 
Summary: sc4026
Exercise Session 6 (with solutions)
Alessandro Abate
a.abate@tudelft.nl
Aleksandar Haber
a.haber@tudelft.nl
Delft Center for Systems and Control, TU Delft
October 20, 2011
Ac.Yr. 2011/12, 1e Sem. Q1 Exercise Session 6 sc4026
A. Abate, A. Haber
Linear Quadratic Regulator, in Theory
Consider an object of mass m = 1 moving along the xaxis
in response to a force input u(t). The objects dynamics can be
described simply as ¨x(t) = u(t). This model is also known as
the double integrator.
· Is the system controllable?
Suppose you would like to design an input u(t) which will move
the object from any initial position and velocity, to come to rest
at the position xe = 0.
· Using the linear quadratic regulator (LQR) discussed in class,
