptotic stability by
design. These beneficial controller properties result from combining adaptive input domain
discretization, extreme input move-blocking, and the integration with common stabilizing
terminal ingredients. The adaptive discretization of the input domain is translated into
time-varying finite control sets and ensures smooth and stabilizing closed-loop control. By
severely reducing the degrees of freedom in control to a single degree of freedom, the exhaustive
search algorithm qualifies as an ideal optimizer. Because of the exponentially increasing
combinatorial complexity, the novel control concept is suitable for systems with small input
dimensions, especially single-input systems, small- to mid-sized state dimensions, and simple
box-constraints. Mechatronic subsystems such as electromagnetic actuators represent this
special group of nonlinear systems and contribute significantly to the overall performance of
complex machinery.
A major part of this dissertation addresses the step-by-step implementation and realization
of the new control concept for numerical benchmark and real mechatronic systems. This dissertation
investigates and elaborates on the beneficial properties of the derivative-free MPC
approach and then narrows the scope of application. Since combinatorial optimization enables
the straightforward inclusion of a non-smooth exact penalty function, the new control
approach features a numerically robust real-time operation even when state constraint violations
occur. The real-time closed-loop control performance is evaluated using the example
of a directional control valve and a servomotor and shows promising results after manual
controller design.
Since the common theoretical closed-loop properties of MPC do not hold with input moveblocking,
this dissertation provides a new approach for general input move-blocked MPC
with arbitrary blocking patterns. The main idea is to integrate input move-blocking with
the framework of suboptimal MPC by defining the restrictive input parameterization as a
source of suboptimality. Finally, this dissertation extends the proposed derivative-free MPC
approach by stabilizing warm-starts according to the suboptimal MPC formulation. The
extended horizon scheme divides the receding horizon into two parts, where only the first
part of variable length is subject to extreme move-blocking. A stabilizing local controller
then completes the second part of the prediction. The approach involves a tailored and
straightforward combinatorial optimization algorithm that searches efficiently for suboptimal
horizon partitions while always reproducing the stabilizing warm-start control sequences in
the nominal setup.
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Keywords
Model predictive control, Input move-blocking, Finite control sets, Asymptotic stability, Mechatronic subsystems, Low-level control, Optimal control, Constrained optimization