Tracking Control of High Order Input Reference Using Integrals State Feedback and Coefficient Diagram Method Tuning

The purpose of the research is tracking control to follow the input reference signal such as step, ramp, parabolic, and high order reference stably. The challenge is rising when high order input references, such as parabolic or polynomial, are used in the advanced system. Like in satellite and missile launcher systems, the triple integrator systems have to follow parabolic or polynomial trajectory with high stability required. The research proposed an integrals state feedback controller to combine simple state feedback control with cascade-layered integral control. The order of the input reference defines the structure and number of integrals used. Along with Coefficient Diagram Method in its tuning process, the proposed controller is guaranteed to have good stability and zero steady-state error. Simulation results and mathematical proofs of stability and zero steady-state error are provided on the paper. The proposed method can follow various input references such as the ramp, parabolic, polynomial, and higher-order reference based on the simulation and mathematical proofs. The stability using the pole location also shown the negative poles that give a stable system

Optimal length and signal amplification in weakly activated signal transduction cascades

Weakly activated signaling cascades can be modeled as linear systems. The input-to-output transfer function and the internal gain of a linear system, provide natural measures for the propagation of the input signal down the cascade and for the characterization of the final outcome. The most efficient design of a cascade for generating sharp signals, is obtained by choosing all the off rates equal, and a ``universal'' finite optimal length.Comment: 27 pages, 10 figures, LaTeX fil

Zero overshoot and fast transient response using a fuzzy logic controller

In some industrial process control systems it is desirable not to allow an overshoot beyond the setpoint or a threshold, this could be a safety constraint or the requirement of the system. This paper outlines our work in designing a fuzzy PID controller to achieve a step-response with zero overshoot while improving the output transient response. Our designed fuzzy PID controller is applied to stable, marginally stable and unstable systems and their step responses are compared with a tuned conventional PID controller. A comparative case study shows that the proposed fuzzy controller is highly effective and outperforms the PID controller in achieving a zero overshoot response and enhancing the output transient response

Sampling from a system-theoretic viewpoint

This paper studies a system-theoretic approach to the problem of reconstructing an analog signal from its samples. The idea, borrowed from earlier treatments in the control literature, is to address the problem as a hybrid model-matching problem in which performance is measured by system norms. \ud \ud The paper is split into three parts. In Part I we present the paradigm and revise the lifting technique, which is our main technical tool. In Part II optimal samplers and holds are designed for various analog signal reconstruction problems. In some cases one component is fixed while the remaining are designed, in other cases all three components are designed simultaneously. No causality requirements are imposed in Part II, which allows to use frequency domain arguments, in particular the lifted frequency response as introduced in Part I. In Part III the main emphasis is placed on a systematic incorporation of causality constraints into the optimal design of reconstructors. We consider reconstruction problems, in which the sampling (acquisition) device is given and the performance is measured by the $L^2$-norm of the reconstruction error. The problem is solved under the constraint that the optimal reconstructor is $l$-causal for a given $l\geq 0,$ i.e., that its impulse response is zero in the time interval $(-\infty,-l h),$ where $h$ is the sampling period. We derive a closed-form state-space solution of the problem, which is based on the spectral factorization of a rational transfer function

Structurally robust biological networks

Background: The molecular circuitry of living organisms performs remarkably robust regulatory tasks, despite the often intrinsic variability of its components. A large body of research has in fact highlighted that robustness is often a structural property of biological systems. However, there are few systematic methods to mathematically model and describe structural robustness. With a few exceptions, numerical studies are often the preferred approach to this type of investigation. Results: In this paper, we propose a framework to analyze robust stability of equilibria in biological networks. We employ Lyapunov and invariant sets theory, focusing on the structure of ordinary differential equation models. Without resorting to extensive numerical simulations, often necessary to explore the behavior of a model in its parameter space, we provide rigorous proofs of robust stability of known bio-molecular networks. Our results are in line with existing literature. Conclusions: The impact of our results is twofold: on the one hand, we highlight that classical and simple control theory methods are extremely useful to characterize the behavior of biological networks analytically. On the other hand, we are able to demonstrate that some biological networks are robust thanks to their structure and some qualitative properties of the interactions, regardless of the specific values of their parameters