Konstantinos G. Papadopoulos

Explicit Analytical PID Tuning Rules for the Design of Type-III Control Loops

The problem of designing PID type-III control loops is investigated. On a theoretical basis and if frequency domain modeling of the control loop is followed, type-III control loops are characterized by the presence of three pure integrators in the open-loop transfer function. Therefore, such a control scheme has the advantage of tracking fast reference signals since it exhibits zero steady-state position, velocity, and acceleration error. This advantage is considered critical in many industry applications, i.e., control of electrical motor drives and control of power converters, since it allows the output variable, i.e., current or speed, to track perfectly step, ramp, and parabolic reference signals. The proposed PID control law has the following characteristics: 1) it consists of analytical expressions that involve all modeled process parameters; 2) it can be straightforwardly applied to any process regardless of its complexity since, for its development, a generalized transfer function process model is employed consisting of n poles and m zeros plus unknown time delay d; and 3) it allows for accurate investigation of the performance of the control action to exogenous and internal disturbances in the control loop and investigation of different operating points. For justifying the potential of the proposed control law, several examples of process models met in many industry applications are investigated.

Analytical tuning rules of digital PID controllers for integrating processes via the Symmetrical Optimum criterion

Explicit tuning rules for digital PID regulators are presented regarding the control of integrating processes. Controller parameters are determined analytically as a function of the process parameters and the sampling time of the controller. The derivation of the proposed PID control law lies in the principle of the Symmetrical Optimum criterion. The performance of the proposed control law is compared with the conventional tuning of the PID regulator via the Symmetrical Optimum criterion when controlling the same process. Simulation examples show improvement of output disturbance rejection of up to 71.05% decrease of settling time.

Digital PID type-III control loop design via the symmetrical optimum criterion

An analytical digital PID control law for the design of type-III control loops is developed. The proposed control law involves both dominant time constants of the controlled process, its unmodelled dynamics plus the sampling time of the controller. Basis of the proposed theory is the well known Symmetrical Optimum criterion. The development of the control law takes place in the frequency domain. For applying the proposed theory an accurate estimation of the plants dominant time constants is required. The final control loop has the advantage of achieving zero steady state position, velocity and acceleration error. The potential of the proposed theory is justified via simulation examples for benchmark process models met frequently in many industry applications.

A Strategic Market Game of Carry Trades and Equilibrium Profits

We formalize carry trade in a two-country, two-period general equilibrium strategic market game model of an economy with no uncertainty where agents are not price takers. We show that when carry trade occurs at a Nash equilibrium it is profitable and is identified with the failure of the uncovered interest rate parity condition. Carry trade profits are attributed to asymmetric elasticities in currency or credit markets across time. Furthermore, at equilibrium, real national interest rates may not equalize across countries thus violating the standard international Fisher effect.

Advanced parametric environment for electrical machines design optimization

The paper describes a template-style front-end to a generic electromagnetic modeling tool, for the analysis and optimization of electrical machines. A two and three-dimensional FEA model for a generator and motor can be created in minutes, using templates with dasiafill in the blankspsila style screens. Accurate virtual prototypes can then be produced to help engineers provide answers on the performance of specific machine designs rapidly, and perform searching dasiawhat-if?psila investigations to identify the design characteristics of the perfect machine. Optimization tools are also available within the environment, enabling engineers to find the dasiabestpsila solution automatically. Equally important is that the environment is structured to allow creation and analysis of customised geometries, including special proprietary features.

Countervailing Power with Large and Small Retailers

When concentration in the retail market increases, retailers gain more market power towards the suppliers and they hence can achieve better wholesale prices. In the 1950s, Galbraith introduced the concept of countervailing power claiming that lower wholesale prices will pass on to consumer as lower retail prices. Consequently higher concentration may turn out to be beneficial for consumers. In this model where a monopolistic supplier sells an intermediate good to M large retailers who are Cournot competitors and a competitive fringe consisting of N retailers, we show that higher concentration does not decrease retail prices and results solely to a reallocation of profits between the supplier and large retailers, thus invalidating Galbraith’s conjecture. The same result carries on when the exogenously given level of bargaining power of large retailers increases.

Explicit analytical tuning rules for digital PID controllers via the magnitude optimum criterion

Analytical tuning rules for digital PID type-I controllers are presented regardless of the process complexity. This explicit solution allows control engineers 1) to make an accurate examination of the effect of the controllers sampling time to the control loops performance both in the time and frequency domain 2) to decide when the control has to be I, PI and when the derivative, D, term has to be added or omitted 3) apply this control action to a series of stable benchmark processes regardless of their complexity. The former advantages are considered critical in industry applications, since 1) most of the times the choice of the digital controllers sampling time is based on heuristics and past criteria, 2) there is little a-priori knowledge of the controlled process making the choice of the type of the controller a trial and error exercise 3) model parameters change often depending on the control loops operating point making in this way, the problem of retuning the controllers parameter a much challenging issue. Basis of the proposed control law is the principle of the PID tuning via the Magnitude Optimum criterion. The final control law involves the controllers sampling time Ts within the explicit solution of the controllers parameters. Finally, the potential of the proposed method is justified by comparing its performance with the conventional PID tuning when controlling the same process. Further investigation regarding the choice of the controllers sampling time Ts is also presented and useful conclusions for control engineers are derived.