In simulink, it is common to see algebraic loops when the input to a system is an algebraic function of the output of the system. If that is the case with your system, then you could add a memory block to the output signal which is being fed back as the system input and solve this problem.

Thank you for your response, I've tried memory block and unit delay block, the algebraic loop is eliminated  and the model can running.But it turned out a apparently wrong solution(The signal in scope soared to 10^290). My model has algebraic loop can rightly run with a lenient sample time but cause singularity with a strict sample time.  That is really perplexing. 

Although I am not aware of the kind of system you have, I saw similar soaring of the scopes when I had unstable systems. In your system is linear, maybe it could be worthwhile to check the poles of the system. Could it be a possible error in sign or some issues with the parameters of your model?

One of the solution to this problem is you can replace the integrator block if any with a discrete time integrator block. That can solve your problem.

Simulink will struggle to solve if you have two current sources in series (an inductor is modeled internally as a voltage controlled current source). Therefore adding some shunt capacitance or resistance may help to solve

In order to verify if there is algebraic loop you can look at your Matlab window. When you run the model, using a fixed-step solver, if there is an algebraic loop, it will display the elements invoved.

Found algebraic loop containing:

'RT_patent_cells_v31/SM_model/Manual Switch1/SwitchControl' (discontinuity)

'RT_patent_cells_v31/SM_model/9 SM2/Slave8/Sum3'

'RT_patent_cells_v31/SM_model/9 SM2/Slave8/RTE Relational Operator'

'RT_patent_cells_v31/SM_model/9 SM2/Slave8/RTE Conversion2'

'RT_patent_cells_v31/SM_model/9 SM2/Slave8/Product2' (algebraic variable)

In which case, you only need to add a delay or memory block between one of those elements

in your case, since you run the model, it might be related to something else. Furthermore, the model run for large sampling time and has singularity when using small sampling time.

For these reasons, I think you should investigate the derivative more than an algebraic loop. (since you divide by the sampling time in a derivative, smaller time-step leads to a more reactive system.)

I personally try to avoid derivative, but if it can't be avoid, I use the following two steps derivative.

(2*z-2)/((Ts+2*TcD)*z+2*TcD)

Where Ts is the sampling time and TcD is a smoothing constant usually 4*Ts

In my experience there are 3 means to prevent this: a memory (n-sample delay), a transport delay (possibly problematic given the Td/Ts ratio), and a fast first order dynamics. In the end you choose what fits you purpose best.

Anyway, first you have to go through the model algebraic loop as explained above, and try to think where the delay would be caused in real world. Furthermore moving the "delay" block (any of the 3 mentioned) around the loop may also help as simulink has its own order of solving blocks each time step.

If no other way arround, it could be also solved in a own-written math function, that iterates each timestep (similar to what Simulink do in some cases, but you have no direct control of it)

@Luc-Andre Gregoire, Thank you for you response. As expected, in my case the derivative is necessary. Could you illustrate how to implement the two steps derivative : (2*z-2)/((Ts+2*TcD)*z+2*TcD) as you suggest? By using discrete derivative block and discrete transfer fcn?

@Boštjan Pregelj, Thank you for you response. Own-written math function is a good idea. Actually what my objective is to build a time-varying resistor and a mutual inductor by basic simulink blocks(derivative and controlled source). Since I need my self-build block to be able to connect and interact with other simpowersystem elements. Can I solve it by self-write function,or S-function? 

I think the S-functions offer high versatility and more control, but possbily the eembedded matlab function would suffice, (with some persistent variables if required), since you probably do not need complex structure.

There is another answer i found on functions and a MAthworks general info.

http://www.mathworks.com/help/simulink/ug/types-of-custom-blocks.html

http://www.mathworks.com/matlabcentral/answers/679-s-function-or-embedded-matlab-function

Hi

I advice you to see these documents.You will find what you need.

Best regards

http://fr.mathworks.com/help/simulink/ug/algebraic-loops.html

http://www.mathworks.com/matlabcentral/answers/97687-how-can-i-resolve-algebraic-loops-in-my-simulink-model-in-simulink-6-5-r2006b

it is better to avoid derived in simulations, or you should use a very small step in.

My suggestion is to re-write the equation in order to isolate the derivative and obtain it from the sum of the other terms, after you can integrate the value of the sum to obtain the value of the desired variable, i.e.:

x=dx/dt+a+b   -> original equation

dx/dt=x-a-b    -> re-wrrite eqution

integrating dx / dt - you have x

Usually, a 1/z block or memory block incorporated into the feedback line works well. Yet the sampling time of the 1/z should be as small as enough, e.g. the simulation step.

Dear Qingwei, please insert a supplementary PT1 element in your loop!

Thank you Christian, but could you give me a hint on what is PT1 element? is it a simulink block? in which category?

Dear Qingwei, this is --> Simulink --> Blocks --> Continues --> Transfer Fcn (Model linear system by transfer function) with 1/(s + 1). Please use a small time constant whichever not adulterated your results.

You can add a very small delay/ of a filter of very small time constant that effectively keeps your performance same but at the same time removes the problem of algebraic loop 

Try to use the correct solver for your purpose, normally this is the reason why you get a singularity. pragmatically the problem is your model or the combination model/solver that you use.

add 1/z block in your loop and make the step size small will solve the problem.

I have a big simulation file which was working well. I had couple of changes in my variables and now I face the algebraic loop (PLECS Add in). I had couple of 1/z block however it does not solve my problem. And the weird part is I get this error in the middle of simulation not at the beginning!

Sepehr Saadatmand I have the same problem! I don't understand why it cuts off in the middle of the simulation; it just doesn't make any sense. Did anyone experience a similar type of behavior? Am curious how they did it

you can use a delay unit to solve this problem

Mohamad Omar Mansour and Sepehr Saadatmand did you solve the algebraic loop problem in the middle of simulation? I have same problem and i couldnt find solution.

Taner karslı I had to put a unit delay block before the parameter causing the algebraic loop; i.e. the "goto" parameter. Then, I added an initial condition block before the "from to" parameter. Try to use the blocks or a combination of them before and after the parameters causing this problem.

Mohamad Omar Mansour Thank you very much i will try it. I hope it will work.

@taner if it did not work for you, send me a screem shot

I was using Simulink-PS Converters in the feedback loops and faced the same problem. However, when I enabled the second-order filtering in the input handling tab (in Simulink-PS Converter) and decreased the filtering time constant to 1e-9s, the simulation worked fine.