Rafael M. Morales

The Robustness and Design of Constrained Cross-Directional Control Via Integral Quadratic Constraints

A robust stability test for a class of constrained cross-directional controllers is found. Under special circumstances, the stability test is executed on a mode-by-mode basis and greatly simplified to a frequency-domain criterion. The test is also exploited to develop tuning algorithms. The control system involves a quadratic program embedded within an internal model control antiwindup structure and achieves optimal steady-state performance when the plant is known. Both the nonlinearity in the controller and the plant uncertainty satisfy certain integral quadratic inequalities. This allows us to obtain conditions for robust stability that can be expressed as linear matrix inequalities via the Kalman-Yakubovich-Popov lemma.

Anti-windup and the preservation of robustness against structured norm-bounded uncertainty

Abstract We consider robustness preserving anti-windup with structured norm-bounded uncertainty. A sufficient condition for the existence of such anti-windup is given, together with an expression for its construction. Existing results in the literature for additive unstructured uncertainty appear as a special case. The so-called IMC (internal model control) anti-windup does not necessarily preserve robustness for the general case.

Robustness preserving antiwindup: Examples and counterexamples

An anti-windup scheme is said to be robustness preserving if it inherits the robustness properties of the corresponding unsaturated loop. It has recently been shown in the literature that anti-windup based on internal model control preserves robustness against additive uncertainty. In this paper we illustrate examples where other anti-windup schemes are also robustness preserving. We also demonstrate by counterexample that internal model control need not preserve robustness against multiplicative uncertainty. We consider both single-input single-output and multivariable control loops.

Alternative representations of frequency-domain constraints for improved performance in on-blade control systems

Future rotorcraft technologies are being researched and developed for the next generation of helicopters that embed active elements in the main rotor blades to improve vibration, noise and performance. On-blade control algorithms restrict the control actions to a finite consecutive number of Fourier coefficients of a periodic control signal. Recently, Quadratic Programming (QP) has been applied to on-blade control methods to compensate against actuator output constraints. Typically in the literature, box or ∞-norm constraints on selected Fourier coefficients are considered for the optimisation problem. However, this works shows that such constraints are inadequate as they can lead to conservative performance, especially as the dimension of the optimisation problem increases. Hence this paper proposes an alternative QP method based on 1-norm constraints that can achieve performance improvements for such applications. The control ideas are applied to a representative vibration reduction system with active trailing edge flap actuators.

Robustness preserving anti-windup for SISO systems

A control feedback system with saturation nonlinearities is said to have robustness preserving characteristics if the constrained system is as robust as its linear counterpart. Such characteristics can be desirable. It has been proved for some special cases that the anti-windup version of the Internal Model Control architecture can offer such characteristics for first-order plants with delays against norm-bounded (not only LTI) uncertainty. This paper provides general conditions expressed in the frequency domain which allow to test for the preservation of robustness for plants of any order. In addition, a class of robustness preserving controllers is characterised in terms of the Zames-Falb conditions. The test is shown to be easily implementable and exploited for anti-windup tuning.

Robust Stability Analysis of Constrained Cross-Directional Control via Integral Quadratic Constraints

A robust stability test for a class of constrained cross-directional controllers is proposed. The cross-directional controller involves a quadratic program embedded within an internal model control structure and achieves optimal steady-state performance when the plant is fully known. Both the non-linearity in the controller and the unmodeled plant dynamics satisfy certain integral quadratic inequalities. This allows us to obtain conditions for robust stability that can be expressed as linear matrix inequalities via the KYP lemma. Circumstances in which the results can be exploited to decompose the control design into modes are also discussed

Robust analysis of Principal Components active control via IQCs

Principal Component algorithms are widely used in active control applications, specially for applications of active vibration and noise cancellation in the aerospace industry. They are known to offer good adaptability characteristics and also provide a intuitive approach to deal with actuator saturation by limiting the control only to a significant number of modes. Existing stability results for such PC applications are only provided for nominal scenarios and plant uncertainty. The contribution of this paper is to apply the theory of Integral Quadratic Constraints (IQCs) in order to find more general stability criteria when scaling of the control actions take place and estimation of modelling errors coexist. The robustness criterion is expressed as an Linear Matrix Inequality. Stability results are shown with a simulation example.