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AD2S100AP Scheda tecnica(PDF) 5 Page - Analog Devices |
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AD2S100AP Scheda tecnica(HTML) 5 Page - Analog Devices |
5 / 12 page AD2S100 REV. A –5– To relate these stator current to the reference frame the rotor currents assume the same rectangular coordinates, but are now rotated by the operator e j , where ej = Cos + jSin . Here the term vector rotator comes into play where the stator current vector can be represented in rotor-based coordinates or vice versa. The AD2S100 uses e j as the core operator. Here represents the digital position angle which rotates as the rotor moves. In terms of the mathematical function, it rotates the orthogonal ids and iqs components as follows: ids' + jiqs' = (Ids + jIqs) e j where ids', iqs' = stator currents in the rotor reference frame. And e j = Cos + jSin = (Ids + jIqs)(Cos + jSin ) The output from the AD2S100 takes the form of: ids' = Ids Cos – Iqs Sin iqs' = Ids Sin + Iqs Cos The matrix equation is: [ids' ] = [Cos – Sin ][Ids] iqs' Sin Cos Iqs and it is shown in Figure 2. ids iqs ids' iqs' φ ejφ Figure 2. AD2S100 Vector Rotation Operation DIGITAL φ LATCH 3 φ + 2φ TRANSFORMATION SINE AND COSINE MULTIPLIER (DAC) SINE AND COSINE MULTIPLIER (DAC) Cos( θ + φ) Cos( θ +(120 ° + φ)) Cos( θ +(240 ° + φ)) PARK OUTPUT CLARK COS θ COS θ + 120° COS θ + 240° SINθ 2 φ–3φ INPUT CLARK LATCH LATCH Figure 3. Converter Operation Diagram THEORY OF OPERATION A fundamental requirement for high quality induction motor drives is that the magnitude and position of the rotating air-gap rotor flux be known. This is normally carried out by measuring the rotor position via a position sensor and establishing a rotor reference frame that can be related to stator current coordinates. To generate a flux component in the rotor, stator current is ap- plied. A build-up of rotor flux is concluded which must be maintained by controlling the stator current, ids, parallel to the rotor flux. The rotor flux current component is the magnetizing current, imr. Torque is generated by applying a current component which is perpendicular to the magnetizing current. This current is nor- mally called the torque generating current, iqs. To orient and control both the torque and flux stator current vectors, a coordinate transformation is carried out to establish a new reference frame related to the rotor. This complex calcula- tion is carried out by the AD2S100 vector processor. To expand upon the vector operator a description of a single vector rotation is of assistance. If it is considered that the mod- uli of a vector is OP and that through the movement of rotor position by , we require the new position of this vector it can be deduced as follows: Let original vector OP = A (Cos + jSIN ) where A is a constant; so if OQ = OP e j (1) and: e j = Cos + jSin OQ = A (Cos ( + ) + jSin ( + )) = A [Cos Cos φ – Sin Sin φ + jSin Cos φ + jCos Sin φ] = A [(Cos + jSin ) (Cos + jSin )] (2) θ φ θ + φ Q P O a d Figure 1. Vector Rotation in Polar Coordinate The complex stator current vector can be represented as is = ias + aibs + a 2i cs where a = e j 2 π 3 and a 2 = e j 4 π 3 . This can be re- placed by rectangular coordinates as is = ids + jiqs (3) In this equation ids and iqs represent the equivalent of a two- phase stator winding which establishes the same magnitude of MMF in a three-phase system. These inputs can be seen after the three-phase to two-phase transformation in the AD2S100 block diagram. Equation (3) therefore represents a three-phase to two-phase conversion. |
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