The Synthesis main window represents the starting point from which the users can begin the design or the search (Optimization) of a controller for the current model; all the necessary steps for the synthesis/optimization of a particular regulator are presented by means of a succession of windows, whose number and appearance change according to the kind of the selected control law, and the buttons BACK, CLOSE and NEXT allow the users to move inside them.
The different control laws implemented in MIMOtool are divided into the following two groups [2], [3], [4]:
OUTPUT-FEEDBACK
- H-INFINITY *
- H-2 *
- H-MIX *
- MU *
- LQG *: Linear Quadratic Gaussian control
- LQG-LTR: Linear Quadratic Gaussian with Loop Transfer Recovery control
- PID: Proportional-Integral-Derivative control
- EIG-ASSIGN: Eigenstructure Assignment control (output feedback and constrained output feedback versions)
(*
Available also in the Optimization section)
They compute Kof(s) (output feedback) for the standard output-feedback structure:
For these control laws, it's possible to augment the plant input or output with some blocks of integrators in order to improve the low-frequency behavior (response rate, command following, etc.): in this case, if K'of(s) represents the controller computed for the modified plant, Kof(s) is obtained adding conveniently the same blocks to K'of(s).
Pseudo STATE-FEEDBACK
- LQR: Linear Quadratic Regulator
- IMFC: Implicit Model Following Control
- EMFC: Explicit Model Following Control
- EIG-ASSIGN: Eigenstructure Assignment control (state feedback version)
- LQ-SERVO
These control laws achieve normally the feedback of all the states on the inputs through the matrix Ksf (state feedback), as indicated in the following figure
After the computation of Ksf, the final controller Kof is obtained converting the control into an output feedback control according to the law
Kof = Ksf ( C-D Ksf )+
In this manner it's possible to obtain either a "pure" state feedback behavior (if C=I and D=0) or an output feedback control without observer (if C¹I or D¹0).
Note: the law Kof = Ksf (C-D Ksf)+ is obtained from the state feedback control law and
the model output equation
U = - Ksf X + commands
Y = C X + D U
Because
of the presence of the pseudoinverse, the stability of the closed loop is
not guaranteed.
After a controller has been
computed in the last window of a Synthesis or Optimization section, it is stored in
the MIMOtool data structure, have a look to the data structure help page to see how the controller can be accessed directly from the
Matlab command line. At this point, it can also be saved for later use using
the Save Controller as command in the file menu.
SYNTHESIS MAIN WINDOW
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