01

chain80.tar.gz
chain80.zip

101 QPs, 240 variables (bounded), 0 constraints, 0 equality constraints

This test problem aims at regulating a chain of nine masses connected
by springs into a certain steadystate. One end of the chain is fixed on a wall
while the three velocity components of the other end are used as control input with
fixed lower and upper bounds. The prediction horizon of 16 seconds is divided
into 80 control intervals. The model equations are derived from linearisation
of the nonlinear ODE model (with 57 states) at the steadystate. Deviation from
the steadystate, the velocities of all masses and the control action are
penalised via the objective function.
In order to obtain the QP series we simulated in a closedloop manner
integrating the nonlinear ODE system to obtain the movements
of the chain. Starting at the steadystate, a strong perturbation was exerted
to the chain by moving the free end with a given constant velocity for 3 seconds.
Then the MPC controller took over and tried to return the chain into its
original steadystate.

02

chain80w.tar.gz
chain80w.zip

101 QPs, 240 variables (bounded), 709 constraints, 0 equality constraints

This test problem aims at regulating a chain of nine masses connected
by springs into a certain steadystate. One end of the chain is fixed on a wall
while the three velocity components of the other end are used as control input.
Besides fixed lower and upper input bounds, also state constraints are included into
the optimisation problem in order to ensure that the chain does not hit a vertical
wall close to the steadystate. The prediction horizon of 16 seconds is divided
into 80 control intervals. The model equations are derived from linearisation
of the nonlinear ODE model (with 57 states) at the steadystate. Deviation from
the steadystate, the velocities of all masses and the control action are
penalised via the objective function.
In order to obtain the QP series we simulated in a closedloop manner
integrating the nonlinear ODE system to obtain the movements
of the chain. Starting at the steadystate, a strong perturbation was exerted
to the chain by moving the free end with a given constant velocity for 3 seconds. Then the
MPC controller took over and tried to return the chain into its
original steadystate while not hitting against the wall.
