**5.1 Tracking performance and disturbance rejection study**

To demonstrate the performance of the SRM drive with the proposed control scheme, the load torque is abruptly increased from 5 to 10 Nm at 0.05 sec, as an external disturbance, while the reference speed is 200 rpm. The performance of CASMC and RASMC is compared in **Figure 5**. The chattering phenomenon in control effort is completely removed by the RASMC, as depicted in **Figure 5(b)**.

To demonstrate the effectiveness of using acceleration error in control method, a trapezoidal reference including accelerated part is also used to test the controllers. **Figure 6** shows the response of the system to a four-quadrant trapezoidal reference speed profile. It is shown that the speed response with the proposed RASMC is more precise and smoother than CASMC, obtained by adopting the acceleration closedloop control.

**Figure 5.**

**Figure 6.**

**131**

*Four-quadrant speed response of SRM.*

*convergence, (b) control effort.*

*Performance comparison of controllers, when the motor load increases at 0.05 s from 5 to 10 nm, (a) speed*

*Chattering-Free Robust Adaptive Sliding Mode Speed Control for Switched Reluctance Motor*

*DOI: http://dx.doi.org/10.5772/intechopen.91161*

**Figure 4.** *Overview of the proposed RASMC system for speed control.*

*Chattering-Free Robust Adaptive Sliding Mode Speed Control for Switched Reluctance Motor DOI: http://dx.doi.org/10.5772/intechopen.91161*

**Figure 5.**

Remark 1. The exponential terms, formed by *δ*1, *δ*2, *σ*1, and *σ*<sup>2</sup> in (23), are used to prevent chattering in the control signal. The greater value of such parameters provides the smaller chattering in control signal. On the other hand, there is a trade-off between the smoothness of control effort and the speed of tracking error conver-

Remark 2. From a theoretical viewpoint, choosing any *<sup>K</sup>* <sup>&</sup>gt;ð Þ *<sup>δ</sup>*<sup>1</sup> <sup>þ</sup> *<sup>δ</sup>*<sup>2</sup> *<sup>=</sup>ε*<sup>2</sup> ensures

Simulation results are presented here for a SRM with the parameters, given in Appendix B using MATLAB/Simulink. The block diagram of the closed-loop drive control system, using the proposed RASMC, is shown in **Figure 4**. In the following, the system performance is evaluated despite the variation of load torque, as an external disturbance, and compared with that of CASMC. To this end, the CASMC parameters are selected as *K*<sup>1</sup> ¼ 20, *σ* ¼ 8, and *ρ* ¼ 1. The RASMC parameters are *K* ¼ 10, *γ* ¼ 1 and exponential terms are *δ*<sup>1</sup> ¼ *δ*<sup>2</sup> ¼ 5 and *σ*<sup>1</sup> ¼ *σ*<sup>2</sup> ¼ 1*.* Moreover, the turn-on and turnoff angles are assumed to be constant and equal to 56<sup>∘</sup> and 33<sup>∘</sup>

To demonstrate the performance of the SRM drive with the proposed control scheme, the load torque is abruptly increased from 5 to 10 Nm at 0.05 sec, as an external disturbance, while the reference speed is 200 rpm. The performance of CASMC and RASMC is compared in **Figure 5**. The chattering phenomenon in control effort is completely removed by the RASMC, as depicted in **Figure 5(b)**. To demonstrate the effectiveness of using acceleration error in control method, a trapezoidal reference including accelerated part is also used to test the controllers. **Figure 6** shows the response of the system to a four-quadrant trapezoidal reference speed profile. It is shown that the speed response with the proposed RASMC is more precise and smoother than CASMC, obtained by adopting the acceleration closed-

,

holding (37), for any *ε*>0, even if *K* is very large. In practice, selecting an arbitrarily large *K* may not be possible, and a certain error bound is allowed in

**5.1 Tracking performance and disturbance rejection study**

gence.

controller design.

respectively.

loop control.

**Figure 4.**

**130**

*Overview of the proposed RASMC system for speed control.*

**5. Simulation results**

*Control Theory in Engineering*

*Performance comparison of controllers, when the motor load increases at 0.05 s from 5 to 10 nm, (a) speed convergence, (b) control effort.*

**Figure 6.** *Four-quadrant speed response of SRM.*

**Figure 7.** *Performance comparison of the methods in external load disturbance rejection.*

**Figure 8.** *The sliding gain* P^ *for CASMC and α*^ *for RASMC.*

The capability of RASMC in external load disturbance rejection, demonstrated in **Figure 7**, shows that a considerable robustness against the external load is achieved, compared with the CASMC. Due to the increased uncertainties of the system caused by the increase in the load torque, there is a speed error at 0.05 sec. **Figure 8** shows the adaptation of the procedure of the proposed adaptive-based controllers, to overcome such system perturbations.

#### **5.2 Robustness against parametric uncertainty**

To investigate the behavior of RASMC under parametric variations, the inertia of the motor *J*, the motor load friction *B*, and the stator resistance are increased by 100% of the nominal values. Such variations are effectively compensated by the proposed RASMC, as illustrated in **Figure 9**.

**5.3 Rejection of time-varying load perturbations**

**Figure 9.**

**133**

*resistance R.*

Applying the load torque with the mean torque values of 10 Nm in 200 RPM and 7 Nm in 500 RPM is shown in **Figures 10** and **11**, respectively. In both cases, the load torque, applied to the motor, is perturbed by a Gaussian noise with variance

*Speed responses despite the 100% variation in (a) rotational inertia J, (b) viscous friction B, and (c) stator*

*Chattering-Free Robust Adaptive Sliding Mode Speed Control for Switched Reluctance Motor*

*DOI: http://dx.doi.org/10.5772/intechopen.91161*

*Chattering-Free Robust Adaptive Sliding Mode Speed Control for Switched Reluctance Motor DOI: http://dx.doi.org/10.5772/intechopen.91161*

**Figure 9.**

The capability of RASMC in external load disturbance rejection, demonstrated in **Figure 7**, shows that a considerable robustness against the external load is achieved, compared with the CASMC. Due to the increased uncertainties of the system caused by the increase in the load torque, there is a speed error at 0.05 sec. **Figure 8** shows the adaptation of the procedure of the proposed adaptive-based controllers, to

To investigate the behavior of RASMC under parametric variations, the inertia of the motor *J*, the motor load friction *B*, and the stator resistance are increased by 100% of the nominal values. Such variations are effectively compensated by the

overcome such system perturbations.

*The sliding gain* P^ *for CASMC and α*^ *for RASMC.*

**Figure 7.**

*Control Theory in Engineering*

**Figure 8.**

**132**

**5.2 Robustness against parametric uncertainty**

*Performance comparison of the methods in external load disturbance rejection.*

proposed RASMC, as illustrated in **Figure 9**.

*Speed responses despite the 100% variation in (a) rotational inertia J, (b) viscous friction B, and (c) stator resistance R.*

#### **5.3 Rejection of time-varying load perturbations**

Applying the load torque with the mean torque values of 10 Nm in 200 RPM and 7 Nm in 500 RPM is shown in **Figures 10** and **11**, respectively. In both cases, the load torque, applied to the motor, is perturbed by a Gaussian noise with variance

fixed-point TMS320F2812 DSP, which is compatible with Simulink [31]. Such platform includes four dual pulse-width-modulation (PWM) channels (eight channels total), four analog-to-digital converters (ADCs), and a speed encoder input. **Figures 12** and **13** illustrate the laboratory setup and the general layout of the

*Chattering-Free Robust Adaptive Sliding Mode Speed Control for Switched Reluctance Motor*

DSP-based drive system, respectively. The experimental hardware, used for

(i) The asymmetrical converter, implemented by using IXSH 35N120A IGBT with a gate driver TLP250 and fast power diodes DSEI 20-12A with a reverse recovery time, less than 40 nanoseconds. (ii) Hall-type galvanic isolation CSNE151–104 Honeywell sensors for measuring the phase currents. A ten-bit absolute encoder Autonics EP50S8, used to determine the rotor position with high accuracy. (iii) The results are obtained under the speed loop switching frequency of 10 kHz and the current loop of 1 kHz. The DC link voltage is kept

Some experimental results are presented here by implementing the RASMC and CASMC, from a comparison viewpoint. The numerical values of the parameters,

evaluating the 8/6 SRM drive, consists of the following sections:

*DOI: http://dx.doi.org/10.5772/intechopen.91161*

constant at 280 V.

**Figure 12.**

**Figure 13.**

**135**

*The laboratory setup for experimental study.*

*Block diagram of the experimental platform.*

#### **Figure 10.**

*(a) Torque estimation in the presence of a Gaussian perturbation with a mean of 10 nm and a variance of 1 nm in 200 RPM and (b) applied time-varying load perturbation.*

#### **Figure 11.**

*(a) Torque estimation in the presence of a Gaussian perturbation with a mean of 7 nm and a variance of 1 nm in 500 RPM and (b) applied time-varying load perturbation.*

of 1 Nm. These kinds of load torque perturbations are selected to emulate the electric vehicle driving torque condition [30]. The results show only a small ripple remains in the steady state by applying the RASMC.

## **6. Experimental study**

A SRM with same parameters of Appendix B is implemented to experimentally verify the proposed control scheme. The experimental setup is based on a

*Chattering-Free Robust Adaptive Sliding Mode Speed Control for Switched Reluctance Motor DOI: http://dx.doi.org/10.5772/intechopen.91161*

fixed-point TMS320F2812 DSP, which is compatible with Simulink [31]. Such platform includes four dual pulse-width-modulation (PWM) channels (eight channels total), four analog-to-digital converters (ADCs), and a speed encoder input.

**Figures 12** and **13** illustrate the laboratory setup and the general layout of the DSP-based drive system, respectively. The experimental hardware, used for evaluating the 8/6 SRM drive, consists of the following sections:

(i) The asymmetrical converter, implemented by using IXSH 35N120A IGBT with a gate driver TLP250 and fast power diodes DSEI 20-12A with a reverse recovery time, less than 40 nanoseconds. (ii) Hall-type galvanic isolation CSNE151–104 Honeywell sensors for measuring the phase currents. A ten-bit absolute encoder Autonics EP50S8, used to determine the rotor position with high accuracy. (iii) The results are obtained under the speed loop switching frequency of 10 kHz and the current loop of 1 kHz. The DC link voltage is kept constant at 280 V.

Some experimental results are presented here by implementing the RASMC and CASMC, from a comparison viewpoint. The numerical values of the parameters,

**Figure 12.** *The laboratory setup for experimental study.*

**Figure 13.** *Block diagram of the experimental platform.*

of 1 Nm. These kinds of load torque perturbations are selected to emulate the electric vehicle driving torque condition [30]. The results show only a small ripple

*(a) Torque estimation in the presence of a Gaussian perturbation with a mean of 7 nm and a variance of 1 nm*

*(a) Torque estimation in the presence of a Gaussian perturbation with a mean of 10 nm and a variance of 1 nm*

verify the proposed control scheme. The experimental setup is based on a

A SRM with same parameters of Appendix B is implemented to experimentally

remains in the steady state by applying the RASMC.

*in 500 RPM and (b) applied time-varying load perturbation.*

*in 200 RPM and (b) applied time-varying load perturbation.*

**6. Experimental study**

**Figure 10.**

*Control Theory in Engineering*

**Figure 11.**

**134**

**Figure 14.**

*Performance of the proposed RASMC in experiment under abrupt load change, compared with that of CASMC (a) speed response and load current and (b) control effort.*

from 2.7 to 5.2 A is equal to stepping load torque from 5 to 10 Nm. The results show that the RASMC significantly improves the robustness performance. As expected, the RASMC successfully eliminates the chattering in the control efforts, as shown in **Figures 14(b)** and **15(b)**. By comparing the results of experimental work with those

*Performance of the RASMC in experiment, under step increment of reference speed, compared with that of*

*Chattering-Free Robust Adaptive Sliding Mode Speed Control for Switched Reluctance Motor*

*DOI: http://dx.doi.org/10.5772/intechopen.91161*

*CASMC (a) speed response in steady state and (b) control effort.*

discussing, the results of implementing RASMC not only confirm the better performance in smoothing the control effort but also demonstrate the disturbance atten-

of the simulation study, the demonstration in **Figure 5** is confirmed. Briefly

uation property. As a confirmatory data, **Figure 16(a)** and **(b)** depicts the waveforms of experimental current and voltage of two phases for CASMC and RASMC, respectively. It is obvious that the current and voltage signals are smoother

by using the RASMC.

**137**

**Figure 15.**

obtained in the simulation studies by trial and error, are used here in the experimental investigations. **Figures 14(a)** and **15(a)** demonstrate the speed response, respectively, under an abrupt external load change from 5 to 10 Nm at 0.05 sec and under a step change in the reference speed from 100 to 200 RPM. Since a torque sensor was not available, for the electromagnetic torque, only armature current of DC generator as a load is depicted in **Figure 14(a)**. Stepping the armature current

*Chattering-Free Robust Adaptive Sliding Mode Speed Control for Switched Reluctance Motor DOI: http://dx.doi.org/10.5772/intechopen.91161*

**Figure 15.** *Performance of the RASMC in experiment, under step increment of reference speed, compared with that of CASMC (a) speed response in steady state and (b) control effort.*

from 2.7 to 5.2 A is equal to stepping load torque from 5 to 10 Nm. The results show that the RASMC significantly improves the robustness performance. As expected, the RASMC successfully eliminates the chattering in the control efforts, as shown in **Figures 14(b)** and **15(b)**. By comparing the results of experimental work with those of the simulation study, the demonstration in **Figure 5** is confirmed. Briefly discussing, the results of implementing RASMC not only confirm the better performance in smoothing the control effort but also demonstrate the disturbance attenuation property. As a confirmatory data, **Figure 16(a)** and **(b)** depicts the waveforms of experimental current and voltage of two phases for CASMC and RASMC, respectively. It is obvious that the current and voltage signals are smoother by using the RASMC.

obtained in the simulation studies by trial and error, are used here in the experimental investigations. **Figures 14(a)** and **15(a)** demonstrate the speed response, respectively, under an abrupt external load change from 5 to 10 Nm at 0.05 sec and under a step change in the reference speed from 100 to 200 RPM. Since a torque sensor was not available, for the electromagnetic torque, only armature current of DC generator as a load is depicted in **Figure 14(a)**. Stepping the armature current

*Performance of the proposed RASMC in experiment under abrupt load change, compared with that of CASMC*

**Figure 14.**

*Control Theory in Engineering*

**136**

*(a) speed response and load current and (b) control effort.*

**Appendix A. Derivation of Eq. (9) in detail**

*DOI: http://dx.doi.org/10.5772/intechopen.91161*

where *<sup>P</sup>*<sup>~</sup> <sup>¼</sup> *<sup>P</sup>* � *<sup>P</sup>*^ and *<sup>P</sup>* <sup>¼</sup> <sup>1</sup>

Lyapunov function can be written as

Finally it can be simplified as

*<sup>V</sup>*\_ <sup>¼</sup> *<sup>S</sup>*\_

**139**

*<sup>S</sup>* � <sup>1</sup> *ρ P*~ \_ *<sup>V</sup>* <sup>¼</sup> <sup>1</sup> 2 *<sup>S</sup>*<sup>2</sup> <sup>þ</sup> 1 2*ρ*

By substituting (7) into (A.1), and adding and subtracting *K*1*S*<sup>2</sup>

*<sup>V</sup>*\_ ¼ �*K*1*S*<sup>2</sup> <sup>þ</sup> *<sup>S</sup>* �ð Þ *<sup>σ</sup>* <sup>þ</sup> *<sup>a</sup> <sup>ω</sup>*\_ � *b u* <sup>þ</sup> *<sup>P</sup>*^ <sup>þ</sup> *bT*\_ <sup>L</sup> <sup>þ</sup> *<sup>K</sup>*1*<sup>S</sup>* � *<sup>P</sup>*<sup>~</sup> <sup>1</sup>

**Parameters Value** Rated power 4 kW RMS rated phase current 9 A Rated DC link 280 V Number of poles 8/6 Phase stator resistance 0.75 Ω Rotational inertia (J) 0.008 Nms2 Viscous friction (B) 0.00078 Nms Aligned inductance 0.114 mH Unaligned inductance 0.0136 mH

**B. Numerical values of the SRM parameters**

As stated in Section 3, the Lyapunov function is defined in (8) as

*<sup>P</sup>*~<sup>2</sup> ! *<sup>V</sup>*\_ <sup>¼</sup> *<sup>S</sup>*\_

*<sup>P</sup>*^ ¼ �*K*1*S*<sup>2</sup> <sup>þ</sup> *<sup>K</sup>*1*S*<sup>2</sup> <sup>þ</sup> *<sup>S</sup>* �ð Þ *<sup>σ</sup>* <sup>þ</sup> *<sup>a</sup> <sup>ω</sup>*\_ � *bu* <sup>þ</sup> *bT*\_ <sup>L</sup> � *<sup>b</sup> <sup>P</sup>*<sup>~</sup> <sup>þ</sup> *<sup>P</sup>*^ � <sup>1</sup>

*<sup>b</sup> <sup>ω</sup>*\_ <sup>Δ</sup>*<sup>a</sup>* <sup>þ</sup> <sup>Δ</sup>*<sup>b</sup> <sup>T</sup>*\_ *<sup>e</sup>* � *<sup>T</sup>*\_ *<sup>L</sup>*

*Chattering-Free Robust Adaptive Sliding Mode Speed Control for Switched Reluctance Motor*

to be constant during the sampling period. Hence, it can be concluded that ~\_

*S* þ 1 *ρ P*~~\_

defined from (5) are assumed

*ρ* \_

*P* (A.1)

, the derivative of

*<sup>P</sup>*^ <sup>þ</sup> *bS* (A.3)

*<sup>P</sup>* ¼ � \_ *P*^.

> *ρ P*~ \_ *P*^

(A.2)

**Figure 16.** *Two phase currents and voltages for (a) CASMC and (b) RASMC.*
