Nikolaos I. Margaris

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.

PMSM sensorless speed estimation based on sliding mode observers

A new sensorless method of estimating the permanent magnet synchronous motor speed is presented. The method is based on sliding mode observer theory using Lyapunov stability criteria. The observation algorithm makes use of the machine model equations allowing the estimation of flux/current, stator resistance, rotor angle and rotor speed from the motor terminal measurement of currents and voltages. Speed/position observer is based on a modified back EMF state observer, which is considered in cascade with stator flux/current and resistance observers. The presented application has been implemented using an estimated gamma-delta reference frame instead of alpha-beta stationary reference frame. It is shown that the overall observation system gives exceptional estimation results at high and low speed ranges, without initial rotor angle knowledge. Simulation results of permanent magnet synchronous motor sensorless speed estimation are also presented.

Speed and position estimation technique for PMSM based on modified machine model

This paper presents a new sensorless speed and position estimation method for salient-pole Permanent Magnet Synchronous Motor (PMSM) based on a new mathematical model. All the system variables are expressed in a γδ estimated rotating reference frame. The modified back Electromotive Force (EMF) observer estimates the rotor speed and position utilizing the equivalent control signals of a sliding mode observer (SMO). PMSM parameter changes including stator resistance and permanent magnet flux are compensated by means of SMO. Additionally the initial rotor position is not needed for the overall observer implementation. Simulation results demonstrate the effectiveness of the proposed estimation method using Matlab/Simulink facility.

Optimal tuning of PID controllers for integrating processes via the symmetrical optimum criterion

An analytical PI, PID type control law for type-II closed loop control systems is proposed. Type-II closed loop control systems are capable of tracking step and ramp reference signals achieving zero steady state position and velocity error respectively. The development of the proposed control law is based on the well known Symmetrical Optimum criterion and focuses on optimizing output disturbance rejection in comparison with the conventional design. For the derivation of the optimal control law, a generalized transfer function of the process model is employed. Therefore, the proposed theory can be applied in any linear SISO stable or integrating process. For verifying the proposed control law, a comparison between the conventional Symmetrical Optimum criterion and the revised theory is performed for several benchmark processes. The proposed control law shows significant improvement regarding output disturbance rejection, of up to 38%, in comparison with the conventional Symmetrical Optimum design.

Flux weakening method for sensorless PMSM control using torque decoupling technique

The present paper describes a new flux-weakening (FW) algorithm for speed control of permanent magnet synchronous machine (PMSM) using a sliding mode observer (SMO) for rotor speed and position estimation. In flux weakening techniques needed to applications requiring constant torque and power operation, the produced torque is depended on the negative d-axis stator current applied to waken the magnetic flux of the permanent magnets. The proposed method uses a simple torque decoupling technique to regulate the q-axis reference current embeded into the speed controller. A flux weakening controller (FWC) is used to adjust the d-axis stator current based on the q-axis reference voltage. The performance of the overall control system is examined using Matlab/Simulink facility. Simulation results demonstrate the effectiveness of the proposed flux weakening control method.

Sensorless speed and position estimation of PMSM using sliding mode observers in γ-δ reference frame

In this paper a simple sensorless algorithm of estimating the permanent magnet synchronous motor (PMSM) speed and position is presented. The proposed approach introduces a new PMSM mathematical model considered in an estimated gamma-delta reference frame instead of stationary alpha-beta reference frame. A state observer has been implemented by the fundamental excitation method based on sliding mode observer theory. The effectiveness of the proposed method was verified using Matlab/Simulink facility on a salient-pole PMSM. In the simulation, it is assumed that the stator resistance is changed and an external torque disturbance is applied. The overall observation system gives exceptional estimation results at high and low speed ranges, without initial rotor angle knowledge.

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.

Automatic tuning of PID type-III control loops via the symmetrical optimum criterion

The Symmetrical Optimum criterion is extended for the design of PID-type-III control loops. Main advantage of type-III control loops (compared to type-I,~II) is their ability to track fast reference signals since they eliminate higher order errors at steady state (zero steady state position, velocity and acceleration error.) Type-III control loops are characterized by the presence of three pure integrators in the open loop transfer function. The proposed PID control law consists of analytical expressions that can be applied to process models consisting of n poles plus time delay d. The application of the the proposed control law to a large class of processes (model with known transfer function) shows that regardless of the process complexity, the overshoot of the step response of the final closed-loop control system exhibits a certain level. This feature results effortlessly to the automatic tuning of the PID controllers parameters since by exploiting the analytical expressions of the proposed PID control law, controller parameters are tuned such, so that the step response of the control loop exhibits the specific overshoot. For applying the proposed method, an open loop experiment of the process is necessary for starting up the algorithm. The proposed tuning technique assumes that access to the states is impossible as it frequently happens in many industry applications. Simulation results are presented, verifying the current approach.

Antiwindup speed technique for sensorless control of Synchronous Machine using saturation feedback

This paper presents a new antiwindup (AW) speed controller for salient-pole Synchronous Machine (SM) with rotor field winding. The control method is based on antwindup methodology using a sliding mode observer for controller gain adaptation. All the system variables are expressed in a γδ estimated rotating reference frame. Firstly, the unwanted windup phenomena due to the physical limitations are eliminated choosing suitably the controller transfer function. Secondly the speed converges asymptotically leading the saturation element very fast towards to the linear area of the actuator using a relatively simple AW control method. Simulation results demonstrate the effectiveness of the proposed antiwindup speed control method using Matlab/Simulink facility.

An approach of unified voltage correcting algorithm for SVPWM overmodularion

This paper presents a new unified algorithm used for voltage regulation of an inverter operating in overmodulation area of Space Vector Pulse Width Modulation (SVPWM). Overmodulation operation of the proposed strategy is based on a simple amplitude-phase correcting method, which modifies properly the amplitude and the phase angle of the output voltage. The unified Voltage Correcting Function (VCF) is piecewise continuous in entire SVPWM area and symmetrical in each sector with respect the angle π/6 enabling continuous transition from the linear modulation up to the six-step mode. A Fourier series expansion of the compensated phase voltage waveform is also presented. Simulation results are provided to demonstrate the effectiveness of the proposed SVPWM overmodulation method exploring the inverter voltage and motor currents response via Fast Fourier Transform (FFT) and Total Harmonic Distortion (THD) analysis. The new overmodulation algorithm has been applied on sensorless speed control scheme of a salient-pole Synchronous Machine (SM) with rotor field winding.