Ambrose A. Adegbege

Directionality compensation for linear multivariable anti-windup synthesis

We develop new synthesis procedures for optimising anti-windup control applicable to open-loop exponentially stable multivariable plants subject to hard bounds on the inputs. The optimising anti-windup control falls into a class of compensator commonly termed directionality compensation. The computation of the control involves the online solution of a low-order quadratic programme in place of simple saturation. We exploit the structure of the quadratic programme to incorporate directionality information into the offline anti-windup synthesis using a decoupled architecture similar to that proposed in the literature for anti-windup schemes with simple saturation. We demonstrate the effectiveness of the design compared to several schemes using a simulated example.

Multivariable algebraic loops with complementarity constraints enforcing some KKT conditions

In this paper, we address the wellposedness and online resolution of algebraic loop arising from the feedback interconnection of a linear time invariant system and a static nonlinearity whose input-output characteristics enforce some KKT optimality conditions. We establish sufficient conditions for the wellposedness of such algebraic loops using the theory of linear complementarity problems. In particular, we show that wellposedness is equivalent to the existence and uniqueness of solution of a convex optimization problem for which efficient solution algorithms are well established. The application of the results to constrained control problem is illustrated using a multivariable antiwindup design.

Multivariable algebraic loops in linear anti-windup implementations

This paper addresses the implementation aspects of multivariable algebraic loops which arise naturally in many anti-windup control schemes. Using the machinery of linear complementarity problems, a unified framework is developed for establishing well-posedness of such algebraic loops. Enforcing well-posedness is reduced to a feasibility problem that can be solved during the anti-windup design stage. Several existing anti-windup implementations appear as special cases of the unified framework presented in this paper.

Anti-windup synthesis for optimizing internal model control

We develop new design procedures for optimizing anti-windup control applicable to open-loop stable multivariable plants subject to input saturations. The optimizing anti-windup control falls into a class of compensator commonly termed directionality compensation. The computation of the control involves the on-line solution of a low-order quadratic program in place of simple saturation. We exploit the equivalence of the quadratic program to a feedthrough term in parallel with a deadzone-like nonlinearity that satisfies a sector bound condition. This allows for LMI-based anti-windup synthesis using a decoupled structure similar to that proposed in the literature for anti-windup schemes with simple saturation. We demonstrate the effectiveness of the design compared to several schemes using a highly ill-conditioned benchmark example.

Analog circuit for real-time optimization of constrained control

This paper proposes a fast analog circuit implementation for naturally occurring optimization problems in constrained control. This class of problems may be expressed as the feedback interconnection of static nonlinearities and a feedback gain, and has recently received significant interest. The circuit is shown to be globally convergent and stable for a large class of feedback gains which generalizes existing results to cases where the feedback gain may be asymmetric. The proposed implementation is practical and can be realized directly with passive components and operational amplifiers or with a field programmable analog array (FPAA). Examples including MATLAB and Orcad PSpice simulations are included to demonstrate the effectiveness of the solution.

Programmable logic controller based embedded quadratic programming for input-constrained internal model control

Advanced control algorithms such as optimization-based controls are known to offer superior performance as well as systematic constraints handling when compared to classical control strategies. However, the complexity of such advanced control methods makes their implementations difficult, especially on controllers with limited computational capacity such as the programmable logic controllers (PLC). This paper presents the capability of a low-cost low-end PLC for online computation of advanced control. In particular, an online quadratic program within the framework of input-constrained internal model control is implemented, and the effectiveness is illustrated using a hardware-in-the-loop experiment.

Projected Gauss-Seidel algorithm for multivariable algebraic loops with applications to constrained control

This paper proposes a matrix splitting strategy based on the Projected Gauss-Seidel algorithm for the solution of multivariable algebraic loops arising naturally in many constrained control problems. The solution algorithm is globally convergent for a very large class of problems and is orders of magnitude faster than several existing algorithms in the literature. The Projected Gauss-Seidel algorithm is easy to implement with a very minimal computation per iteration and shows promise for real-time and embedded control applications where a fast but approximate solution is of the essence.

A Gauss–Seidel type solver for the fast computation of input-constrained control systems

Abstract An important class of nonlinear control systems can be represented as the feedback interconnection of two parts: a linear time-invariant system and a block of decentralized nonlinearities. When the linear time-invariant part has a nontrivial feedthrough term or the nonlinearity has a feedback gain, control computation involves the online implementation of a multivariable algebraic loop which must be resolved at each sampling instant. The requirements for such online computation may result in several implementation issues, especially in real-time and embedded control applications. This paper considers the implementation of such algebraic loops arising from several input-constrained systems. The proposed solution algorithm is globally convergent for a very large class of feedthrough or feedback gains and shows promise for real-time and embedded control applications where a fast but approximate solution is of the essence.

Robust Anti-windup Synthesis for Directionality Compensation

Abstract We develop new robust synthesis procedures for linear and open-loop exponentially stable multivariable plants subject to input nonlinearities expressed by a quadratic program and incorporating infinity-norm bounded plant uncertainties. The resulting anti-windup control falls into a class of compensators commonly termed directionality compensation. We note that the input-output maps of both the nonlinearities and the uncertainties satisfy certain integral quadratic constraints (IQCs). Thus, the anti-windup synthesis can be reduced to a feasibility problem involving a set of linear matrix inequalities (LMIs). The well-posedness condition of the algebraic loop arising from the anti-windup interconnection is equivalent to the existence and uniqueness of a solution to a convex optimization problem for which efficient solutions are well established. We demonstrate the effectiveness of the design compared to several schemes using a highly ill-conditioned benchmark example.

Stability conditions for constrained two-stage internal model control

A robust stability test for a two-stage internal model control (IMC) antiwindup is presented. The two-stage IMC antiwindup scheme guarantees optimal closed loop performance both at transient and at steady state by solving two quadratic programs (QPs) online at each time step. The controller input-output mappings satisfy certain integral quadratic constraints (IQCs) and thus robust stability conditions can be constructed against any infinity-norm bounded uncertainty. The test is illustrated for a two-input two-output plant with left matrix fraction uncertainty.