Feedback Control Design for Time-Delay Systems Based on the Manabe Polynomial Concept Under Unmodeled Input Delay

The proportional-integral-derivative (PID) controller design for time-delay systems is a classical problem. We consider a general case where the three controller gains (k P , k I , and k D ) and the delay (τ) are all treated as free parameters. Our objective is to characterize the stability set in the parameter space of (k P ; k I ; k D ; τ). The problem is very involved due to the theoretical difficulties. In this paper, we introduce a MATLAB-based toolbox, called PID-Design-Delay toolbox. It is developed based on some recently-reported theoretical results, by which the problem can be systematically solved. The user is only required to input the necessary information via the graphical user interface (GUI) and then the stability analysis may be automatically fulfilled by the toolbox.

The problem of stabilization for time-delay systems with time-varying parametric perturbations is considered in this paper. Two delay-independent stability criteria and a family of memoryless state feedback controllers are proposed. The main feature of the present result is that both the criteria and the controllers do not involve any Riccati equations and are easy to he tested and be implemented. A numerical example is given to demonstrate the effectiveness of the present schemes.

In this paper, the problems of stabilization for interval type-2 fuzzy systems with time-varying delay and parameter uncertainties are investigated. The objective is to design an interval type-2 fuzzy controller such that the closed-loop control system is asymptotically stable. The conditions for the existence of such a controller are delay dependent and membership function dependent in terms of linear matrix inequalities (LMIs). Based on a basic lemma, we formulate and solve the problem with more flexibility due to imperfect premise matching that the number of rules and premise membership functions are not necessary the same between the interval type-2 fuzzy model and interval type-2 fuzzy controller. A systematic approach making use of the information embedded in the lower and upper membership functions is employed to facilitate the stability analysis. A numerical example indicates the effectiveness of the derived results.

This work proposes the coefficient diagram method (CDM)-based two degree of freedom proportional integral (CDM-PI) controller tuning rules for stable and unstable first order plus time delay (FOPTD) processes and pure integrating processes with time delay (PIPTD). To derive the tuning rules, a general first order plus time delay (FOPTD) model, the first order Taylor denominator (TD) approximation technique and the pole allocation strategy named CDM is used. The tuning rules derived here are novel and they relate the controller parameters to the process model parameters directly. The performance of the CDM-PI controller utilising the proposed tuning rules is tested with numerical examples of stable, unstable and pure integrating processes with time delay models. The test results indicate that the proposed tuning rules yield promising results over the other PI controllers. Performance measures confirm the effectiveness of the proposed tuning method.

Importance of Polynomial in Coefficient Diagram Method

In this work, a PI-P control strategy based on the coefficient diagram method (CDM) is proposed. The proposed CDM–PI-P control strategy is tested with the pH neutralization system. The system is modeled as first order plus time delay (FOPTD) transfer function using the experimental step test method. Closed loop simulations are carried out at two different critical operating points and the servo performance of the CDM–PI-P controller in terms of integral square error (ISE), integral absolute error (IAE), total variation (TV), and time domain specifications are reported. The results of the proposed control strategy are compared with other conventional PI control techniques.

A new adaptive controller based on coefficient diagram method (CDM) as an active queue management (AQM) method is introduced. In the developed AQM (ACDM), the output feedback pole placement is implemented in an indirect model reference adaptive control (MRAC) scheme, in which the closed loop characteristic polynomial is determined by CDM and the system parameters are estimated using a modified recursive gradient method. This method preserves existing features of CDM controller in the control of networks with unknown or varying parameters. Simulation results illustrate the good performance of the controller

This paper investigates the stability analysis and state feedback controller design of linear time-invariant (LTI) systems with input time delay. By investigating the real part and the imaginary part of the transcendental equation, the characteristic equation can be transformed into an equation with two vectors related to the system parameters and the feedback gain. The characteristic roots can be determined exactly and concisely that the feedback gain can be designed directly under a given time delay condition. Based on this approach and the pole placement method, preservation of the closed-loop control performance, the state feedback gain and the maximum allowable value of input time delay can be derived by solving an optimization equation. Numerical examples are provided to illustrate the proposed algorithm.

To achieve force control of an industrial robot, this paper proposes an I-PD force control system based on an instantaneous state observer. The structure of the proposed system is based on a resonance ratio control system and a feedback signal of the reaction force response. In this paper, the gain of a pseudo derivation is designed as the feedback gain. From the results of the designed gains, the feedback gain Kf is a negative value. Hence, the resonance ratio control system becomes equivalent to a state feedback. For the stability of the proposed I-PD force control system based on the acceleration control system and a state feedback, a new analysis method is required. This paper analyzes an open-loop of the proposed system considering the bandwidth of the observer. The results of an analysis show that an observer with a wide bandwidth is required. Therefore, the parameters of proposed system using the instantaneous state observer are designed based on the coefficient diagram method. The effectiveness of the proposed method is confirmed by performing numerical simulations based on the model of an industrial robot arm. The results show that the proposed method is effective for the stable force control of an industrial robot arm.

This paper proposes a novel method to graphically compute all feasible gain and phase margin specifications-oriented robust and optimal fractional PID controllers to stabilize time delay processes (TD) of any order. The gain-phase margin tester method is utilized to guarantee the concerned systems certain robust safety margins and test the constant gain margin boundary, constant phase margin boundary, and stability boundary in the parameter plane. The overlapping region of these plotted boundaries, which represents all feasible robust stabilizing PID controllers and allows the considered TD processes to retain pre-specified safety margins, is graphically determined as the gain and phase margin specifications-oriented region (GPMSOR). The variations of the GPMSOR and the stability region with respect to the variations of the noninteger orders of the integral and derivative terms have been investigated. According this, it is possible to slightly enlarge the GPMSOR by altering the noninterger order of the integral and derivative terms. This modifications in GPMSOR through altering the noninteger orders of the integral and derivative terms allows us to find the robust and optimal PID controller gain set for the considered TD systems. In other words, the selected fractional order PID controllers from the GPMSOR not only retain the prescribed GM and PM specifications but minimize the integral of the absolute error (IAE) or the integral of the squared error (ISE) performance criterion. Finally, an illustrative example cited from the literature with computer simulations is provided to demonstrate the effectiveness and confirm the validity of the proposed methodology.

Previous studies have shown that epithelial Na+ channels (ENaCs) are activated by laminar shear stress (LSS). ENaCs with a high intrinsic open probability because of a mutation (betaS518K) or covalent modification of an introduced Cys residue (alphaS580C) in the pre-second transmembrane domain (pre-M2) were not activated by LSS, suggesting that the pre-M2 region participates in conformational rearrangements during channel activation. We examined the role of the pore region of the alpha-subunit in channel gating by studying the kinetics of activation by LSS of wild-type ENaC and channels with Cys mutations in the tract Ser576-Ser592. Whole cell Na+ currents were monitored in oocytes expressing wild-type or mutant ENaCs prior to and following application of LSS. Following a 2.2-s delay, a monoexponential increase in Na+ currents was observed with a time constant (tau) of 8.1 s in oocytes expressing wild-type ENaC. Cys substitutions within the alpha-subunit in the tract Ser580-Ser589 resulted in: (i) a reduction (Ser580-Trp585, Gly587) or increase (Ser589) in delay times preceding channel activation by LSS, (ii) an increase (Gln581, Leu584, Trp585, Phe586, Ser588) or decrease (Ser589) in the rate of channel activation, or (iii) a decrease in the magnitude of the response (Ser583, Gly587, Leu584). Cys substitutions at a putative amiloride-binding site (alphaSer583 or betaGly525) or within the selectivity filter (alphaGly587) resulted in a reduction in the LSS response, and exhibited a multiexponential time course of activation. The corresponding gamma-subunit mutant (alphabetagammaG542C) had a minimal response to LSS and exhibited a high intrinsic open probability. These data suggest that residues in the pore region participate in the sensing and/or transduction of the mechanical stimulus that results in channel activation and are consistent with the hypothesis that the ENaC pore region has a key role in modulating channel gating.

This paper presents an approach for finding regions Of specified gain margins (GM) and phase margins (PM) in the parameter space of a single-input single-output (SISO) control system with adjustable parameters. The method uses the Nyquist stability criterion of encirclement of a point in the polar plot. The necessary of the specified GM or PM regions in the parameter space are fully treated by mapping a point related to specified GM or PM in the polar plane into the parameter space. A general problem with previous mapping techniques is identified where points in the parameter space do not necessarily satisfy the required GM or PM. A searchbased technique is proposed to address this problem. Three examples illustrate the theoretical development. I. Introduction G AIN margin (GM) and phase margin (PM) are perhaps the two most important and widespread accepted criteria in analysis and design of practical control systems. These criteria are related to the open-loop transfer function of systems. In the robust stabilization problem of control systems, however, parameter space methods generally consider the closed-loop characteristic equation of the system.13 Parameter space techniques were initially studied by Vishnegradesky for a third-order system using a graphical technique that was popularized by Nimark and was referred to as D-partition or D-decomposition46 in its early development. This method actually establishes a direct correlation between the variable parameters of the closed-loop characteristic equation and the various important stability regions, e.g., open left half of the complex plane (OLHP). The method is directly suitable for graphical representation, in which case it is convenient to consider two parameters at a time. The idea of correlating the free parameters of the open-loop transfer function of a system and the relative stability regions appears to have been initially given in Ref. 7. Unfortunately , the method was not developed in detail, and the idea of isolating the GM region in the parameter plane was not correct. A recent improvement to the idea was presented by introducing the gain-phase margin tester into the system,8 which attempted to isolate specified GM and PM regions in the parameter space to allow a choice of the adjustable parameters. However, it is argued here that in this latter approach all the possible of the relative stability regions are not in fact considered, and some and possibly all points in the relative stability region do not necessarily satisfy the actual specified relative stability margin. In particular, the so called singular boundaries of the D-partition method6 need to be considered. Finally, arising through frequency loci with re-entrant or convoluted characteristics also need to be considered with care. In this paper, a method for accounting for the

This article proposes an enhanced control of integrating cascade processes. The importance of the scheme shows by controlling a double integrating process with time delay under significant parametric uncertainties and load disturbances. A novel design is proposed based on the Smith predictor principle and uses a fractional-order internal model controller in the outer loop. The required fractional-order tuning parameter follows the desired gain and phase margins. At the same time, another tuning parameter, such as the fractional filter’s time constant, is calculated from the desired performance constraint. Numerical analysis and comparison are performed to showcase the feature of the hybrid structure. The simulation results show that the fractional-order internal model controller–based scheme provides enhanced tracking and faster regulation capabilities and works well under nominal and parameter uncertainty conditions.

Systems with time delays are present in many applications and considerable research efforts have been made for design and analysis of controllers for this class of systems. Since time delay itself is nonlinear in nature, various approximation techniques have been developed based on restrictive assumptions. A common approximation technique for time delay is by using the Pade rational polynomials which expresses time delay transfer function e/sup -ts/ in the form of numerator and denominator in s. In this paper, systems with time delay are investigated directly in discrete time domain. The time delay is modeled accurately without linear assumption and an augmented state space model is obtained. Control law is developed and closed loop stability is proven. An example is given to demonstrate the technique.

Control design for interval type-2 Takagi-Sugeno singular systems with time delay