Control Design and Simulation and DAQ

chin.ho · ‎04-14-2011

I'm learning Control Design and Simulations. I have some questions about it.

1. For System Identification use, we can find the transfer function/model of the system by feeding data measurement from the system. But, how long data do we need to be sufficent for Identification System to estimate the model? Until the get saturated value (steady state)? or any other intervals? What if the system is unstable? How will Identification System Toolkit estimate that case?

2. For connecting to hardware, we just connect the clock in the simulation loop to the hardware? And the simulation loop will simulate the blocks inside once it got the trigger/data from the DAQ? what about the step time and solver? Do they follow the timing from hardware? or they will run on their own supplied values/clock?if we use USB DAQ, we can't have any clock from it (as far as I know it's because USB connection is not that stable for clocking since it might be any jitters or delays.) So, how do we configure the timing parameter for USB DAQ?

3. There is possibility to convert model in transfer function to state space, how do we know the states inside that conversion?

Any helps would be great...

Thanks in advance...

Hossein128 · ‎08-10-2011

Dear Chin ho,

After going through your questions I found some documentation which will be useful for you. But I you still have more questions, you can reply me any time.

1- About the data and amount of it I couldn't find any info but maybe you can use the new functions in LV version 2009 and find your answer.

Estimating States of Nonlinear Stochastic State-Space Models with Extended Kalman Filters

In previous versions of the LabVIEW Control Design and Simulation Module, you can use the Discrete Kalman Filter function and the Continuous Kalman Filter function to estimate the states of a linear discrete or linear continuous stochastic state-space model, respectively. In the LabVIEW 2009 Control Design and Simulation Module, you can use the Continuous Extended Kalman Filter function and the Discrete Extended Kalman Filter function to estimate the states of a nonlinear continuous or a nonlinear discrete stochastic state-space model, respectively.

The Continuous Extended Kalman Filter function and the Discrete Extended Kalman Filter function estimate model states of a partially observable plant based on noisy measurements. First, use the SIM Discrete Nonlinear Plant Model template VI or the SIM Continuous Nonlinear Plant Model template VI, located in the labview\templates\Control and Simulation directory, to define the system model. Then use the the Discrete Nonlinear Noisy Plant function or the Continuous Nonlinear Noisy Plant function to simulate the discrete or continuous nonlinear model, respectively, with the addition of noise. Finally, use the Continuous Extended Kalman Filter function or the Discrete Extended Kalman Filter function to estimate the states of your model.

The Continuous Extended Kalman Filter function and the Discrete Extended Kalman Filter function linearize the nonlinear system either by calculating a Jacobian matrix internally or by using an external Jacobian matrix that you define. Use the SIM Continuous Jacobians template VI or the SIM Discrete Jacobians template VI, located in the labview\templates\Control and Simulation directory, to define an external Jacobian matrix.

Refer to the LabVIEW Control Design User Manual, accessible by navigating to the labview\manuals directory and opening CD_User_Manual.pdf, for more information about estimating the states of nonlinear stochastic state-space models with extended Kalman filters.

2- I think that I found a pdf document about this part of your question which will be helpful. If you would like to give your email address, I can send it to you.

3- About this part you can check the help function in LabVIEW when you open the "CD Convert Transfer function To State-space" function in your front panel.

I pasted some info about the mathematic part below.

The LabVIEW Control Design and Simulation Module provides tools to study the dynamics of systems described by linear time-invariant (LTI) continuous and discrete models. You can create deterministic state-space, transfer function, and zero-pole-gain models. You also can create stochastic state-space models and the second-order statistics noise models. You can use these forms to describe both single-input single-output (SISO) and multiple-input multiple-output (MIMO) systems.

Continuous transfer function and zero-pole-gain models use the s variable to define time, whereas discrete transfer function and zero-pole-gain models use the z variable to define time. Continuous state-space models use the t variable to define time, whereas discrete state-space models use the k variable to define time.

Deterministic State-Space Model

Continuous

x(t) = Ax("t) + Bu(t)

y(t) = Cx(t) + Du(t)

Discrete

x(k + 1) = Ax(k) + Bu(k)

y(k) = Cx(k) + Du(k)

Stochastic State-Space Model

Continuous	x(t) = Ax(t) + Bu(t) + Gw(t) y(t) = Cx(t) + Du(t) + Hw(t) + v(t)
Discrete	x(k + 1) = Ax(k) + Bu(k) + Gw(k)
	y(k) = Cx(k) + Du(k) + Hw(k) + v(k)
Second-Order Statistics Noise Model	Q = E{w . w^T} – E{w} . E^T{w}
	R = E{v . v^T} – E{v} . E^T{v}
	N = E{w . v^T} – E{w} . E^T{v}

where	t is continuous time.
	k is the model sampling time multiplied by the discrete time step, where the discrete time step equals 0, 1, 2, …
	x is the model state vector.
	u is the model input vector.
	y is the model output vector.
	w is the process noise vector.
	v is the measurement noise vector.
	A is an n × n state matrix of the given model.
	B is an n × m input matrix of the given model.
	C is an r × n output matrix of the given model.
	D is an r × m direct transmission matrix of the given model.
	n is the number of model states.
	m is the number of model inputs.
	r is the number of model outputs.
	G is a matrix relating w to the model states.
	H is a matrix relating w to the model outputs.
	Q is the auto-covariance matrix of w.
	R is the auto-covariance matrix of v.
	N is the cross-covariance matrix between w and v.
	E{} denotes the expected value or the mean of the enclosed term(s).

LabVIEW