TECHNICAL FIELD

[0001] The present invention relates an electric machine of a vehicle, and more particularly, the present invention relates to a controller for the electric machine of a vehicle.

BACKGROUND

[0002] An electric machine is usually composed of stator and rotor. Generally, for a BLDC machine having a star winding configuration, and the controller used for such machines are also equipped with six power electronic switches that control the current through three phases of the machine, in such a manner that the current flows through two phases at any instance. The switches are so arranged that two of the switches are connected in series between the power supply and three such configurations are repeated. Further, the middle portion of each configuration is connected to the phase ends of the star winding configuration.

[0003] This results in six stable positions for the magnetic field causing six ripples in a torque waveform for one complete mechanical revolution of the rotor. The ripples have a negative effect on the average torque, which further reduces the available load torque that can be applied to the load. Thus, in such machines, for meeting the load-torque requirements the overall size of the machine is generally larger, which could impede the placement of the machine in a vehicle, more particularly, on small sized vehicles such as a two-wheeler or three wheeler.

[0004] Therefore, there is a need to provide a compact sized machine, which can deliver more average torque for meeting the load-torque requirements of the vehicle.

BRIEF DESCRIPTION OF THE DRAWINGS

[0005] The detailed description is described with reference to the accompanying figures. The same numbers are used throughout the drawings to reference like features and components. [0006] Fig. 1 illustrates a left side view of an exemplary two-wheeled vehicle, in accordance with an embodiment of the present subject matter.

[0007] Fig. 2 illustrates a typical cross section of an electric machine in accordance to an embodiment of the present invention.

[0008] Fig. 3 depicts a block diagram of a control system for assisting an internal combustion engine of a vehicle during starting and during high speed operations in accordance to an embodiment of the present invention.

[0009] Fig. 4 illustrates a provides phase diagram representation of three of the six possible states of the switches of a three-phase switching network of power electronic switches, in accordance to an embodiment of the present invention.

[00010] Fig. 5 illustrates the six-switch network of power electronic switches depicted in Fig. 4, which results in switching of the three-phase electric machine depicted in Fig.2.

[00011] Fig.6 provides the phase diagram representation of the six possible states of the switches of the three-phase switching network of power electronic switches, in accordance to an embodiment of the present invention.

[00012] Fig.7 illustrates the six-switch network of power electronic switches having an additional leg of switches that is electrically connected to the neutral point of the coils of the star winding of the electric machine depicted in Fig.2.

[00013] Fig.8 depicts a torque waveform of a conventional electric machine connected in accordance with the network shown in Fig. 5.

[00014] Fig. 9 depicts a torque waveform of the inventive electric machine connected in accordance with the network depicted in Fig.7.

DETAILED DESCRIPTION

[00015] The present invention describes a machine which is beyond ISG in terms of functionality. This invention is also designed to provide assistance to the engine under high load conditions at high speed so that vehicle and engine operation can be performed to reduce C02 and NOx emissions. [00016] Further, the present invention can be realized with the help of multiple machine topologies, such as Induction machine, switched reluctance machine (SRM), and BLDC (brush less direct current) machine. Induction and switched reluctance machines are operated with corresponding power electronic controllers that regulate the torque based on the input conditions such as present speed of rotation.

[00017] While induction machine and SRM do not have, the speed limited by induced back-emf (electro motive force), BLDCDs speed range suffers due to this induced voltage. This is the voltage induced in the winding coils due to the rate of change of flux in the coils caused by presence of rotating magnets. This voltage limits the current flow into the machine, limiting the possible torque at speeds above zero depending on the supplied voltage.

[00018] When a machine is designed for starting and power assist operations, requirements are conflicting. Starting requires high torque constant, and power assist requires high speed/power operation and in turn low torque constant.

[00019] The present invention provides a BLDC machine and a controller for the BLDC machine having eight power electronic switches with the switches arranged in a manner that two of the switches, with one in top and one in bottom are connected in series between the power supply and four such configurations are repeated. Further, the middle portions of the first three configurations are connected to the phase ends of the star winding configuration, while the middle portion of the fourth configuration is connected to the neutral point of the star winding configuration.

[00020] Further, each of the switches is operated by a microcontroller individually through power electronic switching circuits. Each of the switches is composed of parallel combination of multiple power electronic switching circuit elements.

[00021] The conventional BLDC machine and its controller provided with three configurations having six switches, when operated in a predetermined sequence, in which the switches from two different configurations are operated wherein one of the switch is a top switch and the other is a bottom switch, a rotating magnetic field is established in the stator of the BLDC machine. Generally, the rotating magnetic field causes the rotor to follow the magnetic field for establishing the rotational motion of the rotor.

[00022] In such BLDC machines, the rotating magnetic field is created in steps of 60° electrical angle, which results in rotor torque selected as a combination of 60° of the torque versus angle waveform, which has a peak torque resulting in six repeated torque waveforms. This will have six torque ripples within 360° electrical rotation of the rotor. The average torque of the rotor is generally the mean of the peak torque and the lowest torque of the output torque waveform. In such a case, the average torque of the rotor is lower than the peak torque, which results in machine meeting only lower load torque requirements.

[00023] Hence, in the present invention, an dedicated switch configuration as a fourth switch configuration is implemented such that the middle portion of the fourth configuration is connected to the neutral point of the star winding configuration of the machine. By such a configuration, the present invention achieves a possible switch configuration that can result in finer steps of less than 60° electrical angle, for instance, of 30° electrical angle of the rotating magnetic field.

[00024] For example, in an embodiment, the present invention involves turning on the top switch of the first switch configuration and the bottom switch of the fourth switch configuration to result in a current flow through only one of the phases, for the first 30° electrical angle of the rotating magnetic field. For the next 30° electrical angle of the rotating magnetic field, the top switch of the first switch configuration and the bottom switch of the second switch configuration are turned on resulting in a current flow through two of the phases of the stator winding. Similarly, 30° angle steps of the rotating magnetic field can be achieved. By this configuration, it is possible to increase the lowest torque of the output torque waveform, which in turn increases the average torque of the rotor and still keeping the peak torque same. In such a case, with the higher average torque, it is possible for the BLDC machine to meet higher load torque requirements. [00025] In an implementation, the resulting phase of the magnetic field in the airgap of the electric machine is rotated by 30°in each step. Correspondingly more number of Hall Effect sensors may be placed on the stator of the electric machine to detect the 30° revolution of the rotor. In another embodiment, the position of the rotor is predicted based on the previously known position of the rotor and the calculated speed, resulting from the traditional three Hall Effect sensors that are mounted on the stator.

[00026] The current limit of the controller during the times when only one of the phases is switching is increased such that the peak amplitude of the resulting magnetic field will be maintained same.

[00027] In an embodiment, the present invention enables to achieve BLDC machine of compact size and less weight, enabling it to be fitted in a small size vehicle. Further, the present invention also helps in achieving higher average torque enabling the machine to meet higher load torque requirements of the vehicle. For BLDC machines that are designed for high speed motoring operations, the starting torque is generally lower. However, the present invention provides a BLDC machine that is configured to achieve higher starting torque that can meet the vehicleDs startability requirements, for example, the startability requirement of an powertrain e.g. an internal combustion engine of the vehicle, in addition to catering the high-speed motoring operations.

[00028] In one of the embodiment, the proposed electric machine is used to assist the rotation of crankshaft of the internal combustion engine, with the peak torque at operating current being limited to about 50Nm both during starting of the vehicle and during providing power assistance to the internal combustion engine during running of the vehicle. Further, the peak torque at operating current of the electric machine of the present invention is less than the operational requirement of a traction motor of a hybrid and/or electric vehicle.

[00029] In an embodiment, the present subject matter provides a control system for assisting an internal combustion engine of a vehicle during starting and during high speed operations and achieving higher average torque. The control system of the present invention is provided with an electric machine that is compact and capable of being accommodated in a small vehicle and a power source. The control system is also capable of achieving reduction in exhaust emissions at high speed operations.

[00030] In an embodiment, the control system of the present invention comprises the electric machine of BLDC type. The electric machine includes a stator having a plurality of teeth, each tooth of said plurality of teeth is wound with conducting wire to form a winding connected in a star winding configuration. The electric machine including a rotor having a plurality of permanent magnets that are arranged facing the plurality of teeth of said stator.

[00031] In an embodiment, the control system of the present invention comprises a machine controller including at least one microcontroller. The machine controller includes a first set of switch configuration having six switches arranged in first, second, and third switch configurations, wherein said first, second, and third switch configurations include two switches connected in series between terminals of said power source respectively. The first set includes three top switches and three bottom switches, wherein a first junction portion of each of said two switches that are connected in series is connected to a connector end of a first phase of said star winding configuration. A second junction portion of each of said two switches that are connected in series is connected to a connector end of a second phase of said star winding configuration is provided. A third junction portion of each of said two switches that are connected in series is connected to a connector end of a third phase of said star winding configuration. The machine controller including a second set of switch configuration arranged in a fourth switch configuration having two switches connected in series between the terminals of said power source, said second set includes a fourth junction portion connected to a neutral point of said star winding configuration.

[00032] In an embodiment, the control system includes at least one microcontroller which turns ON a switch configuration of predetermined sequence resulting in a 30° electrical angle steps of a rotating magnetic field.

[00033] Further, in an embodiment, the control system is provided with the at least one microcontroller, which turns on the top switch of the first switch configuration and the bottom switch of the fourth switch configuration causing a current flow through said first phase for a first 30° electrical angle of the rotating magnetic field. The at least one microcontroller turns on the top switch of the first switch configuration and the bottom switch of the second switch configuration causing a current flow through said first phase and said second phase for a second 30° electrical angle of the rotating magnetic field.

[00034] Further, in an embodiment, the at least one microcontroller causes 30° angle steps of the rotating magnetic field by turning ON the first set and the second set of the switch configurations in a predetermined sequence.

[00035] In an implementation, the plurality of permanent magnets of said BLDC electric machine are mounted on a surface of said rotor facing said stator. In an alternative implementation, the plurality of permanent magnets of said BLDC electric machine are embedded inside said rotor.

[00036] Further, in an implementation, the electric machine is a brushless direct current motor having said rotor disposed inside said stator. In another implementation, the electric machine is a brushless direct current motor having said rotor disposed outside said stator.

[00037] In an embodiment, the first set and said second set of switch configurations are composed of parallel combination of multiple power electronic switching circuit elements. In one embodiment, the power source for supplying energy to said electric machine when said electric machine is operating as a motor, and for storing energy in a power source , generated by said electric machine when said electric machine is operating as a generator.

[00038] In an implementation, the control system comprises one or more sensors capable of sensing an operational position of said rotor. In one embodiment, the rotor is capable of rotating by interacting with a magnetic field produced by the stator upon receiving electrical energy from at least one energy storage device, said rotor separated from said stator by an air gap, and wherein said magnetic field is perpendicular to an axis of rotation of said rotor.

[00039] In an alternative embodiment, the rotor is capable of rotating by interacting with a magnetic field produced by the stator upon receiving electrical energy from at least one energy storage device, said rotor separated from said stator by an air gap, and wherein said magnetic field is parallel to an axis of rotation of said rotor.

[00040] In one embodiment, the electric machine is capable of achieving a peak torque at operating current, said peak torque is at most 50 Nm both during starting of the engine and while providing power assistance to the internal combustion engine during running of the vehicle. In an alternative embodiment, the peak torque is at most 10 Nm to 30 Nm in case of three-wheeled vehicles. Similarly, the peak torque can be in the range of at most 7 Nm in case of two-wheeled vehicle, for example, motorcycles and scooter type vehicles with an engine capacity of about l lOcc. In an embodiment, for higher capacity two-wheeled vehicles, for example, motorcycles of engine capacity of about 200cc, the peak torque can be at most lONm.

[00041] These and other advantages of the present subject matter would be described in greater detail in conjunction with the figures in the following description.

[00042] Fig. 1 illustrates a left side view of an exemplary two-wheeled vehicle, in accordance with an embodiment of present subject matter. The vehicle 100 has a frame assembly 105, which acts as the structural member and as skeleton of the vehicle 100. The frame assembly 105 includes a head tube 105 A through which a steering assembly is rotatably journaled. The steering assembly includes a handle bar assembly 111 connected to a front wheel 115 through one or more front suspension(s) 120. A front fender 125 covers at least a portion of the front wheel 120. Further, the frame assembly 105 includes a main tube (not shown) extending rearwardly downward from the head tube 105 A. A fuel tank 130 is mounted to the main tube 105 A. Furthermore, a down tube (not shown) extends substantially horizontally rearward from a rear portion of the main tube. In addition, the frame assembly includes one or more rear tube(s) (not shown) that extends inclinedly rearward from a rear portion of the down tube. In a preferred embodiment, the frame assembly 105 is mono-tube type, which extends from a front portion F to a rear portion R of the vehicle 100. [00043] In one embodiment, a power unit 135 is mounted to the down tube. In an embodiment, the power unit 135 includes an IC engine. The fuel tank 130 is functionally connected to the power unit 135 for supplying fuel. In a preferred embodiment, IC engine is forwardly inclined i.e. a piston axis of the engine is forwardly inclined. Further, the IC engine 135 is functionally coupled to a rear wheel 140. A swing arm 140 is swingably connected to the frame assembly 105 and the rear wheel 145 is rotatably supported by the swing arm 140. One or more rear suspension(s) 150, which are connecting the swing arm 145 at an angle, sustain both the radial and axial forces occurring due to wheel reaction. A rear fender 155 is disposed above the rear wheel 145. A seat assembly 160 is disposed at a rear portion R of the step-through portion defined by the frame assembly 105. In an embodiment, the seat assembly 160 includes a rider seat 160A, and a pillion seat 160B. Further, the pillion seat 160B is positioned above the rear wheel 145. Further, the vehicle 100 is supported by a centre stand (not shown) mounted to the frame assembly 105. A floorboard 165 is mounted to the down tube and is disposed at the step-through portion. The floorboard 165 covers at least a portion of the power unit 135. The vehicle 100 is employed with an auxiliary power unit (not shown) supported by the frame assembly 105, for example, an energy storage device such as battery. Additionally, the vehicle 100 is provided with at least one set of foot rest(s) 180 for the rider/pillion to rest their feet.

[00044] Fig.2 illustrates a cross-section of an electric machine with respect to an embodiment of the present invention. In an embodiment, the electric machine is an outer rotating BLDC machine. In an embodiment, the outer rotating BLDC machine acts as an integrated starter generator (ISG). The electric machine 101 of the present subject matter includes a rotor 104, which further includes a back iron 106 and a plurality of magnets 108 that are disposed on the inner surface of the rotor 104. In an embodiment, the back iron 106 rotates along with the rotation of the rotor 104. In an embodiment, the plurality of magnets 108 is permanent magnet.

[00045] Further, the back iron 106 can be made out of any one of iron, silicon steel, which is either made as one full block of iron or silicon steel. Alternatively, the back iron 106 is made as layers of iron or silicon steel with plurality of electrical insulation layers in between. In an embodiment, the plurality of magnets 108 can be any one of arc type magnets and flat magnets. Further, in one embodiment, the plurality of magnets 108 is disposed adjacently to each other circumferentially, without any gap. Alternatively, the plurality of magnets 108 can be disposed adjacently to each other circumferentially with circumferential air gap between two adjacent magnets of the plurality of magnets 108.

[00046] Further, the electric machine 101 includes a stator 102 having a centrally provided stator core 118 around which a plurality of stator teeth 112 are circumferentially disposed forming a plurality of stator slots 114 therebetween. In an embodiment, the plurality of stator slots 114 is further filled with plurality of winding 116. In an embodiment, the stator 102 is enclosed within the rotor 104 and radially separated by an air gap 110. In an embodiment, each tooth of the plurality of stator teeth 112 includes a stem portion. In one embodiment, the stem portion of the tooth of the plurality of stator teeth 112 is provided with equal width on both ends of the stem portion, i.e., at a first end that is towards the stator core 118 and a second end that is away from the stator core 118. In an alternative embodiment, each slot of the plurality of stator slots 114 is formed to have equal width at both ends, i.e., at an end that is closer to the stator core 118 and at an end that is away from the stator core 118, which is achieved by two adjoining tooth of the plurality of stator teeth 112 having different widths at both its ends. In another alternative embodiment, each of the tooth of the plurality of stator teeth 112 and the each of the slot of the plurality of stator slots 114 are formed in such a manner that the width of the tooth and the slot at both the ends are not equal. In one embodiment, the stem portion of the each of the tooth of the plurality of stator teeth 112 ends with a head portion facing the rotor 104, and has a width that is wider than the stem portion.

[00047] Fig. 3 depicts a block diagram of a control system for assisting an internal combustion engine of a vehicle during starting and during high speed operations in accordance to an embodiment of the present invention. In an embodiment, the control system 200 includes a machine controller 202, which further includes at least one microcontroller 204, and a plurality of switches 214. The machine controller 202 that is powered by an energy storage device, for example, a battery 212 and is capable of receiving inputs from one or more sensors 208. Based on the inputs received from the one or more sensors 208, the machine controller 202 controls the electrical machine 101 to operate effectively both during the starting of the vehicle by providing a boost voltage to the electrical machine 101, and during running operation of the vehicle by providing a voltage from the battery 212.

[00048] In an embodiment, the microcontroller 204 is capable of processing the signals received from the one or more sensors 208 for effective starting operation of the vehicle.

[00049] Fig. 4 illustrates a phase diagram representation of three of the six possible states of the switches of a three-phase switching network of power electronic switches, in accordance to an embodiment of the present invention. In an embodiment, the phase diagram 402 depicts the resulting magnetic field, as represented in 2d vectors along the magnetic field due to phase A of the electric machine 101 and the magnetic field due to phase -B of the electric machine 101. In one embodiment, the phase diagram 404 depicts the resulting magnetic field, as represented in 2d vectors along the magnetic field due to phase A of the electric machine 101 and the magnetic field due to phase -C. Similarly, in an embodiment, the phase diagram 406 depicts the resulting magnetic field, as represented in 2d vectors along the magnetic field due to phase B of the electric machine 101 and the magnetic field due to phase -C of the electric machine. In an embodiment, the above mentioned three sequences ABD, ACD, and BCD are in rotating clockwise sequence separated by 60°.

[00050] Fig. 5 illustrates the six-switch network of power electronic switches depicted in Fig. 4, which results in switching of the three-phase electric machine depicted in Fig.2. In an embodiment, the power electronic circuitry 300 of the machine controller 202 includes a first top switch 314 and a first bottom switch 316 arranged in series forming a first junction portion 308 therebetween. The first top switch 314 is connected to the positive terminal of the battery 212, while the first bottom switch 316 is connected to the negative terminal of the battery 212. Similarly, the power electronic circuitry 300 of the machine controller 202 also includes a second and third top switches 318, 322 arranged in series to second and third bottom switches 320, 324 respectively, forming second and third junction portions 310, 312 at their corresponding intersections. The first top and bottom switches 314, 316 is arranged in parallel to the second top and bottom switches 318, 320, and the third top and bottom switches 322, 324. The first, second, and the third junction portions 308, 310, 312 are further connected to phase ends of the electrical machine 101 , for example, phase ends A, B, C 302, 304, 306 of the electrical machine 101 such that the electrical connection between the machine controller 202 and the electrical machine 101 is established.

[00051] Fig.6 provides the phase diagram representation of the six possible states of the switches of the three-phase switching network of power electronic switches, in accordance to an embodiment of the present invention. In an embodiment, the phase diagram 402 depicts the resulting magnetic field, as represented in 2d vectors along the magnetic field due to phase A of the electric machine 101 and the magnetic field due to phase -B of the electric machine 101. In one embodiment, the phase diagram 404 depicts the resulting magnetic field, as represented in 2d vectors along the magnetic field due to phase A of the electric machine 101 and the magnetic field due to phase -C. Similarly, in an embodiment, the phase diagram 406 depicts the resulting magnetic field, as represented in 2d vectors along the magnetic field due to phase B of the electric machine 101 and the magnetic field due to phase -C of the electric machine. Similarly, the present subject matter provides a phase diagram 602 in which the resulting magnetic field along the magnetic field due to phase -B of the electric machine 101. In an embodiment, the resulting magnetic field due to phase -B and the resulting magnetic field of the phase diagram 402 are in a rotating clockwise sequence separated by 30°. Similarly, the phase diagrams 604 and 606 provides the resulting magnetic field due to phase A and phase -C. Further, the resulting magnetic field due to phase A and the resulting magnetic field of the phase diagram 404 are in a rotating clockwise sequence separated by 30°, while the resulting magnetic field due to phase -C and the resulting magnetic field of the phase diagram 406 are in a rotating clockwise sequence separated by 30°.

[00052] Fig.7 illustrates the six-switch network of power electronic switches having an additional leg of switches that is electrically connected to the neutral point of the coils of the star winding of the electric machine depicted in Fig.2. In an embodiment, the power electronic circuitry 700 of the present invention further includes a fourth top switch sw7 704 and a fourth bottom switch sw8 706 that are arranged in series forming a fourth junction portion N 708 therebetween. In an embodiment, the fourth junction portion N 708 is further connected to a phase end of the electrical machine 101, for example, neutral point N 702 of the star winding configuration of the electrical machine 101, such that when the current passes through one of the above switches through to the neutral point N 702, the resulting magnetic field is separated by 30°, thereby reducing the average

[00053] Fig.8 depicts a torque waveform 500 of a conventional electric machine connected in accordance with the network shown in Fig. 5. In an embodiment, the rotating magnetic field is created in steps of 60° electrical angle, which results in rotor torque selected as a combination of 60° of the torque versus angle waveform, which has a peak torque resulting in six repeated torque waveforms. This will have six torque ripples within 360° electrical rotation of the rotor of the electric machine 101. The average torque of the rotor is generally the mean of the peak torque and the lowest torque of the output torque waveform. In such a case, the average torque of the rotor is lower than the peak torque, which results in machine 101 meeting only lower load torque requirements. For example, the waveform 508 includes ripple 1 that is contributed by top switch in phase A and bottom switch in phase B. Similarly, ripple 2 is contributed by top switch in phase A, bottom switch in phase C. While, ripple 3 is contributed by top switch in B phase, bottom switch in C phase. Similarly, ripple 4 is contributed by top switch in B phase, bottom switch in A phase, and ripple 5 is contributed by top switch in C phase, and bottom switch in A phase. Lastly, ripple 6 is contributed by top switch in C phase and bottom switch in B phase. The cycle repeats in this sequence.

[00054] Fig. 9 depicts a torque waveform 600 of the inventive electric machine connected in accordance with the network depicted in Fig.7. in an embodiment, an additional switch configuration as a fourth switch configuration as shown in Fig. 7 is introduced such that the middle portion of the fourth configuration is connected to the neutral point of the star winding configuration of the machine 101. By such a configuration, the present invention achieves a possible switch configuration that can result in finer steps of less than 60° electrical angle, for instance, of 30° electrical angle of the rotating magnetic field, involves turning on the top switch of the first switch configuration and the bottom switch of the fourth switch configuration to result in a current flow through only one of the phases, for the first 30° electrical angle of the rotating magnetic field. For the next 30° electrical angle of the rotating magnetic field, the top switch of the first switch configuration and the bottom switch of the second switch configuration are turned on resulting in a current flow through two of the phases of the stator winding. Similarly, 30° angle steps of the rotating magnetic field can be achieved. By this configuration, it is possible to increase the lowest torque of the output torque waveform, which in turn increases the average torque of the rotor and still keeping the peak torque same. In such a case, with the higher average torque, it is possible for the BLDC machine 101 to meet higher load torque requirements. For instance, in an implementation, the torque waveform 602 includes ripple 7, which is contributed by top switch in N phase, bottom switch in B phase. Similarly, ripple 8 is contributed by top switch in A phase, bottom switch in B phase. The ripple 9 is contributed by top switch in A phase, bottom switch in N phase, while the ripple 10 is contributed by top switch in A phase, bottom switch in C phase. Similarly, ripple 11 is contributed by top switch in N phase, bottom switch in C phase, while the ripple 12 is contributed by top switch in B phase, bottom switch in C phase. In similar manner, the ripple 13 is contributed by top switch in B phase, bottom switch in N phase, while the ripple 14 is contributed by top switch in B phase, bottom switch in A phase. Similarly, the ripple 15 is contributed by top switch in N phase, bottom switch in A phase, while the ripple 16 is contributed by top switch in C phase, bottom switch in A phase. Lastly, the ripple 17 is contributed by top switch in C phase, bottom switch in N phase, while the ripple 18 is contributed by top switch in C phase and the bottom switch in B phase. The cycle repeats in this sequence, such that it is possible to increase the lowest torque of the output torque waveform, which in turn increases the average torque of the rotor and still keeping the peak torque same. In such a case, with the higher average torque.

[00055] Many modifications and variations of the present subject matter are possible in the light of above disclosure. Therefore, within the scope of claims of the present subject matter, the present disclosure may be practiced other than as specifically described.