Polynomial approach to nonlinear predictive generalized minimum variance control

A relatively simple approach to non-linear predictive generalised minimum variance (NPGMV) control is introduced for non-linear discrete-time multivariable systems. The system is represented by a combination of a stable non-linear subsystem where no structure is assumed and a linear subsystem that may be unstable and modelled in polynomial matrix form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The NPGMV control law involves an assumption on the choice of cost-function weights to ensure the existence of a stable non-linear closed-loop operator. A valuable feature of the control law is that in the asymptotic case, where the plant is linear, the controller reduces to a polynomial matrix version of the well known generalised predictive control (GPC) controller. In the limiting case when the plant is non-linear and the cost-function is single step the controller becomes equal to the polynomial matrix version of the so-called non-linear generalised minimum variance controller. The controller can be implemented in a form related to a non-linear version of the Smith predictor but unlike this compensator a stabilising control law can be obtained for open-loop unstable processes

Controller performance design and assessment using nonlinear generalized minimum variance benchmark : scalar case

A nonlinear version of the Generalized Minimum Variance (GMV) multivariable control law has been recently derived for the control of nonlinear, possibly time-varying systems. This paper presents the results of the controller performance assessment against this Nonlinear GMV controller in the scalar case. The minimum variance of the generalized output is estimated from routine operating data given only the plant time delay and the technique is applied to a nonlinear reactor control example

State-space approach to nonlinear predictive generalized minimum variance control

A Nonlinear Predictive Generalized Minimum Variance (NPGMV) control algorithm is introduced for the control of nonlinear discrete-time multivariable systems. The plant model is represented by the combination of a very general nonlinear operator and also a linear subsystem which can be open-loop unstable and is represented in state-space model form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The solution for the control law is derived in the time-domain using a general operator representation of the process. The controller includes an internal model of the nonlinear process but because of the assumed structure of the system the state observer is only required to be linear. In the asymptotic case, where the plant is linear, the controller reduces to a state-space version of the well known GPC controller

H-infinity control of nonlinear systems with common multi-channel delays

A generalized H-infinity controller is derived for the control of nonlinear, possibly time-varying, multivariable systems with common output or input channel delays. A Nonlinear Generalized Minimum Variance (NGMV) controller has recently been proposed for plants modelled by a combination of linear and nonlinear subsystems, where the disturbance and reference models are linear. The aim in the following is to obtain a related controller but one which minimizes an H-infinity norm, to enable sensitivity functions to be shaped. The cost-function to be minimized involves both error and control signal costing terms, which are related to sensitivity and control sensitivity costing terms

Non-linear GMV control for unstable state dependent multi-variable models

A nonlinear generalized minimum variance control law is derived for systems represented by an input-output state dependent nonlinear subsystem that may be open-loop unstable. The solution is obtained using a model for the multivariable discrete-time process that includes a state-dependent (nonlinear and possibly unstable) model that links the output and any unstructured nonlinear input subsystem. The input subsystem can involve an operator of very general nonlinear form, but this has to be assumed to be stable. This is the first NGMV control solution that is suitable for systems containing an unstable nonlinear sub-system contained in a state-dependent model

Automated tuning of LQG cost function weightings : scalar case

A simple method of selecting the LQG dynamic weighting functions is proposed. This involves minimizing the traditional variance-based cost function but with a controller structure that is determined by a dynamic weighting LQG problem. This effectively forces a controller structure that has traditional integral action and controller roll-off terms. The methodology is similar to the so-called restricted-structure controller design used for optimal tuning of, low-order controllers. The proposed algorithm is applied to a simulated model of a continuous-time process plant. with trans port delay

Rudder roll stabilization with nonlinear GMV control

Application of Nonlinear Generalized Minimum Variance control to ship roll stabilization using rudder input command is considered in this paper. The dynamic weightings in the cost criterion are used to reject the wave disturbance at a specified frequency band while maintaining relatively low controller gain in low and high frequencies to account for rudder angle and rate limits. Moreover, the use of a nonlinear weighting function in the NGMV control law formulation ensures the nonlinearities in the rudder are dealt with in a natural and systematic way. The effectiveness of the approach is demonstrated on a simulated ship model

Multi-channel restricted structure estimators for linear and nonlinear systems

The Restricted Structure(RS)optimal deconvolution filtering problem for Multi-Channel (linear and nonlinear) discrete-time systems is considered in this paper. The main contribution of the paper lies in developing the numerical procedure for designing reduced order estimators in multivariable cases. Two simulation examples are used to illustrate the results. These are: the enhancement of the lung and the heart sound signals and the automotive air-fuel ratio estimation problem

Restricted structure control loop performance assessment and benchmarking

The problem of restricted-structure benchmarking for multi-input, multi-output (MIMO) systems controlled by multi-loop PID controllers is formulated in state space. The particular criterion shown in this paper is that for a linear quadratic generalised predictive controller, which combines the properties of linear quadratic Gaussian with those of generalized predictive control

Calculating setpoint range under actuator saturation and stochastic disturbance

Minimum variance (MV) has been widely used as a benchmark to assess the regulatory performance of control loops. However, due to the physical constraints (saturation) of the actuator, the MV performance cannot be achieved in many cases. In this paper, we investigate the output regulatory performance achievable under actuator saturation. The constrained minimum variance controller is first introduced. The performance of the linear LQG controller under saturation is also discussed. A procedure on how to compute the maximal achievable set-point range under saturation limits is presented. It is believed that with the information on achievable set-point range, the high level optimization can be greatly simplified