NGMV Control Toolbox

Basic Questions About NGMV Control

What is NGMV Control?

NGMV stands for Nonlinear Generalized Minimum Variance. It is a version of the GMV controller that works for nonlinear open-loop stable plant models and is most suitable for the control of systems affected by stochastic disturbances. At the origin of the family is the classic Astrom's minimum variance controller, which minimizes the variance of the output signal, provided the plant is minimum-phase. The GMV and NGMV controllers introduce an extra weighting on the control signal that relaxes this restriction, and also provides a penalty on excessive actuator movement.

What are the benefits of NGMV controller?

It is a potential candidate for a general nonlinear controller and can be implemented in a straightforward way on a wide range of applications since it only requires an input-output model of the plant to be available, in a structured or unstructured form. However, one has to be aware of the limitations of the blackbox approach: although its advantage lies in its simplicity, for more difficult problems a method that is based on the physical knowledge of the system may well be more suitable.

What are the assumptions involved in the NGMV controller design?

The main assumptions for the NGMV control design can be listed as follows:

• The nonlinear part of the plant model must be open-loop stable
• Disturbance signals are modelled as white noise passing through a linear filter
• Only output time delays are assumed
• The weighting functions and are selected so that the nonlinear operator is stably invertible

What about the implementation of the controller?

The implementation is relatively simple since the controller is fixed and involves two LTI filters and two nonlinear operators, as in the figure below:

This basic controller structure contains an algebraic loop which can be solved iteratively by Simulink. An explicit implementation requires splitting the operator into the present (static) and past (possibly dynamic) components. An alternative simple solution, which is suboptimal but often works well, involves inserting a single delay element in the inner feedback loop.

How do you choose the dynamic weightings?

This has traditionally been a difficult question since there is no well-defined procedure to be followed that would work in all cases and for all applications. The problem is much simpler in the linear GMV control case since the closed-loop transfer function for a given weighting selection can readily be computed and assessed for stability and performance. In fact, by reverse engineering, one may define a desired characteristic polynomial and work backwards to the weightings by solving the appropriate Diophatine equation (the function gmvpp doing that for SISO systems is provided in the Toolbox).

In the general nonlinear case, it is still possible to formulate some general guidelines that normally lead to acceptable results. However, in this case it is much harder to analytically determine the closed-loop stability (i.e. the stable invertibility of the nonlinear operator) and consequently this is normally done by simulation using the representative reference and disturbance signal ranges. A few such guidelines, or rules of thumb, can be listed as:

• The error weighting is usually chosen as a lag term and includes an integrator to penalize steady-state offsets
• The control weighting can be defined as a constant or a lead term to penalize high-frequency actuator variations
• Once the dynamic structure of the weightings has been selected, a single constant gain may then be used to achieve the desired trade-off between the error and control variances

In addition, if there exists a linear controller that already stabilizes the delay-free plant model, it can be utilized to define an initial design (see also Chapter 5, Section 2 of the main text for more information about optimal cost-function weighting selection).

What does the NGMV Control Toolbox contain?

It contains the Matlab routines that compute the basic NGMV controller components, as well as its more advanced versions, both in the polynomial and state-space domain. It also features a Simulink blockset which contains the supported NGMV controller structures as Simulink blocks, and which can be used as templates for user's custom designs. Additionally, a set of ready-to-use Simulink models are provided for a quick simulation and design verification of simple control loops.

Isn't it a major limitation to work only with linear disturbance and reference models?

No, actually not. In many cases, LTI models are good approximations for disturbances, as for example a second-order linear approximation of the Pierson-Moskowitz spectrum in marine problems. Also, in some applications the exact disturbance model is not known, and the selected model can simply be considered a design parameter.

How do I get started?

To quickly get a feeling for the Toolbox capabilities and NGMV control in general, it is probably best to go through the Tutorial which describes the whole design procedure on a particular application.

Where can I find out more about NGMV control?

The NGMV Control Toolbox accompanies and illustrates the book "Nonlinear Industrial Control Systems" [1], referred to in this documentation as 'main text', where the theory and design for all the methods are described in detail. There are also several journal and conference papers on the subject of NGMV control, even more on the linear GMV control, and innumerable books and articles on the stochastic control theory in general, and minimum variance control in particular. Some useful links and references can be found in the section Reading More About the NGMV Control.

What Is the NGMV Control Toolbox?

Common Terms Used in NGMV Control