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.

Solution to a Benchmark Control Problem using the CDM Design Method

Vibration suppression controls of two-inertia systems have been proposed by many researchers. However, for three-inertia systems, it is difficult to obtain the adequate gains of the PID controller, which suppress the vibration of the speed of the load side. The Coefficient Diagram Method (CDM) that can design the optimum controller’s gains for the 2-inertia systems has been proposed. In this paper, the control method of vibration of multi-inertia systems, such as 3-inertia and 4-inertia systems, based on the CDM is proposed. Especially, the coefficient diagram is used to determine the controller gains. The validity of the proposed method is shown by the computer simulation for both the 3-inertia system and the 4-inertia one. Furthermore experimental results is also presented for the 3-inertia system.

This paper proposes a novel load frequency control (LFC) approach formulated on an optimal structure of the coefficient diagram method (CDM) in a two-area thermal power system. As part of a realistic analysis, nonlinearities related to governor dead band (GDB) and generation rate constraint (GRC) have been considered. In this article, a hybrid CDM method is combined with the optimization of its mathematical equations to achieve an innovative controller. Furthermore, a new metaheuristic optimization technique called the water cycle algorithm (WCA) is used to determine the optimal coefficients of the CDM controller. For the purpose of demonstrating the validity of the proposed scheme, a wide range of uncertainties in the dynamic parameters of a nonlinear power system were tested. In addition, a comparative study is presented between the results obtained from a classical integral, CDM alone, optimized fuzzy, optimized PID, and the suggested controller. In this new approach to improved control, algebraic support provides a robust and responsive controller that can provide fast and stable dynamic responses and effectively overcome the detrimental effects of nonlinearities and uncertainties in the parameters of the power system.

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

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.

We consider the problem of designing P, PI and PID controllers for interval plants. It is known from the area of parametric robust control that the stabilization problem for an interval plant are reduced to the equivalent problem of stabilizing either a finite set of certain extremal plants. This paper shows that under special conditions imposed on controller parameters and the order of plant, the number of extremal plants required for stabilization on PID controllers are reduced. Thereafter, using Ho's method, it allows one to obtain all the stabilizing set of PID gains for a interval plant family. We assure that the coefficient diagram method (CDM) is very useful for designing a controller because the design in CDM is not only carried out directly in the parameter space but also easy to meet the time domain specification, as shown in a numerical example.

The aim of this paper is to determine which type of control loop is better for each particular type of standard voltage source inverter (VSI) load (static, dynamic, nonlinear rectifier resistive-capacitive RC load). A comparison of three different types of controllers for single-phase VSIs is presented. The first two are of the single input single output (SISO)/proportional-integral-derivative controller (PID) and coefficient diagram method (CDM) types, and the third is of the multi-input single output (MISO)/passivity-based control (PBC) type. The selections of the gains for SISO and MISO controllers are presented, including the problem in the choice of PBC controller gains caused by the imperfection of the pulse width modulation (PWM) modulator. For a standard nonlinear rectifier RC load, the new control quality factor (CQF) is defined to distinguish the properties of the controllers. The results show the superiority of the MISO-PBC controller for the RC load; however, for a linear dynamic load, the MISO-PBC performed worse than the SISO-PID or CDM. Therefore, the choice between either a simple and inexpensive SISO with one measurement trace or an expensive MISO with three measurement traces depends on the purpose of the VSI. The initial simulations and measurements of the experimental models are presented and discussed.

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.

Load frequency control is a major issue in power systems operation.The performance of adaptive particle swarm optimization (PSO) , coefficient diagram method (CDM) and conventional integral (PI) controller are compared for an isolated single area non re-heated turbine microgrid with using both of electric vehicle (EVs) and heat pump water heaters (HPs) as controllable loads.The dynamic response of LFC is studied using MATLAB 2017a Simulink package to validate the effectiveness of the proposed scheme.The results indicated that the system with PSO technique has better convergence and robustness than CDM in face of uncertainties due to load perturbations.

Controlling robot with the mechanical resonance has been receiving increased attention. A new effective control method, a resonance ratio control, has been introduced as a new way to guarantee the robustness and suppress the oscillation during task executions for position and force control system. This work presents a new approach to the controlling of flexible robot system by a switching operation mode resonance ratio control. To calculate the optimal parameters of position/force servoing based on resonance ratio control, a Coefficient Diagram Method (CDM) is employed. In this paper, we introduce a novel approach that automatically adapt algorithm parameters conditional based on the operational tasks. Moreover, a multiencoder based disturbance observer (MEDOB) is shown to estimate the external force on the load side, rather than using a force sensor. The experiments with a linear motor and spring show the validity of the approach. From the experiments, it can reject vibration to improve controlling performance.

PID Controller Design of MIMO Systems by using Coefficient Diagram Method

This paper presents a high-performance and simple guidance method for a short-range missile. Missile control systems are designed along the estimated flight envelope of the missile based on coefficient diagram method. The linear time invariant (LTI) models are obtained by linearizing missile nonlinear model at specific operating points. The governing equations of motion are accurately modeled by taking into account the effect of the mass rate and the center of gravity shift. A novel algebraic approach called coefficient diagram method (CDM) is used to design normal acceleration and roll angle control systems. The proportional navigation law is considered as the guidance law. One case of engagement scenarios is studied and the missile performance is evaluated. The robustness of the proposed controller is tested against parameter uncertainties and wind disturbance.

Time delays are inherent in modern motion-control and electric-drive loops due to sensing, filtering, sampling and computation, communication, and actuation scheduling. When such delays are only partially known, they can markedly reduce stability margins and narrow the admissible range of state-feedback gains, especially in high-bandwidth servo applications. This paper develops a design-oriented state-feedback framework for delay-affected plants based on the Manabe polynomial concept and the Coefficient Diagram Method (CDM). The plant is represented as a chain of integrators of order two to four with an effective input gain, and the feedback gain is synthesized for the nominal delay-free model by matching a standard Manabe/CDM characteristic polynomial using the classical CDM stability-index pattern. When an unmodeled input delay is present, the closed loop is governed by a delay-dependent characteristic equation. By introducing a normalized representation, the analysis yields explicit delay-stability limits that directly translate into a lower bound on the equivalent time constant used for tuning. The degradation of the phase margin and gain margin with increasing normalized delay is quantified as design charts, and a simple phase-margin-based inequality is proposed for selecting the tuning time constant, with gain-margin checks recommended as a verification step.

Coefficient diagram method is a controller design technique for linear time-invariant systems. This design procedure occurs into two different domains: an algebraic and a graphical. The former is closely paired to a conventional pole placement method and the latter consists on a diagram whose reading from the plotted curves leads to insights regarding closed-loop control system time response, stability and robustness. The controller structure has two degrees of freedom and the design process leads to both low overshoot closed-loop time response and good robustness performance regarding mismatches between the real system and the design model. This article presents an overview on this design method. In order to make more transparent the presented theoretical concepts, examples in Matlab ®code are provided. The included code illustrates both the algebraic and the graphical nature of the coefficient diagram design method.