Abstract
In this paper, a practical <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">model predictive control</i> (MPC) for tracking desired reference trajectories is demonstrated for controlling a class of nonlinear systems subject to constraints, which comprises diverse mechanical applications. Owing to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">linear parameter-varying</i> (LPV) formulation of the associated nonlinear dynamics, the online MPC optimization problem is solvable as a single <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">quadratic programming</i> (QP) problem of complexity similar to that of LTI systems. For offset-free tracking, based on the notion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">admissible reference</i> , the controller ensures convergence to any admissible reference while its deviation from the desired reference is penalized in the stage cost of the optimization problem. This mechanism provides a safety feature under the physical limitations of the system. To guarantee stability and recursive feasibility, a terminal cost as a tracking error penalty term and a terminal constraint associated with both the terminal state and the admissible reference are included. We use tube-based concept to deal with the uncertainty of the scheduling parameter over the prediction horizon. Therefore, the online optimization problem is solved for only the nominal system corresponding to the current value of the scheduling parameter and subject to tightened constraint sets. The proposed approach has been implemented successfully in real-time onto a robotic manipulator, the experimental results illustrates its efficiency and practicality.
Highlights
The ultimate goal of a control system is to achieve stability and a desired level of performance for plants which often have nonlinear (NL) dynamics, constrained levels of operation and are subjected to disturbances and measurement noise
The contributions of this paper are as follows: 1) A general Linear parameter-varying (LPV) modeling which can accommodate a wide class of mechanical systems that can be represented by rigid body nonlinear dynamics
PRACTICAL LPVMPC FOR REFERENCE TRACKING Based on the LPV modeling presented in the previous section, we propose a novel Model predictive control (MPC) formulation for LPV systems to track a given desired reference trajectory using the notion of admissible reference
Summary
The ultimate goal of a control system is to achieve stability and a desired level of performance for plants which often have nonlinear (NL) dynamics, constrained levels of operation and are subjected to disturbances and measurement noise. In [20]–[22] LPVMPC algorithms have been proposed for tracking time-varying reference trajectories, e.g., command trajectories in robotics applications All these approaches cannot guarantee recursive feasibility of the associated MPC optimization problem. Inspired by the approach of [23] and [24], for a given desired reference trajectory, the corresponding admissible steady sate and input are parameterized by a parameter vector referred to as the admissible output, which is among the decision variables of the optimization problem, and its deviation from the desired reference is penalized in the MPC cost function This can lead to offset-free tracking if the desired reference is admissible, the system is steered toward the closest admissible reference. The contributions of this paper are as follows: 1) A general LPV modeling which can accommodate a wide class of mechanical systems that can be represented by rigid body nonlinear dynamics This allows a straight forward formulation for the MPC reference tracking problem.
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