Abstract. This paper considers a scalar plant with current parametric uncertainty in which only the input and output are measured. For such plants, an adaptive control design approach based on simplified adaptability conditions is presented. The approach refers to indirect self-tuning control using the current parametric identification algorithm and an implicit reference model. The tuned model structure in the identification algorithm is selected as simple as possible, corresponding to the main motion of the controlled plant and an elementary dynamic link or links. As a result, the current estimates in this model approximate the plant’s motion, which is confirmed by the convergence criterion of the identification residual. Also, it is required to satisfy definite requirements for the current parameter estimates. The estimates, even if imprecise, are used to construct a control law ensuring given properties of the closed-loop control system. This postulate is interpreted as a refinement of the well-known certainty equivalence principle except for the asymptotically accurate parameter estimation requirement to achieve adaptive properties of a self-tuning control system in output-feedback control problems. The main relationships are given for an example when the plant’s dominant dynamics are close to an oscillatory process without an additional time delay. The identification algorithm is applied in the form of a recurrent least-squares method with a forgetting factor and some modifications. Two illustrative examples of adaptive control system design are provided: control of the angular motion of an overhead crane and counteraction to the vibrations of an elastic three-mass drive. The approach under consideration is called the identification–approximation one. The possibilities and ways of its further improvement are outlined.
Keywords: adaptive control with self-tuning, current parametric uncertainty, current parametric identification algorithm, certainty equivalence principle, convergence of parameter estimates.
Acknowledgments. This work was supported by the Russian Science Foundation, project no. 23-29-00654; https://rscf.ru/project/23-29-00654/.
Adaptive Control of a Scalar Plant in the Input–Output Form Based on the Identification–Approximation Approach