Solution to a Benchmark Control Problem using the CDM Design Method

Importance of Polynomial in Coefficient Diagram Method

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.

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.

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

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.

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.

CASE STUDIES OF COEFFICIEANT DIAGRAM METHOD – PRACTICAL POLYNOMIAL DESIGN APPROACHES

PID Controller Design of MIMO Systems by using Coefficient Diagram Method

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.

A new robust control strategy coefficient diagram method (CDM), which is an algebraic approach applied to a polynomial loop in the parameter space, is studied in this paper. Here, a model-based CDM is developed and proposed for uncertain systems. A special diagram called a coefficient diagram, which is used as a vehicle to carry the necessary information and as the criteria of good performance, is designed and modified accordingly. The performance of this novel controller is illustrated through several examples, and numerical results are provided.

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.

Proton Exchange Membrane Fuel Cell (PEMFC) are emerging as the new renewable energy source. The output voltage of PEMFC is not sufficient to fulfill the load demands which varies with variations in temperature and load. So, it is integrated with a properly designed power conditioning unit to enhance and stabilize the voltage. In this paper Nexa 1.2 KW PEMFC is initially modeled using successive trust region. Next, a DC-DC boost converter connected to the fuel cell is designed using interval analysis to boost and regulate the output voltage adhering to the changes in the temperature and loading conditions. To stabilize the output of PEMFC fed boost converter, double loop robust controllers are implemented which are designed by Coefficient Diagram Method (CDM). All the responses of the CDM controlled boost converter settle down smoothly at the desired settling time with zero overshoot. The proposed controller fair quite well as compared to other similar controllers in the existing literatures.