This section, which can be started by pressing the button SIMULATION or by selecting the command Open Simulink Model from the Simulation menu, is dedicated to the time simulation of the closed loop system built with the controller that has been previously computed at the end of a synthesis or optimization section; the closed loop simulation is performed through a Simulink scheme that is externally independent from the model and that appears in a window separated from the current one of MIMOtool.
In case of the output feedback controls H-INFINITY, H-2, H-MIX, MU, LQG, LQG \ LTR and PID, the closed loop scheme is always
where the vector YR represents the reference command for the plant output and the block pinv(G(0)) aims to cancel, when it's possible, the incidental static error.
In case of LQR, EIG \ ASSIGN and LQ-SERVO, the simulation scheme varies in accordance with the possibility to compute the set point: if the set point cannot exist (the dynamic matrix of the plant is not maximum rank) the closed loop system is built as pointed out in the previous picture, otherwise the following structure is used
where the COMMANDS block provides the desired output vector and the Kpf block contains a subsystem that performs the computation of the set point.
In case of IMFC and EMFC, whose purpose is to find a closed loop control law that lets the plant track the dynamics of the model, the Simulink scheme is different from the general one because of the presence of both the model and the new references for the plant output:
In these cases, the CONTROLLER block contains also the transfer function of the model, which is part of the control loop only in the EMFC method, while the Kpf block contains a subsystem that performs the computation of the set point.
Anyway, the internal structure of both the OUTPUTS and COMMANDS blocks depends on the number of plant outputs, and the internal structure of the CONTROLLER block depends on the type of control. Each time the simulation window is activated, the corresponding structure is built and the blocks indicated above are conveniently copied from a library file.
The COMMANDS block contains a step and a signal generator for each reference command, while the OUTPUTS block contains a scope for each couple output + reference command (the library file includes the structures of every block relative to systems with a number of outputs less or equal to 15).
After the creation of the window, all the functionalities of the Simulink interface are enabled and the user can start the simulation with the Start command of the relative menu [7].
Note: it's possible to access to the simulation
data and to export them to other application, by selecting the corresponding
property of the scopes.