I'm not sure that it's feasible to meet all of the stated requirements, particularly "If the signal is not saturated, [it should] equal the commanded position signal." One option that may be close to what you want is to drive the input through a high bandwidth, low pass filter, and use the appropriate thresholds on the states in the filter. Like this:
Set the velocity and the acceleeration limits in the block parameters of the second order integrator. Choose the gains to give a smooth and fast response relative to your input. One option would be:
K1 = w^3; K2 = 3*w/K1; K3 = 3*w^2/K1;
where w is chosen such w/3 is about 10 times larger than the largest frequency in the position command. You might have to play with that parameter for the specific position commands of interest.
This approach should yield position, velocity, and acceleration that are consistent with each other, but the position won't ever be exactly equal to the position command. It will get closer as w increases, which will also decrease the simulation step size, assuming use of a variable step solver.