Appropriate realization of gain-scheduled controllers with application to wind turbine regulation

Linear parameter varying control of wind turbines covering both partial load and full load conditions

“…A remedy is to take advantage of the partitioning used for constructing X cl . In [23], four different modifications to (11) have been investigated and it has been found promising to modify the variables for the construction algorithm in order to distribute the conditioning more evenly. This can be done by performing the variable substitution in (15)…”

“…This approach is denoted as gain scheduling and in [7][8][9] this is done by interpolating the outputs of a set of local controllers (either by linear interpolation or by switching). Alternatively, parameters of the controller are updated according to a pre-specified function of a measured/estimated variable [10][11][12].…”

Gain-Scheduled Control: Relaxing Slow Variation Requirements by Velocity-Based Design

“…m denote the space consisting of the product of the state, x, with the input, r. The set of equilibrium operating points of the nonlinear system, (14), forms a locus of points, (x o , r o ), in Φ and the response of the system to a general time-varying input, r(t), is depicted by a trajectory in Φ.…”

“…It should be noted that the expansion is carried out relative to the fixed operating point, (x 1 ,r 1 ), as opposed to a trajectory passing through (x 1 ,r 1 ), and the derivative of x 1 is, therefore, zero. It is emphasised that (16)- (18) is a well-defined system in its own right, distinct from the nonlinear system (14), with state δ x . Furthermore, the point, (x 1 ,r 1 ), need not be an equilibrium operating point and, indeed, may lie far from the locus of equilibrium operating points.…”

“…The set of equilibrium operating points of the nonlinear system, (14), consists of those points, (x o , r o ), for which…”