Trajectory planning and tracking control for MIMO-LTI sampled data systems in continuous time
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In industrial applications usually sampled data controllers are employed. If the sample time is suf?ciently small the sampled data structure may be neglected and the system is treated quasi-continuously. If the sample time is longer, the system is treated in discrete time neglecting the behaviour in between the samples and the z-transform is used. This paper combines these two approaches.
The plant is moved by an input signal which consists of a sequence of values u[k] and a function m(t) forming the
control pulses. Using the modi?ed z-transform the plant is modelled by a parametric transfer function matrix G(z, ? ) with the parameter ? ? [0, T ] with the sample time T . Thus the output signal y(t) = y(kT + ? ) is calculated not only at the points of sampling kT but also in between. A right coprime matrix fraction description of which only the numerator depends on ? is derived. Based on that basis variables are de?ned in the z-domain. The corresponding basis sequences can be chosen arbitrarily and with them the input sequences u[k] and the output functions y(t) are ?xed and can be calculated without solving a differential or difference equation. This mathematical law is applied to plan trajectories in continuous time. Hence the entire output trajectory in continuous time can be taken into account.