Abstract
In this paper, Receding Horizon Model Predictive Control (RH-MPC) having a quadratic objective function is studied through the Singular Value Decomposition (SVD) and Singular Vectors of its Hessian Matrix. Contrary to the previous work, non-equal and medium sized control and prediction horizons are considered and it is shown that the Singular Values converge to the open loop magnitude response of the system and singular vectors contain the phase information. Earlier results focused on classical formulation of Generalized Predictive Control (GPC), whereas, current work proves the applicability to modern formulation. Although, method can easily be extended to MIMO systems, only SISO system examples are presented.
Highlights
Model Predictive Control is a time domain class of control strategies, with very attractive features suitable for modern digital applicability
Ability to deal with Multi-Input Multi-Output (MIMO) systems of higher orders, effectively dealing with constraints imposed on input, change in input, output and state variables are the unique features of MPC that make it ideal
Some work has been done into the area by Rojas and Goodwin [6,7] and Quang et el [6] to formulate the connection between the open loop frequency response and Singular Value Decomposition (SVD) of the Toeplitz matrix of MPC
Summary
Model Predictive Control is a time domain class of control strategies, with very attractive features suitable for modern digital applicability. Some work has been done into the area by Rojas and Goodwin [6,7] and Quang et el [6] to formulate the connection between the open loop frequency response and Singular Value Decomposition (SVD) of the Toeplitz matrix of MPC. In [6] frequency response connection is established to the classical generalized predictive control (GPC), whereas, we validate the results for receding horizon MPC and non-equal prediction and control horizons. 2. Recending Horizon Model Predictive Control(RH-MPC) Consider the discrete state space representation of a SISO plant with no effect of input on output i.e. U opt is determined at each sampling time instant It contains elements but only first element is applied as the controlling input to minimize the error and the whole prediction.
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