Itzhak Barkana

Improving the performance of existing missile autopilot using simple adaptive control

Abstract A simple add-on adaptive control algorithm is presented. It is demonstrated via example that the performance of existing missile autopilot can be improved. The algorithm involves the synthesis of parallel feedforward which guarantees that the controlled plant is almost strictly positive real (ASPR). It is proved in the paper that such a parallel feedforward always exists. The proof is based on the parameterization of a set of stabilizing controllers. This parameterization enables straight-forward design and implementation of the add-on simple adaptive control (SAC) algorithm.

A modified invariance principle and gain convergence in adaptive control

In spite of successful implementations of simple adaptive control systems, the convergence of the adaptive control gains has remained an open question for more that 30 years. Moreover, the customary opinion is that the control gains do not actually converge and instead they may continue wandering without reaching any limit at all. Recently, this open question, that may give pause to practitioners and potential users of adaptive control, has recently been solved. The paper shows how a modified LaSalles invariance principle in combination with Gromwall-Bellman Lemma have finally allowed solving the gain convergence problem. It is shown that the control gains do reach a constant value at the end of a process of steepest descent error minimization, thus allowing the conclusion that simple and robust adaptive control systems can successfully be implemented in real-world systems.

ON OUTPUT FEEDBACK STABILITY AND PASSIVITY IN DISCRETE LINEAR SYSTEMS

Abstract Recent publications have shown that under some conditions continuous linear time-invariant systems become strictly positive real with constant feedback. This paper expands the applicability of this result to discrete linear systems. The paper shows the sufficient conditions that allow a discrete system to become stable and strictly passive via static (constant or nonstationary) output feedback.

ADAPTIVE MODEL TRACKING WITH MITIGATED PASSIVITY CONDITIONS

Abstract Standard passivity conditions in multivariable linear time-invariant systems [A, B, C] imply that the product CB must be positive definite symmetric. A recent paper has managed to mitigate the symmetry condition, requiring instead that the positive definite matrix CB be diagonalizable. Although the mitigated conditions were used to proving pure stabilizability with Adaptive Controllers, the Model Tracking question has remained open. This paper extends the previous results, showing that the mitigated conditions can be used to guarantee both stability and asymptotically perfect model tracking.

Improving performance of servo systems using adaptive control

A simple Add-On adaptive control algorithm is presented that can improve the performance of any stable linear time-invariant plant. It is proved that such algorithm always exists. The proof is constructive and shows that it is simple and straight forward to design and implement the control algorithm. The algorithm is presented as a set of equations and in a block diagram that demonstrate the simplicity of the algorithm. It is demonstrated that this approach completely solves the portability problem. The paper is oriented towards the practitioner and therefore any proof that already appears in the literature is only cited. An example demonstrates the improvement in performance.

SPR and ASPR Untangled

Abstract The theory, proofs, use and implementation of robust adaptive control algorithms require the understanding of the concepts of Strictly Positive Real (SPR) and Almost Strictly Positive Real (ASPR) plants. Although these concepts are defined in the existing literature, both in time and frequency domains, their grasp is not straight forward for the practicing control engineer that deals with real-world plants. Here, we attempt to present the interpretation and meaning of these concepts in a more intuitive way for the practicing control engineer. That is, we use the Bode, Nyquist, Nichols and Root-Locus domains that may help the control engineer better grasp their implications. The paper is oriented towards the practitioner and therefore any proof that already appears in the literature is only cited. An important result that is formalized and proved is that any stable system can be made ASPR. An example is also given in order to demonstrate these concepts.

On implementing passivity in discrete linear systems

Recent publications have shown that under some conditions continuous linear time-invariant systems become strictly positive real with constant feedback. This paper expands the applicability of this result to discrete linear systems. The paper shows the sufficient conditions that allow a discrete system to become stable and strictly passive via static (constant or nonstationary) output feedback. However, as the passivity conditions require a direct input-output connection that ends in an algebraic loop that includes the adaptive or nonlinear controller, they have been considered to be impossible to implement in realistic discrete-time systems. Therefore, this paper also finally solves the apparently inherent algebraic loop, thus allowing satisfaction of the passivity condition and implementation of adaptive and nonlinear control techniques in discrete-time positive real systems.

Simple implementation of Almost Passivity in PID controlled systems

The theory, use and implementation of robust adaptive control algorithms require the understanding of Passivity and Almost Passivity. For LTI system these are the Strictly Positive Realness (SPR) and Almost Strictly Positive Realness (ASPR) concepts. Although these concepts have been defined in the existing literature, their grasp is not straightforward for the practicing control engineer that deals with real-world plants. In an attempt to present the interpretation and meaning of these concepts in a more intuitive way, in this paper we use various frequency domains illustrations that may help the control engineer better grasp their implications. An important result that is formalized and proved is that any system controlled by PID controller can be made to become ASPR and thus, robust adaptive control can be used towards improvement of performance. An example is also given in order to demonstrate these concepts.

SIMPLE ADAPTIVE CONTROL - A STABLE DIRECT MODEL REFERENCE ADAPTIVE CONTROL METHODOLOGY - BRIEF SURVEY

Abstract In spite of successful proofs of stability and even successful demonstrations of performance, the use of Model Reference Adaptive Control (MRAC) methodologies in practical real world systems has met a rather strong resistance from practitioners and has remained very limited. Apparently, the practitioners have a hard time understanding the conditions for stable operations of adaptive control systems under realistic operational environments. Besides, it is difficult to measure the robustness of adaptive control system stability when compared with the common measure of phase margin and gain margin that is utilized by present, mainly LTI, controllers. This paper attempts to revisit the fundamental qualities of the common gradient-based MRAC methodology and to show that some of its basic drawbacks have been addressed and eliminated within the so-called Simple Adaptive Control methodology. Sufficient conditions that guarantee stability are clearly stated and lead to similarly clear proofs of stability and to successful and stable applications of SAC.

On stability and gain convergence in discrete simple adaptive control

Abstract Successful implementations of simple direct adaptive control techniques in various domains of application have been presented over the last two decades in the technical literature. The theoretical background concerning basic conditions needed for stability of the controller and the open questions relating the convergence of the adaptive gains have been recently clarified, yet only for the continuous-time algorithms. Apparently, asymptotic tracking in discrete time systems is possible only with step input commands and the scope of the so called “almost strictly positive real” condition is also not clear. This paper will expand the feasibility of discrete simple adaptive control methodology to include any desired input commands and almost all real-world systems. The proofs of stability are also rigorously revised to solve the ultimate adaptive gain values question that has remained open until now.