0 0 (1)

vu s2  2Dω0s  ω0 2

where ω0 is the eigen-frequency of the system, D the dumping ratio, C the gain factor and T0 a delay time. The delay time depends on the system configuration (cable length and con-ductivity conditions) and servo-valve features and is equal to (4 - 8ms). The other parameters are strong dependent on the piston velocity and can vary (for the same system) many times: gain C (0.05 – 1.5 (m/s)/V), ω0 < 120 – 30 rad/s>, D <1.6-0.22>, while the piston velocity v is variable within range <0.05 – 2 m/s> [4]. These parameters variations create many problems at design of controller parameters. The most disturbing is the oscillating behavior of system (1) at high velocity, which combined with small damping D=0.22 induc-es large overshoot, while eg. PID control algorithm is used. The used state space control algorithm has to prevent an over-shoot in the positioning so in the first 200 ms it drives as fast as possible Fig.2b, but in the last phase of the movement (ca. 600 ms!!!) it very carefully and slowly approaches to the re-quired final position. This slow phase of the movement makes an average piston velocity to be small (three times less than it is possible). Other observation is very important too: the ac-tivity of the servo-valve (after first 80 ms) is PWM-like, Fig.2.b, and yields many steps of subsequent filling and emp-tying of the cylinder volumes with a compressed air. It results in an unnecessary air consumption and a loud noise.

a.

Piston velocity

Piston Position

b.

Fig.2. Transients of: a) piston position and velocity, b) controller output in the pneumatic servo-system with the state-space control,

The main aim of the proposed control approach is to reduce the air consumption in the positioning system. It is imple-mented in two ways: replacing the expensive, proportional 5/3 valve by four fast on-off switching valves with remarkable less internal air leakage (what forces control system to an ad-ditional activity in steady state), Fig.2b, and the application of quasi time-optimal control composed of only several steps: opening/emptying cylinder volumes at start and two addi-

tional control pulses at the end of the piston movement, what results in small air consumption and short control time.

2. PROPOSED WAY OF CONTROL

The idea of time-optimal control of a pneumatic drive is based on the application of four fast on/off switching valves, Fig.1b, that are controlled indirectly [2,6], and final position is reached without overshoot or with a negligible one. A resis-tive position transducer is used for the supervision of the pis-ton movement and adaptation in the case of an observed mal-function. An example of simulated transients of this type of control is presented in Fig.3.

Valve control

Piston velocity

Piston position

t1 t2 t3

Fig.3. Simulated position control with quasi time-optimal algorithm

The considered control strategy is based on the pre-calculation of switching times [2,6] for each of four valves before the piston movement. In the first phase of the control movement two valves are active: the switch I. (Fig.1b) is sup-plying a cylinder volume with the high pressure air, while the switch IV. is emptying another cylinder volume. A time length of this interval <0,t1> controls a piston displacement. The second time interval <t2, t3> is used for the filling of both volumes with the compressed air, in order to achieve a high air pressure in both volumes and to hold the piston hard in the final position. The time instant t2 selection is done with the use of a special algorithm [2] to avoid an overshoot in the last phase of the movement. In the simulation research the kinetic friction force has been introduced and verified with measured transients. The final conditions for air masses variations at the given piston displacement x are known: