LTI Compensator Research Articles

On a generalized fractional-order LTI compensator: exact formulas for compensation at two different frequencies

Nowadays, design and tuning of controllers with predefined structures are among the most popular topics in control system theory. During the last decade, many studies have focused on designing fixed-structure fractional-order compensators. This paper presents a generalized version of fractional-order compensators to achieve the required magnitudes and phases at two given frequencies (for example, to achieve desired phase and gain margins with adjustable cross frequencies). In this generalization, at first some basic analysis of the phase behaviour of this introduced type of fractional-order compensators is presented. Also, exact formulas are found for designing this family of compensators in order to provide the aforementioned control objective. Finally, a numerical example is presented to confirm the effectiveness of the proposed design method in control systems.

Synthesis of modulated–demodulated control systems

We propose systematic design methods for realization of a given LTI compensator with complex poles using a modulated–demodulated control framework. Applicability of the proposed realization methods is established through simulations performed on an undamped resonant plant compensated by a low gain controller to obtain better noise rejection performance. It is demonstrated how a modulated–demodulated structure may reduce the sampling rate in a hybrid control system. In addition, superior robust performance is achieved against variations in baseband parameters using direct reference injection into the modulated–demodulated control systems compared to the indirect injection approach.

Delay-Independent Stability of Reset Systems

Reset control systems have potential advantages to overcome fundamental limitations of LTI compensation. However, since a reset compensator may destabilize a stable base LTI system, stability needs to be guaranteed in advance for a proper practical application of reset control. This works extends previous stability results of reset control systems to consider the case of LTI plants with time-delays. Stability independent of the delay criteria are developed both by means of LMIs and in the frequency domain by using the KYP Lemma.

The Periodic Optimality of LQ Controllers Satisfying Strong Stabilization

A II test is presented for determining when a controller with periodic gains is superior to a LTI compensator for a class of LQ strong stabilization problems. For systems with strictly proper transfer functions, it is proven that stable high frequency periodic controllers based on weak variations from the LTI case cannot give better performance than stable LTI compensators. In the development, a means to evaluate the second partials of functions with respect to matrix valued parameters is introduced. Two examples detailing the application of the n test are provided.

Formula omitted] and [formula omitted] optimal controllers for periodic and multirate systems

In this paper we present the solutions to the optimal l 2 to l 2 disturbance rejection problem ( H ∞ ) as well as to the LQG ( H 2 ) problem in periodic systems using the lifting technique. Both problems involve a causality condition on the optimal LTI compensator when viewed in the lifted domain. The H ∞ problem is solved using Nehari's theorem whereas in the H 2 problem the solution is obtained using the Projection theorem. Exactly the same methods of solution can be applied in the case of multirate sampled data systems. Finally, stability robustness issues in periodic and multirate systems are analyzed.

On the gain margin improvement using dynamic compensation based on generalized sampled-data hold functions

This paper shows that the use of dynamic compensation based on generalized sampled-data hold functions (GSHF) can arbitrarily improve the gain margin for continuous-time nonminimum phase linear systems. The GSHF compensator is a particular periodic digital controller. The effect of sampling period on the gain margin is analyzed. Furthermore, it is proved that under a mild condition, the gain margin improvement can be achieved without forcing the sampling period small. An important advantage of periodic compensation over LTI compensation is found to be the capability of reducing conflict between gain margin and sensitivity. >

Simultaneous stabilization using an LTI compensator with a sampler and hold

This paper considers problems of simultaneous stabilization using a linear time-invariant compensator incorporated with a sampler and zeroth-order hold function. It is shown that this controller strongly stabilizes a number of plants which may not be stabilizable by a conventional linear time-invariant controller. A controller design procedure is given which is illustrated by an example.