Search

This paper experimentally controls a flexible joint via explicit model predictive control (Explicit MPC) method. The scheme divides the state space into different partitions, then solves the associated multi parametric optimization in off-line computations. The result stores in a look-up table to be used in on-line algorithm. First, the state space equations of the flexible joint are derived and linearized around the working point. Then, in order to meet the plant’s specifications, desired performance and the limitation of processor/memory, the constraints, weights, sampling time and prediction horizon are determined for the system. Finally, the algorithm is applied on the experimental plant. Numerous simulations, the result of the experiment and comparison with other methods confirmed that the method was able to control the vibrations of the constrained flexible joint.

The purpose of this paper is to evaluate the performance and computation time of Laguerre based model predictive control in the longitudinal motion of an aircraft. A Laguerre based model predictive algorithm is developed to control the longitudinal dynamics of an aircraft subject to state and input constraints. Then, the performance and the computation time of the designed controller are compared to the ones of the standard version of model predictive control. The results show that the Laguerre based model predictive control improves the computation time as much as 7.2% with a negligible trade-off in performance degradation. Because performing aircraft maneuvers needs to solve constrained optimization problems in short time samples, this study suggests the application of Laguerre based model predictive control for such purpose. Furthermore, by allowing to use shorter sampling times, the method could be used in real-time implementation of agile aircraft with fast dynamics.

It is well known that some practical difficulties are involved in the implementation of stabilising model predictive control for time-varying systems. In order to address the difficulty of computational load, this paper extends the orthonormal function method for model predictive control to linear time-varying systems. We provide sufficient conditions for a sub-optimal model predictive controller to be stabilising for a time-varying system. It is also shown that the orthonormal parametrisation method enables us to reduce the number of decision variables significantly and with a satisfactory performance. In addition, it is shown that orthonormality and, the called for, long prediction horizons are not necessary for stability. Examples are provided, illustrating the effectiveness of the method for linear time-varying systems.

This paper presents a Laguerre parametrization approach to employ Model Predictive Control (MPC) for the trajectory tracking problem of a non-holonomic mobile robot with input and state constraints. A time-varying error model is obtained for the trajectory tracking of the mobile robot. Then, a Laguerre based MPC (LMPC) for time-varying systems is designed and tuned to ensure asymptotic stability of the system. The proposed algorithm considers input and states, including velocity and acceleration, constraints to provide stability. It is shown that the proposed method is able to reduce the computation times. In order to confirm the effectiveness of the proposed method, extensive simulations results are provided.

It has been shown that Laguerre functions successfully reduce the number of decision variables in model predictive control of linear time invariant (LTI) systems. In this paper we extend the use of Laguerre functions to deal with linear time-varying (LTV) systems in the model predictive control framework. It is shown that Laguerre functions enable us to reduce the number of decision variables significantly and with a satisfactory performance. An example illustrating the unconstrained and constrained cases is provided.