Sampled-Data Regulation Based on Realizable Reconstruction Filter

Abstract

This dissertation deals with the output feedback sampled-data regulation of a continuous system usually referred to as the plant. The output of the plant is required to asymptotically track a continuous reference signal, which in turn is assumed to be generated by an exogenous system. Only the samples of both the output of the plant as well as the reference signal are available for measurement. The problem is to design discrete observers for state estimation of both the plant and the exogenous system followed by a discrete controller. The discrete control signal generated by the controller is to be connected to the input of the plant by using some generalized hold device (GHD). The conventional zero order hold device is not a suitable candidate for tracking applications in general. A GHD incorporates required signal dynamics and hence captures the inter-sampling behavior through its impulsive nature. The result is an augmented system incorporating dynamics of the plant, exogenous system and GHD. The customary methods of designing a GHD may result in a higher order solution that could possibly compromise the stabilizability of the overall system. On the other hand, the classical reconstruction filter that recovers a continuous signal from its samples is not an option due to its non-causal nature. The commonly used approximations to the ideal reconstruction filter introduce a delay and hence are not suitable for closed-loop applications. A realizable reconstruction filter (RRF) is introduced in this dissertation that addresses the aforementioned limitations. RRF is essentially a specialized GHD that has its utility in both closed-loop and signal processing applications. The application of RRF for sampled-data regulation is explored for three important classes of systems. To begin with, a control scheme is developed for linear time invariant (LTI) systems. A couple of examples of its application on physical systems along with stability analysis demonstrate the effectiveness of the proposed scheme. Next, single input single output feedback linearizable systems are investigated in the framework of the suggested theory. An impulsive observer estimates the states and disturbances using samples of the plant output. Batch processed least square estimation for initialization results in improved transient behavior. Subsequently, a linearizing control enables to utilize the theory developed for LTI systems on this problem. The overall control scheme is demonstrated by examples. The proposed method is then extended to the sampled-data regulation of feedback linearizable MIMO systems with focus on n-link robotic manipulators. An example of PUMA 560 robotic manipulator is included in the discussion. A class of linear time varying systems can be transformed into LTI systems (usually though sinusoidal transformation). The consequence is that constant references get converted into sinusoidal signals. Active control of gyroscopic systems is one such example. This problem is also presented in the dissertation. Simulation of impulsive systems requires special considerations that are not handled by commonly available simulators. A simulation method is specifically developed for impulsive systems to facilitate closed-loop simulations.