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

Online Help

ControlDesign

  

ComputePoles

  

compute the poles used in an Ackermann pole placement design based on a desired time constant of the closed-loop system

 

Calling Sequence

Parameters

Options

Description

Examples

Calling Sequence

ComputePoles(sys, Tc, opts)

Parameters

sys

-

System; system object

Tc

-

And(positive, numeric); desired closed-loop time constant (in seconds)

opts

-

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

Options

• 

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 ComputePoles command returns a list of poles needed to design a state feedback controller for sys by pole placement with the Ackermann command. The returned list will contain as many poles as the number of states of sys.

• 

The computation of the poles is done based on the desired time constant, Tc (seconds), of the closed-loop system.

• 

The system sys is a continuous or discrete-time linear system object created using the DynamicSystems package. The system object must have a single input and must be controllable and in state-space (SS) form.

• 

If sys is uncontrollable, try the ReduceSystem command to remove any structurally uncontrollable states of sys.

Examples

Use parameters option

• 

Consider a state-space system corresponding to a DC Motor:

(1)
• 

The numeric values of the model parameters are as follows:

• 

Extract a subsystem with the desired input and output.

(2)
• 

Check if the subsystem is controllable:

(3)
• 

Compute the poles for a desired time constant of 1 second:

(4)
• 

Use the previous results to compute the state feedback gain:

(5)

Use ReduceSystem

• 

Consider the following state-space system

• 

The numeric values of the system parameters are

• 

Create the state-space model, using the parameters option so that they do not have to be later passed to subsequent function calls as was done in the previous example.

(6)
• 

Extract a subsystem with the desired input and output.

(7)
• 

Check if the system is controllable:

(8)

(9)
• 

The subsystem is observable but uncontrollable. Try removing structural uncontrollable states

(10)

(11)

(12)
• 

Compute the poles for a desired time constant of 1 second:

(13)

(14)

See Also

ControlDesign

ControlDesign[StateFeedback][Ackermann]

 


Download Help Document