# LINEAR MOTOR CONTROL IN ACTIVE SUSPENSION SYSTEMS

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2 2 LINEAR MOTORS The beauty of linear motors is that they directly translate electrical energy into usable linear mechanical force and motion, and vice versa. The motors are produced in synchronous and asynchronous versions. Compared to conventional rotational electro motors, the stator and the shaft (translator) of direct-drive linear motors are linear-shaped. One can imagine such a motor taking infinite stator diameter. Linear motor translator movements take place with high velocities (up to approximately 200m/min), large accelerations (up to g multiples), and forces (up to kn). As mentioned above, the electromagnetic force can be applied directly to the payload without the intervention of a mechanical transmission, what results in high rigidity of the whole system, its higher reliability and longer lifetime. In practice, the most often used type is the synchronous three-phase linear motor. For the most part, linear motors function within a system in the same manner as other types of motors. The major difference lies in commutation. Linear motors commutate based on linear position; rotary motors commutate based on angular position. For a brushless motor to produce force, the windings must be switched in polarity and amplitude relative to the permanent magnetic field. In the case of brush-type motors, the magnets are usually stationary (stator). In brushless motors, the magnets are typically on the moving shaft, either rotating or sliding. Commutation is cyclical in nature, and is based on a fixed ratio of magnetic poles to electric coils. With rotary motors, these cycles repeat every revolution. With linear motors, the cycles repeat over a fixed distance. 3 ACCUMULATION OF ENERGY The power amplifier requires a DC power supply for the switch bridge. If the motor works as an actuator, the electrical energy is lead in the terminal U 0 (see Fig.1). In the braking mode, it is possible to get back the accumulated energy from the terminal. To achieve a good function of the power amplifier, the level of the voltage U 0 cannot exceed a permitted range. Because the maximum of the linear motor force is limited within the given permitted range, it is useful to hold U 0 at the upper limit. There are several ways of energy accumulation, but some of them do not allow holding U 0 at the upper limit of the range. One of the possibilities is shown in Fig.1a. U 0 is held constant and equal to U max. Figure 1a,b - Energy accumulation The electrical energy is impressed across the terminal U 0 from vehicle supply network here represented by the capacitor C with the help of a DC/DC step-up converter. The voltage of the capacitor C is held within the range of 0 U max [V]. With respect to the short-time (hundreds of ms) instantaneous power (of the order of kw), both the converters have to be adjusted to such a high peak power. Consider the average efficiency of each converter as equal to η=0,85. The recuperated energy can be reused with the efficiency of η 2 =0,72. It results in a disadvantage when 28% of the recuperated energy is lost during one cycle of the energy accumulation and its following reusage. If the vehicle R010-2

3 supply network is represented by a capacitor C then its accumulation capacity (taken in the range of 0 U max ) enables to store the energy of: 1 2 E CL = CU max (1) 2 Another way how to accumulate the electrical energy is shown in Fig.1b. In this case, it is assumed that the voltage U 0 does not have to be necessarily time-invariant and varies within the range of U min U max. Now, the capacitor C is connected directly to the terminal U 0. The peak-power dimensioned auxiliary voltage supply is non-active for U 0 >U min. Vice-versa, the energy dissipator dissipates energy in case of exposure of the capacitor when U 0 >U max. The main advantages of such a solution are: its simplicity, the fact that the energy taken from the terminal U 0 is stored with the efficiency of 100% (loss resistance of the capacitor C is neglected), and no problems concerning the DC/DC converters (efficiency, disturbances, cooling etc.). As the main disadvantage is taken the fact that the stored energy is limited by: E c = C(U max U min ) (2) 2 To store the same energy as in the first case, it is necessary to use the capacitor with E C1 /E c2 - times higher capacity. 4 LINEAR MOTOR MODEL To verify control algorithms a linear motor model including the power amplifier has been created in Matlab/Simulink. The model enables to demonstrate the conversion of the electrical energy to mechanical energy. In the model, it is assumed that: the magnetic field of the secondary part with permanent magnets is sinusoidal, the phases of the primary part coils are star-connected, and the vector control method is used to control the phase current. Here, PWM voltage signal is substituted by its mean value to shorten (about 10 times) the simulation period (inaccuracies caused by such a substitution can be neglected). The principal inner representation of the model is shown in Fig.2. The model input vector is given by the instantaneous position [m] (necessary to compute the commutation current of the coils), instantaneous velocity [m/s] (the induced voltage of the coils depends on the position and velocity) and desired force [N]. Figure 2 - Principal inner model representation R010-3

4 The designed model function has been verified comparing dynamics of the model and the real motor. The simulation parameters correspond to the catalogue parameters of TBX3810 linear motor fy Thrust-tube. For example, time responses cased by changes of the desired force has been compared. The linear motor input-output model is shown in Fig. 3. Figure 3 - Linear motor input/output model for dynamics verification Figs. 4 and 5 represent simulated and real time responses (step series: 0N 200N/200N 0N, power supply: 150V, velocity: 0m/s). Figure 4 Simulated time responses Figure 5 Real time responses R010-4

5 On the base of the experiments completed on the model, the value of the electric power necessary to be supplied or consumed when the velocity and force of the motor are constant has been gained. The model output vector is given by the actual value of the force [N], electric power [W] has been consumed at the switch bridge terminal since the start point of the simulation (its negative value represents the recuperated electrical energy), and instantaneous electric power demand of the motor [W]. In Fig. 6 there is represented an input/output model (with concrete simulation values) of the linear motor. Figure 6 - Linear motor input-output model To obtain the simulation results given in Tab.1, the linear motor motion of constant velocity and constant force has been simulated (the results given above are valid for the supply voltage of 300V). Table 1 Simulation results velocity [m/s] force [N] 0 0,1 0,2 0,6 1 1,2 1, xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx The direction of the force is oriented contrariwise for positive values of the force. After transient response settling, the supply power of the linear motor (the power supplied into the motor from the power supply or vice versa) has been measured. The positive values correspond to the electric power R010-5

6 necessary to be supplied into the motor. Vice versa, the negative values represent the accumulateable power. xxxx symbols in the fields signify that the desired force is not reachable under the given velocity. The simulation parameters correspond to the catalogue parameters of TBX3810 linear motor fy Thrust-tube. 5 RESULTS Comparing the time responses in Fig.4 and Fig.5 it can bee seen a very good matching level of the behavior of the model and real motor. On the base of the simulation results, it is obvious that the power of the order of up to hundreds of W can be obtained when the motor velocity exceeds 0,4 ms -1 and the force does not exceed about 200N. As an example, it is possible to note that under the motor velocity of 1,5 ms -1 the energy can be obtained if and only if the braking force does not exceed 1400N. 6 CONCLUSION It results from the experiments made with the linear motor TBX3810 that the designed model describes the real linear motor equipped with necessary auxiliary circuits very authentically and enables to verify control algorithms developed to control the linear motor as an actuator of the active suspension system. References [1] HYNIOVÁ, K.; STŘÍBRSKÝ, A.; HONCŮ, J. Fuzzy Control of Mechanical Vibrating Systems. In.: International Carpatian Control Conference ICCC 2001, Krytica, 2001, pp , ISBN [2] MINAŘÍK, D. Fuzzy Control System for Active Suspension of Vehicles, Diploma thesis, FEE CTU Prague, 2002 [3] SOUČEK, P.; BUBÁK, A. Vysoce dynamické pohony posuvu obráběcích strojů, Společnost pro obráběcí stroje, Praha, 2002 [4] STŘÍBRSKÝ, A.;HYNIOVÁ, K.; HONCŮ, J. Using Fuzzy Logic to Control Active Suspension of Vehicles. In.: Intelligent Systems in Practice, Luhačovice, 2000, pp.41-49, ISBN [5] STŘÍBRSKÝ, A.; HYNIOVÁ, K.;HONCŮ, J. Reduction of Vibrations in Mechanical Systems. In.: Proceedings of Workshop Part A, CTU Prague, 2001, pp , ISBN Acknowledgement This research has been supported by MŠMT projects No.LN00B073. R010-6

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