Portal de Periódicos da CAPES

Advanced Speed‐and‐current control approach for dynamic electric car modelling

2021; Institution of Engineering and Technology; Volume: 11; Issue: 3 Linguagem: Inglês

10.1049/els2.12015

2042-9746

Buddhadeva Sahoo, Sangram Keshari Routray, Pravat Kumar Rout,

Electric Vehicles and Infrastructure

IET Electrical Systems in TransportationVolume 11, Issue 3 p. 200-217 ORIGINAL RESEARCH PAPEROpen Access Advanced Speed-and-current control approach for dynamic electric car modelling Buddhadeva Sahoo, Corresponding Author buddhadeva14@gmail.com orcid.org/0000-0002-5601-1513 Department of Electrical Engineering, Siksha 'O' Anusandhan University, Odisha, India Correspondence Buddhadeva Sahoo, ITER, Dumduma, Jagamara, Department of Electrical and Electronics Engineering, Siksha 'O' Anusandhan (Deemed to be University), Bhubaneswar, 751030, Odisha. Email: buddhadeva14@gmail.comSearch for more papers by this authorSangram Keshari Routray, orcid.org/0000-0002-0508-8705 Department of Electrical and Electronics Engineering, Siksha 'O' Anusandhan University, Odisha, IndiaSearch for more papers by this authorPravat Kumar Rout, Department of Electrical and Electronics Engineering, Siksha 'O' Anusandhan University, Odisha, IndiaSearch for more papers by this author Buddhadeva Sahoo, Corresponding Author buddhadeva14@gmail.com orcid.org/0000-0002-5601-1513 Department of Electrical Engineering, Siksha 'O' Anusandhan University, Odisha, India Correspondence Buddhadeva Sahoo, ITER, Dumduma, Jagamara, Department of Electrical and Electronics Engineering, Siksha 'O' Anusandhan (Deemed to be University), Bhubaneswar, 751030, Odisha. Email: buddhadeva14@gmail.comSearch for more papers by this authorSangram Keshari Routray, orcid.org/0000-0002-0508-8705 Department of Electrical and Electronics Engineering, Siksha 'O' Anusandhan University, Odisha, IndiaSearch for more papers by this authorPravat Kumar Rout, Department of Electrical and Electronics Engineering, Siksha 'O' Anusandhan University, Odisha, IndiaSearch for more papers by this author First published: 30 March 2021 https://doi.org/10.1049/els2.12015AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract Considering environmental conditions and reduced fuel availability, electric cars (ECs) play a vital role in many applications such as consumer cars and short-distance transportation. This paper proposes a detailed dynamic modelling of battery, motor, and inverter developed for the design of an EC. In addition, an improved controller is developed with a different geometrical method using the sensitivity gain of the current sensor and tachometer to assure the optimal performance of the EC. For achieving linear vehicle operation and improved stability, a system transfer function model is designed by considering various uncertainties such as force acting on the car, wheel, road, and wind speed conditions. To offer better regulation and excellent tracking operation of the EC, a combined proportional–integral–derivative controller-based outer-speed and inner-current control approach is suggested to regulate the nonlinear parameters for different driving profile applications. The proposed designed control approach and system model are tested using two input conditions such as step and driving profile inputs through MATLAB/Simulink software, and performance is analysed through various open-loop and closed-loop test scenarios. 1 INTRODUCTION Considering environmental conditions and greater awareness about energy conservation, researchers have been paying more attention to the design of zero-polluting electric cars (ECs) of late. Recently, improvements in EC/hybrid-EC modelling have attracted greater interest at an augmented pace [1]. Particularly, lesser-weight ECs are becoming popular for many applications such as patrol and short-distance transportation cars. Many EC modelling techniques have been suggested to offer a longer driving range and linear operation [2]. Generally, EC modelling is designed by considering two subsystems, such as electric motors (EMs) for the drive system with a car platform, as shown in Figure 1. The main components of ECs are battery energy storage (BES) devices, central control structures, a tachometer, and a voltage source converter to convert DC–AC power. A single EM is used to drive each wheel [3]. However, with increasing costs and complex modelling, [4] the EC can lose its attraction for real-time applications. To achieve greater simplicity and easier control action, the DC EM is popularly selected for the traction of ECs [5]. In addition, DC motors also supply high starting torque. Therefore, to develop a robust/light, high-efficiency, reduced-cost EC, it is necessary to derive an appropriate mathematical model of ECs and EMs for different driving profile operations. FIGURE 1Open in figure viewerPowerPoint Complete system architecture of electric car Simple EC design leads to a simple control strategy that decreases the overall cost of the vehicle. However, the development of the simple EC model is difficult because of uncertainty and non-linearity in the environment and wheel and road conditions [6, 7]. Mostly, disturbances are categorised into two types: (1) parametric uncertainty and (2) inner/outer disturbances. The first type of disturbance is caused by a lack of appropriate information regarding EC modelling, friction modelling, and parameter fault conditions, and the second type of disturbance is generated by unidentified effects of existing physical constraints in the environment [8, 9]. Therefore, there is a necessity to design improved mathematical modelling of EC by considering possible real-time disturbances. Generally, ECs are known as 'power management' machines [10, 11]. Therefore, there is a requirement to design a coordinated control strategy to provide satisfactory driving performance and linear operation by optimally consuming power [12]. Because of the significant growth of microprocessors like digital signal processor boards, it is easier to develop a complex control algorithm for optimal EC operation [13]. The just-mentioned capabilities of the microprocessor-based controller enhance EC performance by improving the safety conditions for specific applications [14]. Many power engineers have proposed various adaptive methods to overcome the first type of problem [15]. Because of the incapability of adaptive filters to solve the second type of problem, a robust adaptive controller is proposed to tackle real-time problems [16-18]. To overcome non-linearity and disturbance conditions, adaptive feedback linearisation techniques are used to approximate a disturbance component [19]. However, offline disturbance identification control techniques are not well suited because of changes in disturbances over time. As a solution, various online adaptation techniques such as fuzzy logic controller (FLC)- and artificial neural network (ANN)-based control techniques deal with the unknown disturbances. Because they use various linguistic variables, FLC techniques are widely accepted as offering better solutions than other soft techniques [20]. In reviewing the related literature such as [21-24], it can be seen that adaptive FLC is divided into two specific classes, direct and indirect, depending on the system condition and applications. In a direct adaptive FLC, fuzzy systems are used as a controller using IF-THEN fuzzy rules [21, 22]. In an indirect FLC, fuzzy systems are used to describe the system model through the IF-THEN rule [23, 24]. However, FLC-based systems reduce performance because of the requirement for an increasing number of fuzzy rules during real-time and multi-input–multi-output systems [22-25]. Moreover, owing to the increasing number of rules, the structure of an FLC becomes more complex in design and provides an additional computational burden on the design model. Similarly, the ANN-based control approach is used as an alternative to deal with the uncertainty because of its excellent tracking capability [24-26]. In adaptive ANN-based approaches, the direct and indirect classes are used to track the unknown disturbances to save time and reduce the effort of complex system modelling [27]. For real-time applications, ANN-based approaches have decreased importance because of their requirements for larger nodes, excess tracking time, slower training speeds, and appropriate input and output data as well as problems with tracking of local minima and filtering. Therefore, there is a necessity to design an improved controller for optimal performance of EC operation in real-time applications. The major objectives of the proposed approach are as follows: For designing a lighter-weight and reduced-cost EC system, the detailed mathematical modelling of EC and EM is presented. By viewing the inner and outer disturbances, two load models are designed. Different subsystem transfer functions of EC components such as the battery, inverter, and motor model are developed. Improved control models are designed using various geometrical methods using the sensitivity gain of both current sensors and tachometer. Using only the speed sensor and combined current-and-speed sensor, two EC models such as model-1 and model-2 are designed. To offer linear output and linear EC operation, a combined proportional–integral–derivative (PID) control-based outer-speed and inner-current control approach is suggested. The performance of the individual designed models is studied during open-loop, speed, and combined speed and current closed-loop control applications. 2 OVERALL STRUCTURE AND DETAILED MODELLING OF ELECTRIC CAR Figure 1 shows the complete system architecture of the EC model. The basic model of the EC is designed by focussing on two subsystems, dynamic modelling of an electric motor (DMEM) and dynamic modelling of an electric car (DMEC). The modelled EC is coupled with wheel rotational speed through an EM to achieve the desired speed. In addition, the actual performance of the EC depends on the force acting on it. Therefore, considering all the above factors, there is a necessity to develop an appropriate EC model. An appropriate torque and power model is computed to provide the detailed dynamic modelling of the respective EM and EC presented below. 2.1 Dynamic modelling of electric motor The main role of an EM is to provide necessary force for EC speed regulation as indicated in Figure 2. Therefore, appropriate mathematical modelling of the EM is much more important for EC operation. To assure a suitable speed-up time, the driving EM necessitates excess torque output at slower speeds and reduced torque output at higher speeds. In addition, to achieve sustained high speeds, a driving EM is necessary to attain a certain power output during high-speed operation [28]. The appropriate dynamic equation of EM is obtained by combining Newton's and Kirchhoff's laws. FIGURE 2Open in figure viewerPowerPoint Simplified equivalent circuit of electric motor The basic mathematical equations of any EM are presented as follows: V s = R f i f + d Ψ f d t ± ω f Ψ f Ψ f = L f i f + L m ( i f + i a ) Ψ f m = L m ( i f + i a ) } (1) V r = R a i a + d Ψ a d t ± ( ω f − ω e ) Ψ a ψ a = L a i a + L m ( i f + i a ) Ψ a m = L m ( i f + i a ) } (2)where Vs and Vr are the field and armature voltages of EM, Rf and Lf are the field resistance and inductance of EM, Ra and La are the armature resistance and inductance of EM, Lm is the mutual inductance of EM, Ψ f and Ψ a are the field and armature fluxes of EM, Ψ f m and Ψ a m are the mutual field and armature flux components, and If and Ia are the field and armature currents of EM. A simplified equivalent circuit of an EM is illustrated in Figure 2. In Figure 2, both electrical and mechanical components of the EM are illustrated. A detailed explanation of the electrical and mechanical modelling of the motor is provided below. 2.1.1 Electrical modelling of motor As shown in Figure 2, by providing an input voltage (Vin) to the EM, the EM coil generates an electrical torque (Te) in the armature winding. The generated Te is computed by multiplying the armature current (Ia) with the torque constant (Kt) and represented as T e = K t × I a (3) During the armature action between the stator field, the EM produces an electromotive force (Eb) reverse to the direction of Ia. Eb is computed by multiplying the Eb constant (Kb) with an angular speed of the motor ( ω e ) and represented as E b ( t ) = K b × d θ e ( t ) d t = K b ω e (4) Applying Kirchhoff's law to the electrical side of the motor, the total voltage (VT) is computed as V T = ∑ V = V i n − V R a − V L a − E b = 0 (5)where VRa and VLa are denoted as the voltage drop across armature resistance and inductance, respectively. The armature current of the motor can be computed as V i n = R a I a + L a d I a d t + K b d θ d t (6) The Laplace transform of Equation 6 becomes V i n ( s ) = R a I a ( s ) + L a s I a ( s ) + K b ω e ( s ) (7) I a ( s ) = V i n ( s ) − K b ω e ( s ) ( R a + L a s ) (8) 2.1.2 Mechanical modelling of motor Because of the moment of inertia of motor (JM), damping motor friction constant (BM), and load, the torque produced by the motor generates an angular speed ( ω M = d θ M / d t ). By balancing the energy of the motor, the mathematical modelling describing the mechanical characteristics of the motor can be presented as follows: T θ M = J M × d 2 θ M d t 2 (9) T M = K t × I a (10) T ω M = B M d θ M d t (11) The total torque (Tt) equation becomes ∑ T t = T M − T θ M − T ω M = 0 (12) T = K t × I a − J M × d 2 θ M d t 2 − B M ( d θ M d t ) = 0 (13) Taking the Laplace transform of Equation 13, T ( s ) = K t × I a ( s ) − J M × s 2 θ M ( s ) − B M s θ M ( s ) = 0 (14) I a ( s ) = ( s J M + B M ) s θ M ( s ) K t (15) 2.1.3 Developing the motor open-loop transfer function From Equations 8 and 15, the transfer function values are presented as follows: I a ( s ) V i n ( s ) − K b ω e ( s ) = 1 ( R a + L a s ) (16) ω M ( s ) I a ( s ) K t = 1 ( s J M + B M ) (17) Substituting Equation (16) into Equation (14), the equation becomes K t V i n ( s ) − K b ω e ( s ) ( R a + L a s ) = ( J M × s + B M ) s θ M ( s ) (18) Rearranging Equation (18) without load angle, the open-loop transfer function (Ga(s)) related to the input voltage (Vin) and output angle ( θ M ( s ) ) of the motor can be computed as G a ( s ) = θ M ( s ) V i n ( s ) = K t s { ( s L a + R a ) ( s J M + B M ) + K t K b } (19) Rearranging Equation (18) without load, the speed open-loop transfer function (Gs(s)) related to the input voltage (Vin), and output angular velocity ( ω M ( s ) ) of the motor can be computed as G s ( s ) = ω M ( s ) V i n ( s ) = K t ( s L a + R a ) ( s J M + B M ) + K t K b (20) To design an appropriate open-loop transfer function for EC operation, it is necessary to compute all moments of inertia for better results. Generally, the EC platform can be a shape of cuboid or cubic shape. Therefore, the total moment of inertia (JT) and total damping factor (BT) at the armature of EM with gear ratio (n) is computed using the conservation principle: B T = B M + B L ( N l N m ) (21) J T = J M + J L ( N l N m ) (22) J L = M T V 2 ω M 2 (23)where JL is the load inertia, MT is the total mass of the system, and Nl and Nm are defined as the number of teeth presented in the load and motor gears, respectively. By considering the linear velocity of EC (V), the angular speed of the motor ( ω M ), tyre radius (r), and gear ratio (n), the moment of inertia of load (JL) is computed as ω M = ω s × n = V × n r (24) V = ω M × r n (25) Applying Equation (25) to Equation (23), JL becomes, J L = M T r 2 n 2 (26) By considering the above-discussed equations, the equivalent EC open-loop transfer function (Gs(s)) can be presented as G s ( s ) = ω M ( s ) V i n ( s ) = K t / n ( s L a + R a ) ( s J T + B T ) + K t K b (27) By considering the armature voltage input (Vin) and the output voltage of the tachometer (Vtach) with the corresponding load torque (TL), the EC open-loop transfer function (Go(s)) can be presented as G o ( s ) = V o ( s ) V i n ( s ) = K t a c h × ω M ( s ) V i n ( s ) = K t × K t a c h ( s L a + R a ) ( s J T + B T ) + ( s L a + R a ) × T + K t K b (28)where T is denoted as the disturbance torque including the Coulomb friction (TF). To track the actual speed of the EC and feed it back to the control system, a tachometer is used in the EC. The tachometer dynamics and corresponding transfer function are illustrated in Equation (29). To achieve a linear speed for the EC of 23 m/s, the tachometer constant (Ktach) selected is 0.4696 [28]: V o ( t ) = K tach × d θ M ( t ) d t ⇒ V o ( s ) = K tach × ω M ( s ) (29)where Vo is denoted as the system output voltage. 2.2 Dynamic modelling of electric car Figure 3 illustrates the overall motion diagram of ECs by showing various forces. By balancing the magneto and electromotive forces of the electric motor and operating resistive forces [28], the speed of the EC is decided. To derive an accurate DMEC, it is much more important to track the dynamics among road, wheel condition and acting forces such as the wind force (FW), inertia force (FI), rolling force (FR), traction force (FT), and normal force (FN) on the EC. EC torque disturbance is the resultant torque produced by all the resistive forces acting on the EC as presented below: F T = M C V ˙ C ⏞ F I + M C . g . sin ( θ ) ⏞ F g + s i g n ( V C ) M C . g . cos ( θ ) ⏞ F N . C r ⏟ F R + s i g n ( V C + V W ) 1 2 ρ C d A f ( V C + V W ) 2 ⏟ F W + [ ( M C + J W r 2 ) × V ˙ C ] ⏟ F a _ a c c (30) F a _ a c c = I a [ G r ] 2 (31)where MC is the mass of the car (kg), VC is the velocity of EC (m/s), V˙C is the acceleration of EC (m/s2), g is the gravitational force on EC (m/s2), θ is the driving angle of EC (rad), Cr is the rolling coefficient of EC, ρ is the density of air at 20°C, Cd is the drag coefficient of EC, Af is the front area of EC, VW is the wind velocity (m/s), JW is the wheel moment of inertia of EC, r is the radius of the wheel, G is the gear ratio, Ia is the armature current of the motor, and Fa_acc is the angular acceleration force. FIGURE 3Open in figure viewerPowerPoint Free body diagram of electric car with different forces After computing the possible force acting on the EC model, it is necessary to design the battery model. The battery is used only to provide the supply voltage for EC operation. Before computing the battery capacity of the EC, it is necessary to estimate the total required electrical energy for EC operation. The power demand is measured in kW, and the power is used to regulate the speed of the EC. The electric power (Pe) is computed by multiplying the total traction force (FT) and VC, and is represented as follows: P e = ∑ F × V C = F T × V C (32) The battery is the key element for EC applications. In recent times, many different types of batteries, such as lead-acid, nickel hydride, and lithium-ion, have been used for various purposes [28]. However, from a real-time application point of view, a lithium-ion-based battery storage device is selected due to the relative increase in specific energy and power [2-4]. 2.2.1 Battery electric model The equivalent battery model is illustrated in Figure 4. As shown, the equivalent battery model is designed using the internal voltage source (Vbi), battery voltage (Vb), charging and discharging diode (Dbc and Dbd), and charging and discharging resistance (Rbc, and Rbd), respectively. Db is known as the forward diode of the battery, and Ib is known as the obtained battery current. The two diodes are generally ideal and used only to facilitate charging and discharging operations. Charging currents are denoted with a '+' sign, and discharging currents are denoted with a '-' sign. The ratings of Vbi, Rbd, and Rbc depend on the depth of battery discharge capability. As indicated in Figure 2, equivalent circuit Vb is computed as follows: V b = { V b i − R b d I b ≥ 0 V b i − R b c I b 〈 0 (33) FIGURE 4Open in figure viewerPowerPoint Equivalent battery model After generating the necessary electric power from the battery (Pe = VC*I) and power available in the wheel of the EC (Pw), the driving angle ( θ) of the EC is computed as follows: θ = P w − P e M C × V C (34) After the successful modelling of the battery and DMEC, to obtain more accurate precision for the value of the disturbance force (FD) acting on the EC, additional factors are considered. By viewing the accuracy demand of the EC, various constraints such as total driving resistance force (Fdr) and EC dynamics can be considered. For smooth acceleration of the EC, the EM of the EC must be able to overcome the Fdr. The modelling of the EC dynamics is simplified in [26-28], and the corresponding equations are presented below. A detailed explanation of the following equations is presented in [29]: F D ( t ) = R w M C g sin ( θ ) + M C g r C r + 1 2 ρ A f C d r ( V W + V C ) 2 (35) T D ( t ) = 1 2 r 2 M C d ω d t + 1 2 M C g r sin ( θ ) + ω C r (36) F D ( t ) = M C V ˙ C ( t ) + 1 2 ρ ( V W ( t ) + V C ( t ) ) 2 A f C d + M C g r C r (37) F D ( t ) = M C K m a + 1 2 M C g sin ( θ ) ( V W ( t ) + V C ( t ) ) 2 A f C d + M C g C r cos ( θ ) (38)where Rw is the wheel resistance, Km is the equilibrium constant and 'a' is the acceleration constant of the EC. From the derived dynamic equations presented as Equations (30, 35–38-35–38), two load models are derived and presented in Figure 5a,b. To meet the accuracy level, all the related parameters stated above are considered for the design of the accurate load model. The combined load model to provide an accurate idea of disturbance torque (TD) is illustrated in Figure 6. G F ( s ) = 2 K t a c h K t 2 B e s ( s L a + R a ) + r 2 M C s ( L a + R a ) + C r ( s L a + R a ) + 2 J e ( s L a + R a ) + 2 K b K t (39) FIGURE 5Open in figure viewerPowerPoint Disturbance torque model of electric car considering various forces. (a) Possible load model by using Equations (35–38-35–38) and (b) Load model by using Equation (30) FIGURE 6Open in figure viewerPowerPoint Combined load model for computation of disturbance torque Simplifying Equation (39), GF(s) becomes, G F ( s ) = 2 K t a c h K t ( s L a + R a ) ( 2 J e + 2 B e s + C r ) + s ( L a + R a ) r 2 M C + 2 K b K t (40) Depending on all the derived force/torque equations, armature input voltage (Vin (s)), and output voltage of the tachometer (Vtach), and by considering all the combined load parameters, a simplified open-loop transfer (GF(s)) function for the EC model is presented in Equation (39). The fundamental closed-loop transfer function Simulink model is illustrated in Figure 9a by considering DMEC, wheel rotational velocity, tachometer voltage, EM modelling, and disturbance forces acting on the system. 3 RESULTS After considering uncertainty and assessing costs and complexity, two types of EC model (model-1 and model-2) are suggested. Model-1 is designed by considering only the speed sensor. Similarly, model-2 is designed by combining both the speed and the current sensor. In this section, individual model results are tested through both a single-loop and a two-loop control system. The individual test results are analysed in the following sections. 3.1 Comparison and validation of the proposed controller In this section, the performance of the open-loop test model EC presented in Equation 40 is compared with the proportional–integral (PI) control-based EC model through different responses such as frequency response, impulse response, Hankel singular values and relative error between the two systems as shown in Figure 7. As illustrated in the Figure 7a bode diagram, the closed-loop PI control-based EC model captures a resonance of less than 50 rad/s. Although it looks like a substantially impressive result, the tracking of the lower frequency region (<5 rad/s) is poor. Because of the different load torque, the conventional PI control-based closed-loop model does not fully track the dynamics of the proposed EC model within 30–50 rad/s. As a result, the possibility of large errors and lower gain in the EC model arises at a lower frequency range. Therefore, large errors at low frequency contribute little to increasing the overall error. FIGURE 7Open in figure viewerPowerPoint (a) Bode diagram of electric car (EC) (b) Impulse response of EC (c) Hankel singular value response (d) Relative error response of EC 3.1.1 Solution To overcome the above problem, this proposed approach uses a multiplicative error method such as 'bstmr'. This technique emphasises relative error rather than absolute error because this technique does not work under near-zero gain. Therefore, in this approach, a minimum gain threshold is added to the original open-loop EC model. After adding the gain, the open-loop model is converted to a closed-loop EC model using a PI controller. The PI controller-based model is not worried about errors below −100 dB gain. In addition, a minimum value nearer to 1e−5 is added to the gain to reduce the error. To validate system performance, a comparative impulsive response is presented using the above approach as illustrated in Figure 7b. The impulse response is plotted between the open-loop EC and proposed PI control-based EC models. Figure 7b shows that the settling time of the open-loop system is 10.7 s, and the settling time of the PI control-based closed-loop system is 6.8 s. The illustrated impulse response gives a clear idea about the improvement of the PI control-based EC model (GF,closed) over the open-loop EC model (GF,open) through the settling time. 3.1.2 Validation of results Generally, all techniques offer bounds on the approximation error. In this approach, using additive-error methods like 'balancmr', the approximation error is measured through the maximum peak gain (Pg,max) of the error model GF,closed across all frequencies. This Pg,max is also identified as the H ∞ norm of the GF,closed. The error bound for the additive-error technique is expressed as follows: G F , o p e n − G F , c l o s e d ≤ 2 ∑ i = 9 45 σ i = e r r o r b o u n d (41)where the sum is over all discarded Hankel singular values of GF,open (entries 9 through 45 of Hankel singular values of GF,open) indicated in Figure 7c. The Hankel singular value response illustrates that there are four dominant modes in GF,open. However, the contribution of the remaining modes is still significant. In this approach, a line is drawn at eight states, and the remaining ones are discarded, to find the eighth-order reduced GF,closed that best approximates the original system response GF,open. From the relative error plot indicated in Figure 7d, there is up to 65% relative error at 25.5 rad/s frequency and 8.54 dB Pg,max, which may be represent a better choice that offers a better response than that of GF,open alone. Therefore, in this proposed approach, the combined load-based EC model is operated through both PI-control-based speed and current loop. 3.2 Scenario-1: open-loop testing model of electric car By considering the developed system models DMEM and DMEC, the overall mathematical model of the EC is designed. Step input signals (Vin = 36) and driving cycle-based reference input signals are used to test the performance of the designed EC model. The driving cycle-based input signal is modelled by considering the acceleration of EC at rated EC speed and braking of the EC until null velocity is achieved. This scenario is tested to show the accuracy of the control system and the overall performance of the designed EC. Figure 8 shows the results of linear speed, armature current, motor torqu