State-space approach to nonlinear predictive generalised minimum variance control

Abstract

A Nonlinear Predictive Generuli::ed Minimum Variance (NPG!vfV) control algorithm is introduced for the control of nonlinear discrete-time multivariable Ａ Ｇ ｊ ｾ ｹ ｳ ｴ ･ ｭ ｳ The plant model is repre ented by the combination of a very gen ral nonlinear op rator and also a linear subsystem which can be open-loop unstable and is represented in state-pac mod I form. The multi-step predictive control cost index to be minimised involve both weighted error and control signal costing terms. The solution for the control law is derived in the time-domain using a general op rator representation of the process. he controller include, an int rnal m del of the nonlinear proce s but because of the assumed structure of the system the state observ I' is only required to be linear. In the asymptotic case, where the plant is linear, the controll I' reduces to a state-space v rsion of the well known GPC controller.

Optimal Generalized Predictive Functional Control with Applications to Extended PID Control for Quadruple Tank

“…The complete system, is depicted in Fig. 1 and consist of, a linear plant model along with reference, disturbance sources and measurement noise [7]. The disturbance signal is assumed to be represented by LTI model excited via zero mean white noise and a measured output disturbance d(t).…”

“…Noting that, the linear subsystem models that describe the augmented system, will not be studied entirely here since it is already discussed in [7], [8].…”

“…where = + , and , collects, deterministic disturbance terms in (7). The i-steps ahead prediction of error signal, can be produced assuming future actions of the control are identified.…”

Restricted structure predictive control for linear and nonlinear systems

“…A similar problem is now considered but one that reveals the link with traditional transport-delay compensation methods and with NGMV control problems Grimble 2005, Majecki (2010a and2010b). The unstructured input sub-system  1k is included in this case.…”

Non‐linear predictive generalised minimum variance state‐dependent control

“…To establish this equivalence consider the more usual problem, where system outputs controlled are the same as those measured and where absolute control is costed. The algebra is similar to the non-state-dependent problems considered in [13]. The controller, which should not be implemented in this form, is shown in Fig.…”