Pole assignment by multirate sampled-data output feedback

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, a multirate sampled-data ‘gain‘ controller can always be constructed so that the poles of the closed-loop system become an arbitrarily-given symmetric set of complex numbers. It is also shown that the input sampling rate (JV,,[tdot],NJ can be chosen equal to the Kronecker invariants, or other locally minimum controllability indices. Here, ‘locally minimum controllability indices’ are defined as a set of integers (nlt[tdot], nm) such that ≪(+n2+[tdot]+ m, equals the dimension of the state vector and the matrix [b, [tdot] A‴∼1b1[tdot] bm[tdot] A″ m∼ 'b] is non-singular. This capability gives a new perspective to the application of multirate sampled-data controllers.

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.

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.

A frequency analysis procedure for single and multirate sampled-data control systems is presented. The method is taking the inter-sample behaviour into account, and for a sinusoidal input the system power gain is calculated. Also the close correspondence between this method and the principal gain for continuous-time MIMO systems is discussed. Finally our method is illustrated on a sampled-data SISO system.

Design of a sampled-data state feedback controller for stabilizing a nonlinear continuous-time plant is studied. The sampled-data state feedback controller is designed based on an approximate discrete-time model of the plant and it is able to exponentially stabilize the approximate discrete-time model. When the sampled-data controller applies to the continuous-time plant, the closed loop system is a hybrid system. This paper gives a sufficient condition under which the sampled-data controller exponentially stabilizes the hybrid system consisting of the continuous-time plant and the sampled-data controller.

This article, presents discrete sliding mode control algorithm using multirate output feedback for control of stepper motor. The algorithm developed by the authors uses past output samples and past control inputs. When all the states of the system are neither physical variable nor available for measurement, multirate output feedback can be used. The stepper motor is known to be a differentially flat system. The dynamics of the stepper motor are highly nonlinear, hence feedback linearization based on endogenous feedback has been used. The linear model is obtained and multirate output feedback-based discrete sliding mode control has been designed. The discrete sliding mode control with multirate output feedback has been applied for regulator as well as tracking case for the motor. The proposed algorithm uses only two outputs. It is essentially shown that first output needs to be sampled only once and second output must be sampled at least thrice in every τ sampling interval in order to achieve acceptable performance. The system parameter variation has been considered and the results obtained are found to be satisfactory. Thus, it has been shown that discrete sliding mode control algorithm using multirate output feed back can be extended to a class of nonlinear MIMO system.

For a class of inherently nonlinear systems with uncertain parameters, the global stabilization problem via sampled-data control is investigated in this paper. First of all,based on the technique of adding a power integrator and a recursive argument, a class of sampled-data state feedback controllers are proposed. Then under the proposed controller, by using a suitable Lyapunov functional, it is shown that there is a maximum allowable sampling period which can guarantee the global asymptotical stability of the closed-loop system. Since the proposed controller is discrete-time, it can be easily implemented by computers. Finally, an example is given to verify the efficiency of the proposed method.

This paper investigates the global output feedback sampled-data control of a class of nonlinear systems with mismatched disturbances. A linear state observer is constructed to estimate the states. A disturbance observer is designed to estimate the mismatched disturbances. The sampled-data controller is proposed with the estimated states and the estimated disturbances. The output feedback controller can ensure that the nonlinear system is globally stable. Finally, an example is given to show the effectiveness of the proposed control scheme.

Pole assignment is a well-established controller synthesis technique used in control engineering. An important drawback of the pole assignment technique is poor numerical accuracy of the resulting compensators especially for high order systems, when fixed precision arithmetic is used in calculations. Obviously there are several parameters that affect the performance of the pole assignment algorithms. It has been, for example, already shown that increasing the order of the system causes an exponential increase in the numerical errors made in pole assignment. In this paper, the effect of the ratio of real poles to all poles of the open-loop (and closed-loop) system (real pole ratio - RPR) to the performance of the pole assignment algorithms is investigated for the first time.

Extended dissipative exponential synchronization of complex dynamical systems with coupling delay and sampled-data control

Synchronization of memristive BAM neural networks with leakage delay and additive time-varying delay components via sampled-data control

An adaptive control algorithm that insures global stabilization for a class of (possibly nonstably invertible) linear time invariant discrete-time plants of known order is given. An essential feature of our controller is that no appeal is made to persistency of excitation arguments or the use of projections.

We apply certain recent results pertaining to the rank minimization problem under LMI constraints to determine non-trivial lower and upper bounds for the minimal order dynamic output feedback which stabilizes a given linear time invariant plant, via semi-definite programs.

This paper presents a variational approach to H/sup /spl infin// control with transients in the state feedback case. The problem was formulated in Khargonekar et al. (1991). The approach here provides a precise description with equality, instead of inequality, in the necessary and sufficient conditions for the existence of a linear controller. Furthermore, the solution existence and uniqueness are also proved in terms of certain properties of the indefinite Riccati equations derived in this paper. The linear time-variant plant (LTV) on a finite horizon is considered first, and then the results are extended to the linear time-invariant (LTIV) plant on an infinite horizon. By this approach, it can be directly concluded that only sub-optimal H/sup /spl infin// state feedback control can be achieved from an input/output point of view and that the performance measure /spl gamma/(/spl mu//sup 1/2/ used in this paper) is a strict upper bound.

An anti-windup technique for LMI regions