In-domain control of a heat equation: an approach combining zero-dynamics inverse and differential flatness

This paper addresses the set-point control problem of a heat equation with in-domain actuation. The proposed scheme is based on the framework of zero dynamics inverse combined with flat system control. Moreover, the set-point control is cast into a motion planing problem of a multiple-input, multiple-out system, which is solved by a Green's function-based reference trajectory decomposition. The validity of the proposed method is assessed through convergence and solvability analysis of the control algorithm. The performance of the developed control scheme and the viability of the proposed approach are confirmed by numerical simulation of a representative system.Comment: Preprint of an original research pape

Robust Controllers for Regular Linear Systems with Infinite-Dimensional Exosystems

We construct two error feedback controllers for robust output tracking and disturbance rejection of a regular linear system with nonsmooth reference and disturbance signals. We show that for sufficiently smooth signals the output converges to the reference at a rate that depends on the behaviour of the transfer function of the plant on the imaginary axis. In addition, we construct a controller that can be designed to achieve robustness with respect to a given class of uncertainties in the system, and present a novel controller structure for output tracking and disturbance rejection without the robustness requirement. We also generalize the internal model principle for regular linear systems with boundary disturbance and for controllers with unbounded input and output operators. The construction of controllers is illustrated with an example where we consider output tracking of a nonsmooth periodic reference signal for a two-dimensional heat equation with boundary control and observation, and with periodic disturbances on the boundary.Comment: 30 pages, 3 figures, to appear in SIAM Journal on Control & Optimizatio

MIMO First and Second Order Discrete Sliding Mode Controls of Uncertain Linear Systems under Implementation Imprecisions

The performance of a conventional model-based controller significantly depends on the accuracy of the modeled dynamics. The model of a plant's dynamics is subjected to errors in estimating the numerical values of the physical parameters, and variations over operating environment conditions and time. These errors and variations in the parameters of a model are the major sources of uncertainty within the controller structure. Digital implementation of controller software on an actual electronic control unit (ECU) introduces another layer of uncertainty at the controller inputs/outputs. The implementation uncertainties are mostly due to data sampling and quantization via the analog-to-digital conversion (ADC) unit. The failure to address the model and ADC uncertainties during the early stages of a controller design cycle results in a costly and time consuming verification and validation (V&V) process. In this paper, new formulations of the first and second order discrete sliding mode controllers (DSMC) are presented for a general class of uncertain linear systems. The knowledge of the ADC imprecisions is incorporated into the proposed DSMCs via an online ADC uncertainty prediction mechanism to improve the controller robustness characteristics. Moreover, the DSMCs are equipped with adaptation laws to remove two different types of modeling uncertainties (multiplicative and additive) from the parameters of the linear system model. The proposed adaptive DSMCs are evaluated on a DC motor speed control problem in real-time using a processor-in-the-loop (PIL) setup with an actual ECU. The results show that the proposed SISO and MIMO second order DSMCs improve the conventional SISO first order DSMC tracking performance by 69% and 84%, respectively. Moreover, the proposed adaptation mechanism is able to remove the uncertainties in the model by up to 90%.Comment: 10 pages, 11 figures, ASME 2017 Dynamic Systems and Control Conferenc