StateFeedbackClosedLoop - MapleSim Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

ControlDesign

  

StateFeedbackClosedLoop

  

determine the closed-loop equations of a system with state feedback controller

 

Calling Sequence

Parameters

Options

Description

Examples

Calling Sequence

StateFeedbackClosedLoop(sys, Kc, opts)

Parameters

sys

-

System; system object

Kc

-

Matrix; state feedback gain

opts

-

(optional) equation(s) of the form option = value; specify options for the StateFeedbackClosedLoop command

Options

• 

Kr = Matrix or 0

  

Specify a feedforward gain  (reference input). If Kr = 0, there are no reference inputs  and the returned closed-loop system is autonomous. The default value is 0.

• 

augment_output = true or false

  

True means append the sys inputs to the output vector of the closed-loop system. The default is false.

• 

outputtype = tf, coeff, zpk, ss, or de

  

Determines the subtype of the returned system object.  The default return type is based on the type of the system object specified in the sys parameter.

• 

parameters = {list, set}(name = complexcons)

  

Specifies numeric values for the parameters of sys. These values override any parameters previously specified for sys. The numeric value on the right-hand side of each equation is substituted for the name on the left-hand side in the sys equations. The default is the value of sys given by DynamicSystems:-SystemOptions(parameters).

Description

• 

The StateFeedbackClosedLoop command calculates the closed-loop system equations of the state feedback controller with  gain and plant sys.

• 

When the option Kr is specified, the state feedback controller is governed by the control law , where  is the state vector of sys,  is the reference vector,  is the feedback gain and  is the direct or feedforward gain.

• 

The sys is a SISO (single input, single output) or MIMO (multiple input, multiple output) linear system object created using the DynamicSystems package. The system object can be of types: transfer function (TF), zero-pole-gain (ZPK), coefficients (Coeff), state-space (SS), and diff-equation (DE). It is assumed that the state feedback controller gains are obtained using the sys representation obtained by DynamicSystems[StateSpace].

• 

The StateFeedbackClosedLoop command returns a system object whose type is the same as the type of sys, unless the option outputtype is specified.

• 

The closed-loop system inputs are

– 

the reference inputs  (when a non-zero Kr Matrix is specified)

  

The reference vector  contains a reference signal for each sys output .

• 

The closed-loop system outputs are

– 

the outputs  of sys

– 

the controller outputs  (if augment_output = true)

Examples

A DC motor with stator inductance , stator resistance , electromotive force (emf) constant , rotor moment of inertia , and damping ratio  is modeled using the following differential equations.

The input variables are the source voltage  and the torque load , and the output variables are the rotor angular speed  and the stator current .

In state-space form:

(1)

For control, the controlled input is the voltage  and the controlled output is the DC motor speed . The corresponding subsystem is obtained.

(2)

Designing the state feedback controller with gains  and  () by  pole placement with desired poles  and .

Obtaining the feedback gain :

(3)

The closed-loop equations of the state feedback control system are obtained next.

(4)

Using outputtype and augment_output, the transfer function of closed-loop system is obtained.  The output vector will contain the controller output .

(5)

Assign numerical values for the parameters:

Next, the numeric values for the desired poles are obtained. For 0.1% overshoot, settling time of about 1 sec, the damping ratio   and the natural frequency  are defined as follows:

(6)

Then, the numeric values for the feedback gain  and the feed-forward gain  are:

(7)

(8)

Plotting the closed-loop system step response:

Obtain the properties of the step response such as steady-state value and settling-point.

(9)

See Also

ControlDesign

ControlDesign[LQR]

ControlDesign[StateFeedback]

ControlDesign[StateFeedback][Ackermann]

ControlDesign[StateFeedback][PolePlacement]

 


Download Help Document