A system for remotely controlling pressure within each of i zones respectively connectable to i measurement chambers through conduits i, by controlling flow of a fluid into and out of each measurement chamber i, and through each conduit i into each zone i, wherein i=1, . . . , N, the system comprising:
- a plurality of measurement chambers, i, wherein each measurement chamber is controllably closable by operation of an inlet proportional valve and outlet proportional valve connected to the measurement chamber, wherein each outlet proportional valve is connected to a vacuum exhaust, and wherein the plurality of measurement chambers, i, are connected to one another at the respective outputs of the proportional valves by a flow constrictor manifold;
- a plurality of zones i, wherein each zone is connected to a respective measurement chamber through a respective conduit, wherein each zone is a remote zone relative to the respective measurement chamber;
- a pressure measurement system configured to measure pressure of the fluid in each of the measurement chambers;
- a valve system including, for each measurement chamber i, at least one inlet proportional valve configured to regulate an input flow rate of the fluid into the measurement chamber i, and at least one outlet proportional valve configured to regulate an output flow rate of the fluid out of the measurement chamber i;
- a zone pressure estimator coupled to the pressure measurement system and configured to, for each zone i, receive a measured pressure in the measurement chamber i from the pressure measurement system, and compute an estimated pressure within the zone i as a function of the measured pressure in the measurement chamber i, and as a function of known characteristics of the conduit i and the zone i;
- and
- a controller configured to control pressure within each zone i by operating the inlet proportional valve and the outlet proportional valve of each measurement chamber i so as to control the input flow rate of the fluid into the measurement chamber i and the outlet flow rate of the fluid out of the measurement chamber i as a function of a pressure set point for the zone i and the estimated pressure within the zone i from the zone pressure estimator;
- wherein for the plurality of measurement chambers i, the controller is further configured to effect PI control of the input flow rate and the output flow rate of each measurement chamber;
- wherein an input flow command signal from the controller to the inlet proportional valve of measurement chamber i comprises:
- Qin,i=κPin(P1−Pz,i)+κlin∂(P1−Pz,i)dt;
- wherein an output flow command signal from the controller to the outlet proportional valve of enclosure i is given by:
- Qout,i=κPout(P1−Pz,i)+κIout∂(P1−Pz,i)dt;
- and
- and wherein,
- Qin,i denotes the input flow rate into measurement chamber i,
- Qout denotes the output flow rate out of measurement chamber i,
- κPin denotes a proportional gain for the input flow rate,
- κlin denotes an integral gain for the input flow rate,
- κPout denotes a proportional gain for the output flow rate,
- κIout denotes an integral gain for the output flow rate,
- Pz,i denotes the estimated pressure within the zone i,
- P1 denotes a desired pressure trajectory from one pressure setpoint to another pressure setpoint, and
- P1−Pz,i denotes a tracking error.