Compute a new controller for the same system with no W 1.

## Advanced H∞ Control

Plant, specified as a dynamic system model such as a state-space ss model. P can be any LTI model with inputs [ w ; u ] and outputs [ z ; y ], where:. Construct P such that measurement outputs y are the last outputs, and the control inputs u are the last inputs. The function converts P to a state-space model of the form:. If P is a generalized state-space model with uncertain or tunable control design blocks, then hinfsyn uses the nominal or current value of those elements. For further information, see mixsyn.

For the default Riccati method, the plant is further restricted in that P 12 and P 21 must have no zeros on the imaginary axis continuous-time plants or the unit circle discrete-time plants. In continuous time, this restriction means that. By default, hinfsyn automatically adds extra disturbances and errors to the plant to ensure that the restriction on P 12 and P 21 is met.

## Mixed H2/H∞ Control Approach and its Application in Satellite Attitude Control System

This process is called regularization. If you are certain your plant meets the conditions, you can turn off regularization using the Regularize option of hinfsynOptions. Number of measurement output signals in the plant, specified as a nonnegative integer. The function takes the last nmeas plant outputs as the measurements y. The returned controller K has nmeas inputs. Number of control input signals in the plant, specified as a nonnegative integer.

The function takes the last ncont plant inputs as the controls u. The returned controller K has ncont outputs. Target performance level, specified as a positive scalar. If gamTry is not achievable, hinfsyn returns an empty controller. Performance range for search, specified as a vector of the form [gmin,gmax].

The hinfsyn command tests only performance levels within that range. It returns a controller with performance:.

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In this case, hinfsyn returns [] for K and CL. If you know a range of feasible performance levels, specifying this range can speed up computation by reducing the number of iterations performed by hinfsyn to test different performance levels. Additional options for the computation, specified as an options object you create using hinfsynOptions. Available options include:. For information about all options, see hinfsynOptions. Controller, returned as a state-space ss model object or []. The controller stabilizes P and has the same number of states as P.

The controller has nmeas inputs and ncont outputs. Closed-loop transfer function, returned as a state-space ss model object or []. Controller performance, returned as a nonnegative scalar value or Inf. If you do not provide performance levels to test using gamTry or gamRange , then gamma is the best achievable performance level. If you provide gamTry or gamRange , then gamma is the actual performance level achieved by the controller computed for the best passing performance level that hinfsyn tries.

## H-infinity control applications

Additional synthesis data, returned as a structure or [] if the specified performance level is not achievable. For the default Riccati-based synthesis method, info has the following fields.

go Performance level used to compute the controller K , returned as a nonnegative scalar. Typically, hinfsyn tests multiple target performance levels and returns a controller corresponding to the best passing performance level see Algorithms. The value info. For more information, see Algorithms and [5]. State feedback gains of controller K expressed in observer form, returned as matrices. For more information about the observer-form controller, see Tips. Observer gains of controller K expressed in observer form, returned as matrices.

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Regularized plant used for hinfsyn computation, returned as a state-space ss model object. By default, hinfsyn automatically adds extra disturbances and errors to the plant to ensure that it meets certain conditions see the input argument P. The field info. Preg contains the resulting plant model.

All-solutions controller parameterization, returned as a state-space ss model object. Use hinfsynOptions to change the synthesis method. In general, the solution to the infinity-norm optimal control problem is nonunique. The controller returned by hinfsyn is only one particular solution, K. For the default Riccati-based method, info. AS contains the all-solution controller parameterization K AS.

In other words, the solutions include every stabilizing controller K s that makes. Here, T y 1 u 1 is the closed-loop transfer function CL. These controllers K s are given by:. The observer form of the controller K is:.

### Frequency $H_{2}/H_{∞}$ optimizing control for isolated microgrid based on IPSO algorithm

Here, w e is an estimate of the worst-case perturbation and the innovation term e is given by:. To do so, tabulate the plant matrices and the controller gain matrices as a function of the scheduling variables using the Matrix Interpolation block. Then, use the observer form of the controller to update the controller variables as the scheduling variables change. By default, hinfsyn uses the two-Riccati formulae [1] , [2] with loop shifting [3].

You can use hinfsynOptions to change to an LMI-based method [4] , [5] , [6]. You can also specify a maximum-entropy method. For continuous-time systems, this integral is:. A similar integral is used for discrete-time systems. This step is equivalent to verifying the conditions:. You can change this criterion using hinfsynOptions. For discrete-time controllers, the algorithm performs additional computations to construct the feedthrough matrix D K.

D 12 and D 21 have full rank. When these rank conditions do not hold, the controller may have undesirable properties. As of Rb, using Name,Value syntax to specify options for hinfsyn is not recommended. Instead, to set a target performance range, use the gamRange input argument. For other options, create an options set with hinfsynOptions. The following table shows how to update your calls to hinfsyn to use the recommended ways of specifying options. For more information, see hinfsynOptions.

The fields of the optional output argument info changed in Rb. Prior to that release, info was a structure with the following fields. AS is still available, but its scaling has changed. See Scaling of info. KFI , info. Breakdown is the knee of diode characteristics curve.

A thermistor is a type of resistor whose resistance strongly depends on temperature. The battery was 9 volts and is the power supply in the lab. When a light dependent resistor is kept in dark, its resistance is very high.