Frequency analysis for single and multirate sampled-data control

Basing on lifting technology, this paper researches a design method for multirate sampled-data control system in the background of flight control system design, which consummates the theory of multirate sampled-date control system design for further steps, and provides a method to design multirate sampled-data controller. As the reason of uncertainty in the aircraft model and the need of different sampling frequencies in different control loops, H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> -optimal multirate sampled-data control is considered. First, multirate sampled-data control system is outlined, and then the signal description are presented. Because of multirate sampled-data system is time-variant, the direct digital controller design becomes difficult. The equivalent discrete time-invariant systems can be converted from the linear time-variant systems through lifting technology. Then the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> discretization of multirate sampled-data systems is researched. After the sampled-data control system was lifted, the equivalent L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> [0, h) -induced norm is proven. Base on the above, the method of H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> -optimal multirate sampled-data control is summarized. A height control is simulated using a simplified aircraft model to illustrate the design. The simulation shows that the multirate Sampled-data control system can achieve the satisfactory objective accurately and optimally.

This paper presents an analytic design of multirate controllers to guarantee stable haptic interaction and high fidelity. When the reflective force is computed by using slowly simulated virtual model, the control frequency of the conventional controller becomes low. This increases the zero-order-hold effect, and makes the system unstable. We propose a multirate control method to reduce the zero-order-hold effect. The multirate controller is implemented by adding a high frequency controller to the conventional controller. The high-frequency controller is designed to compensate the energy generated by the conventional controller. The stability analysis of the multirate haptic control system shows that the stiffness of the virtual model can be increased while maintaining the stability. A nonlinear virtual coupling is designed using this multirate control scheme. The multirate controller is evaluated by mathematical analysis and experiments.

Multirate sampled-data control of a linear time-invariant continuous-time plant is considered. It is shown that, if the plant is controllable and observable, we can always construct a multirate sampled-data gain controller such that the poles of the closed-loop system become a given symmetric set of n complex numbers (n is the dimension of the state vector of the plant). It is also shown that the input sampling rate {N1,...,Np} can be chosen equal to the Kronecker invariants or other "locally minimum controllability indices." This capability gives a new perspective to the application of multirate sampled-data controllers.

This paper is concerned with haptic simulation in multi-user virtual environments in which the users can haptically interact in a shared virtual world from separate workstations over an Ethernet local-area Network (LAN). High-fidelity haptic rendering requires a minimum control update rate of 1000Hz which is beyond the capability of popular network protocols such as the UDP and TCP/IP. Consequently, a multi-rate control strategy is adopted in which local force-feedback loops are executed at higher rates than data packet transmission between the user workstations. Two control architectures, i.e. centralized and distributed, are presented and their stability margins are compared. Two methods for mathematical modelling and analysis of the proposed multi-rate haptic control systems are examined. Analytical and experimental results demonstrate that the distributed control architecture is superior to the centralized controller from performance and stability perspectives. This is confirmed through experiments with a dual-user dual-finger haptic rendering platform.

Multirate, sampled-data control systems are analyzed in the frequency domain, taking the inter-sample behavior into account. The focus of the analysis is both on the rejection of disturbances within a certain frequency region, and on the robust stability properties. Due to the periodic behavior of such systems, a distinction is made between the performance frequency response (PFR) and the robust frequency response (RFR). The RFR is related to current frequency response approaches for sampled-data systems.

We consider multirate digital control systems which consist of an interconnection of a continuous-time nonlinear plant (described by ordinary differential equations) and a digital lifted controller (described by ordinary difference equations). The input to the digital controller consists of the multirate sampled output of the plant and the input to the continuous-time plant consists of the multirate hold output of the digital controller. We show that when quantizer nonlinearities are neglected, then under reasonable conditions (which exclude the critical cases), the stability properties (in the Lyapunov sense) of the trivial solution of the nonlinear multirate digital control system can be deduced from the stability properties of the trivial solution of its linearization. When quantizer nonlinearities are not neglected, corresponding results can be established for Lagrange stability rather than Lyapunov stability of an equilibrium.

In this paper, we study robust stability and stabilizability of sampled-data control systems composed of a continuous-time plant and a discrete-time compensator together with sample/hold devices, using the frequency domain method. Our study is not confined only to the case of standard (i.e., single-rate) sampled-data controllers but also extended to the case of multirate sampled-data controllers. Specifically, we compare, by numerical examples, the tolerable amounts of the uncertainty of a given continuous-time plant for which the robust stabilization can be attained in the three cases: the cases of a continuous-time controller, a single-rate sampled-data controller, and a multirate sampled-data controller. The result will be useful for estimating the deterioration caused by use of sampled-data controllers in place of continuous ones, or evaluating the advantages of the multirate sampled-data scheme over the standard one.

Design of Consensus Controllers for Multi-rate Sampled-data Strict-Feedback Multi-agent Systems

In haptic communication via the network, transmission period is not able to be designed uniquely since it restricted by the line bandwidth, transmission protocol, hardware constraints and so on. To address this problem, downsampling is often employed. Additionally, to enhance the performance of downsampled system, multirate control is proposed. However, the quantitative analysis on downsampling and multirate control are not treated. Therefore, this paper treats downsampling and multirate control system, and performs quantitative analysis by using hybrid parameter. In order to reveal the most effective combination of holder and single or multirate, holders (ZOH, DFOH and PFOH) are considered explicitly, and it is formulated to Laplace domain. The effectiveness of each combination is verified through experiments.

This paper presents an optimization-based algorithm for state estimation of multirate digital control systems. The algorithm features a predictor estimator structure and it is derived by employing a time invariant modelling approach to multirate systems. Special care is taken to ensure the causality of the derived estimation algorithm and to reduce the dimensionality inherent in multirate system modelling while maintaining a reasonably simple implementation. The proposed algorithm is developed to ensure convergence in state estimation between base sampling instants as well as between model rate sampling instants.

Internet-based control is the way of monitoring and adjusting plants from a remote site over the Internet. The major challenge of this new kind of control systems is how to deal with Internet time delay. Our recent study illustrated that there is a great potential to overcome Internet time delay from the control system architecture aspect such as by using multi-rate control schemes. In this paper, we formulate a new class of dual-rate control systems with Internet time delay at both feedback and feed-forward channels and investigate their asymptotic stability properties. Some new necessary and sufficient criteria of asymptotic stability for such dual-rate control systems are established. Two examples are given to illustrate the effectiveness of the theoretical results.

Neutralizing zero dynamics attack on sampled-data systems via generalized holds

Automatica Prize Paper Awards 2014

This paper considers robust control design for large-scale uncertain systems with state, input and output overlapping decompositions. The extension principle, which is a generalized notion of overlapping decomposition, is investigated from a robust control viewpoint. It is shown that if a controller designed for the expanded system achieves robustness in the expanded spaces, then the contracted controller achieves required robustness of the original system. This paper also defines and develops a framework of the extension principle for multirate control systems with hybrid signals. An approach to robust performance design with the overlapping multirate control is proposed.

The main results in inherent design limitations for linear single rate sampled data feedback system are extended to SISO output multirate control case in this paper. It turns out that just as in single rate control, unstable plant poles, non-minimum phase plant zeros, non-minimum phase hold zeros and non-minimum phase controller zeros also impose significant design constraints on the SISO output multi-rate feedback control. Moreover, compared with single rate control extra constraints will apply because of the multirate sampling control.