I am using a Model Predictive Controller for controlling a vehicle. In SIMULINK i have used the state-space continuous time plant model and by default the MPC block is generating digital control input into the ss continuous plant. Also the output from the plant is continuous, which is going through the MPC for feedback.
My concern is, is it possible or not?
If not possible, do i need A/D or D/A converters??
Why zero-hold or other conversion method of D to A signals, causing a delay?? as a result when i implement a D/A conversion i dnt get real time signal in the output.
For example, if the disturbance in the plant is acting at 4th second of the simulation, the output starts to change on the 5th second,in digital time frame. but if i use continuous frame, the outputs are displayed at real time.
Moreover, i dont find any convenient way to convert D/A (corrected*) in simulink.
sorry for a long explanation.
any help will be highly appreciated.
I'm not familiar with the MPC block. As a general rule, I prefer to "role-my-own" Simulink blocks so I know exactly how they work and what is going on inside them - to avoid the type of problem/concern you are describing here.
Anyway ...
It might be better to discretize your continuous time plant yourself, by placing your own zero-order-hold (ZOH) in front of it, and doing the required calculations "by hand" (see link). The discrete-time ZOH+plant transfer function that results will then go in your Simulink model. Then go to configuration parameters and specify no continuous-time states and get everything to operate at a common sampling time, T. The only restriction here is that you will require all inputs (disturbances or other) to begin and end at a whole multiple of T. But I think that is reasonable.
If you would like some background material on this, you could have a look at the attached lecture notes.
Research An introduction to digital control systems - Lecture
"...the plant is continuous, which is going through the MPC for feedback.
My concern is, is it possible or not?"
Yes it is possible.
"If not possible, do i need A/D or D/A converters??"
You don't need it. In your case MPC block uses z-transform.
"Why zero-hold or other conversion method of D to A signals, causing a delay??"
Zero-hold don't causing a delay, but first-order hold causing it.
"Moreover, i dont find any convenient way to convert A/D in Simulink."
Find zero-order hold block in Simulink library for A to D convertion or first-order hold block.
Yuriy,
thnx alot for clarified answers.
i am sorry to say, i wronged part of the question. i found A/D converter in simulink, however, what i didnt find is D\A block in simulink.
thnx alot again.
Hi Ahmed,
If you are to design discrete time controller for a continuous time system, the best way to do it is to find discrete time equivalent of this continuous system via Z-transform and use any of discrete time control system design techniques to design a controller.
However, since the system is continuous in nature you must check its continuous time response anyway. To do this, you create your controller model in discrete time(z domain), and the plant model in continuous time(s domain) in same simulink model file.
After that, convert your manipulated control signal(output of the controller) into continuous time just before entering your continuous time modeled plant by using any of these:
1) Gain block with gain 1 and sample time as "0"
2) Zero order hold block with sample time "0"
I agree with the response of U. karaìnar- Simply represent the plant ++a zero -order sampling and hold in z- transform . Equivalently, use the state-space discretization of the palnt for a sampling period T ( the input goes out of the integral of the forced response over each samplimg period on the interval [kT, (k+1)T)- So, you calculate the state transition matrix evaluated for a time t=T andf the control matrix for such an interval and you write the state pace description for the sampled version :
x(k+1)= = FI *x(k) +Gamma*u(k)
Then you can design u(k) from a discrete controller. This styrategy can be sufficient for global stabilization and, even, for tracking ( at sampling points) but it can occur mistmatching/overshoots - normally bounded- in-between sampling instants .
Umut thank you very much.
actually i have tried to use the zero order hold block with sample time 0 but unfortunately, pops up a message that continuous sample time is not allowable.so cud not convert the manipulated signal into continuous time.
about he gain block, i can find only gain option not any sample time option, so with the gain 1 the input and output both are same.
You can get rid of that error by selecting any solver other than the "discrete(no continuous states)". Then you can specify discrete and continuous time parts of your model with "sample time" parameter of each block.
Thank you very much, really appreciate your quick response.
but it does not support,
http://www.mathworks.com/help/simulink/slref/zeroorderhold.html
'Do not specify a continuous sample time, either 0 or [0,0]. This block supports only discrete sample times. When this parameter is -1, the inherited sample time must be discrete and not continuous.'
I am using MATLAB 2015a
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