MATLAB prompt. Select Start from the Simulation menu to begin the simulation. Simulink scope windows show the engine speed, the throttle commands which drive. In practice the PID controller contains more parameters, since the derivative part needs to be filtered, the integral part needs to have some anti-windup.
The Vdc closed-loop representation with the outer-loop controller included. From the closed-loop transfer functions 23 and 25 , it is proved that the dominant system response of the speed and DC-voltage states is asymptotically stable with a time constant selected by the designer. It is evident that the inner-loop system stability is a pre-requirement for the stability of the outer-loop controllers.
System Examination and Results A detailed design of the three cascaded controller loops was implemented and examined through simulations on a Simulink environment deployed exclusively for the entire EV electromechanical and controller scheme. All the components and system parts have been accurately implemented by their mathematical models. Parameters for all the several EV subsystems are summarized in Table 1, while all controller gains were chosen in accordance to the stability analysis presented in the previous section.
In the present case, however, our intention is to indicate the good transient and steady state performance of the proposed controller. Therefore only a small part of the NEDC cycle was selected, actually the one corresponding to the urban driving cycle UDC that involves adequate speed and torque changes for the evaluation of the dynamic response. The mechanical torque Tm during the selected route was calculated in a standard manner by using the car force model that takes into account the gravitational, rolling resistance, wind and inertial forces.
The analytic expressions are thoroughly described in bibliography [11]. In accordance to the UDC modeling and the car force model the different constant levels of the external torque Tm as well as its changing rates are depicted in Figure 4. Both responses satisfied the outer-loop controllers tasks since they follow very close the reference inputs.
It is remarkable to note that rather large changes of torque result in very smooth responses. The inner-loop control responses are evaluated through the responses of the currents shown in Figures 7—9. In Figure 8 it is indicated that the q-axis current response follows the torque variations.
The duty-ratio d- and q-axis input components mds and mqs of the voltage source converter as these are realized by the proposed control scheme are presented in Figures 10 and 11, respectively. All the three duty-ratio input signals have a very satisfactory form and effectively drive the whole system to the stable equilibria without significant overshoots or oscillations.
In all the simulated cases, the desired operating conditions are achieved in a smooth and stable manner. Figure 4. External mechanical torque Tm. Figure 5. Mechanical angular velocity vs. Energies , 12, 16 of 21 Figure 6. DC-link voltage Vdc. Figure 7. The d-axis stator current Ids. Figure 8. The q-axis stator current Iqs. Figure 9. Battery array current Ibat. Energies , 12, 17 of 21 Figure The d-axis duty-ratio component mds. Figure Battery-side boost converter duty-ratio component mbat.
In order to have better comparisons we focus on a limited duration between 55 and 95 s. One can easily see the superiority of the proposed controllers since overshoots and oscillations are observed when the conventional controllers are applied.
This is an expected result, known in the literature [49], while the improvement of the proposed approach is due to the fact it provides a complete design tool that enables effective gain tuning for both the inner- and outer-loop controllers. It is worth noting that since the motor speed directly impacts on the vehicle velocity response, even a small speed overshoot or oscillation is clearly inconvenient for the EV passengers and therefore this point constitutes a critical design parameter.
Energies , 12, 18 of 21 Figure A detail of DC-link voltage Vdc responses between 55 and 95 s considering a classic PI and the proposed control scheme. Furthermore, a complete stability analysis is conducted, by exploiting some basic characteristics of the nonlinear, full system model.
The analysis proves asymptotic stability at the desired equilibrium, while certain control design guidelines are provided for the selection of the controllers gains. Particularly, the main novelties proposed in this research work can be summarized into: i application of independent controllers for each input, ii development of a suitable procedure for the design of the proposed controllers, iii design verification supported by a rigorous stability analysis, and iv validation of the system good performance concluded by extended simulations.
Thus, the main aim of the proposed approach, that is to keep simple controller structures familiar to the industrial engineers, and simultaneously to guarantee stable operation is completely fulfilled. The detailed analysis deployed by considering the system as a whole, constitutes the basic contribution of the present work that in contrast to the conventional heuristic applications of simple P and PI control schemes, provides a global methodology for the controller gains selection.
The results fully verify the effectiveness of the theoretical deployment and confirm the stable driving at the desired operation point, indicating a smooth and satisfactory transient response. Author Contributions: Both authors contribute to this research article, with the fist author to be the main investigator. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.
Energies , 12, 19 of 21 Nomenclature b viscous friction coefficient C capacitance of the DC-link CL long term battery capacitance component CS short term battery capacitance component J moment of inertia Lbat inductance of the battery boost converter Lds d-axis stator inductance Lqs q-axis stator inductance p pole pairs RL long term battery resistance component RS short term battery resistance component rs stator resistance Rdc resistance of the DC-link Rser series output battery resistance P Proportional controller PI Proportional-Integral controller References 1.
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Power electronics for renewable energy systems By Florin Iov. Advanced Electric Drive Vehicles By toan do. Control of Electric Vehicle By rkar phyo. Grid-connected control of PV-Wind hybrid energy system By hocine belmili. Install matlab a for your PC and enjoy. Plot transfer function response. Bode plot. Lecture Pole Zero Plot. Calculate poles and zeros from a given transfer function.
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When the actuator desaturates it may then take a long time for the system to recover. It may also happen that the actuator bounces several time between high and low values before the system recovers. Because of the saturation in the actuator, the control signal saturates immediately when the step is applied. The control signal then remains in saturation level and the feedback is broken.
The integral part continues to increase because the error SP - PV is positive. The integral part starts to decrease when the process output PV has become larger than the setpoint SP , but the process output remains saturated because of the large integral part. Slowly the process output decreases towards the setpoint. The net effect is that there is a large overshoot. This phenomenon is called "integrator windup". A good insight in windup is found when looking at the proportional band.
The values of the process output that correspond to the minimum and maximum output are denoted as ymax and ymin. The controller operates linearly only if the process output is in the range ymax , ymin. The controller output saturates when the process output is outside this band. A good insight into the windup problem is obtained by investigating the range ymax , ymin.
An illustration of the proportional band is given below. The same linear system is used with the same controller. Integrator windup can be avoided, by making sure that the integral is kept to a proper value when the actuator saturates, so that the controller is ready to resume action, as soon as the control error changes. This anti-windup scheme is known as tracking or back calculation. As well known form of tracking is linear feedback anti windup.
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