engleski

Optimal control of a tower crane based on the polytopic linear parameter varying model

The main objective of this thesis is the optimal control of a 3D tower crane based on the polytopic linear parameter-varying model. The crane is modeled as three dynamically coupled subsystems, where the coupling among them is treated as a variation in the system’s parameters. The first part of the thesis proposes a control scheme that consists of a feedback controller with an additional neural network- based friction compensator. Neural network parameter adaptation law is derived using the Lyapunov stability analysis. The second part of the thesis concentrates on a distributed non- linear model predictive control that exploits the model structure. Two stabilizing model predictive control algorithms are proposed. In the first algorithm, stability is ensured via terminal cost and a terminal set constraint calculated for each subsystem. To guarantee the finite time convergence of all three subsystems in their corresponding terminal sets, a dual-mode control law is used for the first two subsystems. To guarantee recursive feasibility, system states are kept in a set of states in which constraint satisfaction can be guaranteed at all times regardless of parameter variation. In addition, non-linear model predictive control based on the off-line computation of a sequence of one-step controllable sets is proposed. During the online operation, a finite time optimal control problem is solved subject to constraints on the first state. A condition that enables a flexible convergence towards a suitably-chosen terminal set is proposed. In addition, an algorithm for computation of a sequence of piece- wise ellipsoidal one-step controllable sets is derived. The proposed approaches are verified using the experimental setup.

Tower crane; linear parameter-varying systems; linear matrix inequalities; distributed model predictive control

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