Design of generalized minimum variance controllers for nonlinear multivariable systems

The design and implementation of Generalized Minimum Variance control laws for nonlinear multivariable systems that can include severe nonlinearities is considered. The quadratic cost index minimised involves dynamically weighted error and nonlinear control signal costing terms. The aim here is to show the controller obtained is simple to design and implement. The features of the control law are explored. The controller obtained includes an internal model of the process and in one form is a nonlinear version of the Smith Predictor

GMV control of nonlinear multivariable systems

A Generalized Minimum Variance control law is derived for the control of nonlinear, possibly time-varying multivariable systems. The solution for the control law is original and was obtained in the time-domain using a simple operator representation of the process. The quadratic cost index involves both error and control signal costing terms. The controller obtained is simple to implement and includes an internal model of the process. In one form might be considered a nonlinear version of the Smith Predictor. However, unlike the Smith Predictor a stabilizing control law can be obtained even for some open-loop unstable processe

Admissible target paths in economic models

Social Psychology;econometrics

NGMV control of delayed piecewise affine systems

A Nonlinear Generalized Minimum Variance (NGMV) control algorithm is introduced for the control of piecewise affine (PWA) systems. Under some conditions, discrete-time PWA systems can be transferred into an equivalent state-dependent nonlinear system form. The equivalent state-dependent systems maintain the hybrid nature of the original PWA systems and include both the discrete and continuous signals in one general description. In a more general way, the process is assumed to include common delays in input or output channels of magnitude k. Then the NGMV control strategy [1] can be applied. The NGMV controller is related to a well-known and accepted solution for time delay systems (Smith Predictor) but has the advantage that it may stabilize open-loop unstable processes [2]

A numerical study on active control for tiltrotor whirl flutter stability augmentation

The use of active control to augment whirl flutter stability of tiltrotor aircraft is studied by means of a multibody simulation. The numerical model is based on a 1/5 scale semi-span aeroelastic wind tunnel model of a generic tiltrotor concept and possesses a gimballed, stiff-in-plane rotor that is windmilling. A single-input single-output controller and two types of multi-input multi-output algorithms, Linear Quadratic Gaussian Control and Generalized Predictive Control, are studied. They are using measured wing deflections in order to calculate appropriate swashplate input. Results on the closed-loop behavior of three wing and two gimbal natural modes are given. Robustness analyses with respect to major parameters like wing natural frequencies or structural damping are also briefly discussed. The rotor shear force is shown in the uncontrolled condition and in presence of a controller in order to illustrate the whirl flutter mechanism. The single-input single-output controller yielded substantial gain in stability and turned out to be most suitable for industrial application, whereas the Linear Quadratic Gaussian Regulator yielded even higher damping and still had good robustness characteristics

State dependent NGMV control of delayed piecewise affine systems

A Nonlinear Generalized Minimum Variance (NGMV) control algorithm is introduced for the control of delayed piecewise affine (PWA) systems which are an important subclass of hybrid systems. Under some conditions, discrete-time PWA systems can be transferred into their equivalent state dependent nonlinear systems form. The equivalent state dependent systems that include reference and disturbances models are very general. The process is assumed to include common delays in input or output channels of magnitude k. Then the NGMV control strategy [16] can be applied. The NGMV controller is related to a well-known and accepted solution for time delay systems but has the advantage that it can stabilize open-loop unstable processes [17]

Proportional-integral-plus (PIP) control of the ALSTOM gasifier problem

Although it is able to exploit the full power of optimal state variable feedback within a non-minimum state-space (NMSS) setting, the proportional-integral-plus (PIP) controller is simple to implement and provides a logical extension of conventional proportional-integral and proportional-integral-derivative (PI/PID) controllers, with additional dynamic feedback and input compensators introduced automatically by the NMSS formulation of the problem when the process is of greater than first order or has appreciable pure time delays. The present paper applies the PIP methodology to the ALSTOM benchmark challenge, which takes the form of a highly coupled multi-variable linear model, representing the gasifier system of an integrated gasification combined cycle (IGCC) power plant. In particular, a straightforwardly tuned discrete-time PIP control system based on a reduced-order backward-shift model of the gasifier is found to yield good control of the benchmark, meeting most of the specified performance requirements at three different operating points

Proportional-integral-plus (PIP) control of the ALSTOM gasifier problem

Although it is able to exploit the full power of optimal state variable feedback within a non-minimum state-space (NMSS) setting, the proportional-integral-plus (PIP) controller is simple to implement and provides a logical extension of conventional proportional-integral and proportional-integral-derivative (PI/PID) controllers, with additional dynamic feedback and input compensators introduced automatically by the NMSS formulation of the problem when the process is of greater than first order or has appreciable pure time delays. The present paper applies the PIP methodology to the ALSTOM benchmark challenge, which takes the form of a highly coupled multi-variable linear model, representing the gasifier system of an integrated gasification combined cycle (IGCC) power plant. In particular, a straightforwardly tuned discrete-time PIP control system based on a reduced-order backward-shift model of the gasifier is found to yield good control of the benchmark, meeting most of the specified performance requirements at three different operating points