# Force Fight and Its Elimination in a Prototype of a Redundant Direct-Drive Avionic Actuator
## 3 Control Strategy  
For the designed actuator, a position control is developed using four independent control strategies for the four BLAC motors. Figure 8 shows the control strategy of one BLAC motor (motor lane) with an inverter (Inv) to supply one three-phase stator and a power supply stage (PS) to supply the inverter (DC link).  
Position control is based on multiloop control design and the autopilot current control of PMSM in dq plan deduced from the analytical model of each BLAC motor [8; 9]. In this strategy, \(\rm V_{d}^{*}\) and \(\rm V_{q^{\prime}}^{*}\) given by Equations (1) and (2), are the voltages to use for the generation of Pulse Width Modulation (PWM) signals:  
\[\rm V_{d}^{*} = \rm V_{sd1}-\rm e_{sd} \tag{1}\] \[\rm V_{q}^{*} = \rm V_{sq1}-\rm e_{sq} \tag{2}\]  
Figure 8: Control strategy of each brushless alternative current (BLAC) motor, ECU: Electronic Control Unit, Inv: Inverter, MON: Monitor, PS: Power Supply.  
In these equations, \(\rm V_{sd1}\) and \(\rm V_{sq1}\) are considered to be the control signals provided by the current controllers while \(\rm e_{sd}\) and \(\rm e_{sq}\) are considered to be the link terms. These terms are deduced by identification using electrical equations of the BLAC motor model [10; 11]:  
\[\rm V_{sd1}=\ R_{a}I_{d}+L_{d}\frac{dI_{d}}{dt} \tag{3}\]  
\[\rm V_{sq1}=\ R_{a}I_{q}+L_{q}\frac{dI_{q}}{dt} \tag{4}\]  
\[\rm e_{sd}=\ p\ \Omega\ L_{q}I_{q} \tag{5}\]  
\[\rm e_{sq}=\ -(p\ \Omega\ L_{d}I_{d}+pk_{m}\Omega) \tag{6}\]  
where:  
\(\rm R_{a}\): winding resistor (Ohms);  
\(\rm L_{d}\): d axis inductance (H);  
\(\rm L_{q}\): q axis inductance (H);  
p: number of poles pair;  
\(\rm k_{m}\): torque constant (Nm/A);  
\(\rm i_{q},i_{d}\): currents in dq plan (A);  
\(\Omega\): velocity (rad/s);  
Figure 9 gives the position control of each motor lane. The current control is carried out in dq plan where two PI controllers are designed to provide \(\rm V_{sd1}\) and \(\rm V_{sq1}\). The signal controls \(\rm V_{sd}\) and \(\rm V_{sq}\) used for the generation of PWM signals are deduced taking into account the link terms \(\rm e_{s1}\) and \(\rm e_{s2}\) given by Equations (5) and (6). With this strategy, the link terms allow to get a torque, which depends only on \(\rm Iq\) and a flux which depends only on \(\rm I_{d}\).  
Figure 9: Position control of each BLAC motor (* = set point)  
Using placement pole method, two PI current controllers are designed from Equations (3) and (4). For these loops, two set points are chosen; Id* is equal to zero while Iq* is provided by the velocity controllers. This choice is due to the operation range of the designed actuator characterized by a constant torque at low velocity range. For the velocity control, a PI controller is designed taking into account the mechanical time constant of each motor lane. The velocity set point \(\omega\)* of this loop is provided by a position proportional controller designed according to performance criteria of the designed actuator. For this controller, a set point \(\Theta\)* is provided by the supervisor for each motor lane.