A bilateral teleoperation system is composed of five interconnected elements, including a human operator, local and remote manipulators, communication channel and an environment. Human operator exerts torques on a local manipulator and the action will be sent to the remote manipulator by a command. As we know, this communication often involves large distances and in most cases can result in substantial delays between the manipulator’s moves. Consequently, this may affect the overall stability of the teleoperation system. There are so many ways to control these systems And one of the best ways among them, are those which use properties of passivity of the system. Does anybody have an idea why these methods are more famous among the others and what do they offer about the system while others do not?
Given the circumstances, I will try to give it as compact as possible.
1- Passivity is a special form of dissipativity, where dissipativity is a concept strongly related to the Lyapunov stability. (For brevity I will skip the definition of dissipativity, but you need to understand it properly, read literature about this, I recommend Willems. When you do so, you will be familiar with the concepts of "storage function" or "supply rate". In fact, you will realize that a storage function is a Lyapunov candidate). Then if the supply rate is bilinear, then it implies passivity. It is a system property (linear or non-linear). But it of course can be used for control, in fact for this reason it is powerful. Then, we need to talk about "passivation", or controllers that ensures the passivity of the "controlled system".
2- Through passivation, one can achieve a "weakly minimum phase" behavior of a nonlinear system. With strict passivation, this means a "minimum phase" behavior. Now, if you are familiar with the linear system theory, you know that when the linear system is minimum phase, it means all its poles are in the left half of the S-domain, making it stable. Now, a passivating controller can potentially do this also for a non-linear system, Cool, huh?
3- Not to forget mentioning, passivity is a property of a (controlled/uncontrolled) system property, which is also closely connected to the "Input-Output Stability". In fact, if you read the Khalil book, you will see there that L-2 stability is same as passivity with some finite gain property (due to the bilinear relationship).
4- Bileteral teleoperation systems are hard to model, i.e. it is not easy to have an accurate model of the overall system, and use it in a classical model-based controller. One reason is that there is "human anatomy" in the loop, and well, there is no reliable mathematical model of it. Hence, for controlling such a system, you need a method that can cope with Input/Output data. Due to the item "3" above, passivity is a proper method for it. Due to the item "2" above it can achieve a stable behavior of the overall teleoperation system. This is done thanks to the item "1" above.
I hope this answers your question.
Cheers!
Dear Elnaz Firouzmand
Passivity-based controllers present a change of paradigm: from signal based to energy based. Control problems have been approached traditionally adopting a signal-processing viewpoint; Very useful for linear time-invariant systems, where signals can be discriminated via filtering. For nonlinear systems, frequency mixing makes things harder. Passivity-based controllers consider the physical structure of the system were energy plays an essential role in the description.
Regards
Passivity based control is fashionable way to insure stability of complex systems.
Due tu the fact, that the interconnected passive systems makes a passive "super-system" as well, passivity based control simplifies the control problem to the study of individual sub-systems which reduces the complexity of the task.
It should be noticed, anyway, that passivity is more conservative than pure stability.
maybe i can help you but need more explanation what you want exactly!
To support Neil's comments, you can see DOI: 10.1109/ICSMC.2008.4811706 in which a passivity-based approach is employed for synchronization of multi-manipulator systems.
Let us take it easy.
In a perfectly LTI systems,you do not have to mention passivity. You just have to know the pole positions of its Transfer Function (or the matrix eigenvalues of its state-space representation) in the Left Half Plane (LHP) and everything is alright.
However, as soon as things start changing, either as some function of time or as a nonlinear dependence, things stop being simple.
The simplest case is when you know that your plant is perfectly linear yet one single gain K may change, You also know that the system remains stable for any value of K between 1 and 10. But now you find out that, due to environmental situations or even due to some control policy, the gain may vary. The question is: Can you let it vary at will within the admissible bounds 1 and 10?
Two great names, (the Russian) Aizerman and Kalman thought that the answer was YES and this seems to be very intuitive.
However, counterexamples then showed that this is not necessarily so. In other words, you may try some nonstationary gain policy between the "admissible" limits and may find out that things 'work" and the system seems to remain perfectly stable. However, some very small change in this policy may lead to total destruction.
Therefore, in nonlinear systems you must find a way to guarantee that the system is stable indeed and passivity happens to be the term that guarantees this stability.
If you write "Aizerman's Conjecture" on Google, you get a good start.
Best regards,
Itzhak
You are talking about a nonlinear system with time delay, or complex linear system with time delay. Passivity is famous because it is intuitive. It models the whole system as a two ports element which has input and output at each port, or flow and effort at each port. Then by simply multiplying the flows and efforts like a dot product between the flows vector and the efforts vector, the total energy consumption of the system is found. If the system generates energy, then it is not stable and also active or non-passive, however, if the system just consumes energy, then it is stable and passive.
Given the circumstances, I will try to give it as compact as possible.
1- Passivity is a special form of dissipativity, where dissipativity is a concept strongly related to the Lyapunov stability. (For brevity I will skip the definition of dissipativity, but you need to understand it properly, read literature about this, I recommend Willems. When you do so, you will be familiar with the concepts of "storage function" or "supply rate". In fact, you will realize that a storage function is a Lyapunov candidate). Then if the supply rate is bilinear, then it implies passivity. It is a system property (linear or non-linear). But it of course can be used for control, in fact for this reason it is powerful. Then, we need to talk about "passivation", or controllers that ensures the passivity of the "controlled system".
2- Through passivation, one can achieve a "weakly minimum phase" behavior of a nonlinear system. With strict passivation, this means a "minimum phase" behavior. Now, if you are familiar with the linear system theory, you know that when the linear system is minimum phase, it means all its poles are in the left half of the S-domain, making it stable. Now, a passivating controller can potentially do this also for a non-linear system, Cool, huh?
3- Not to forget mentioning, passivity is a property of a (controlled/uncontrolled) system property, which is also closely connected to the "Input-Output Stability". In fact, if you read the Khalil book, you will see there that L-2 stability is same as passivity with some finite gain property (due to the bilinear relationship).
4- Bileteral teleoperation systems are hard to model, i.e. it is not easy to have an accurate model of the overall system, and use it in a classical model-based controller. One reason is that there is "human anatomy" in the loop, and well, there is no reliable mathematical model of it. Hence, for controlling such a system, you need a method that can cope with Input/Output data. Due to the item "3" above, passivity is a proper method for it. Due to the item "2" above it can achieve a stable behavior of the overall teleoperation system. This is done thanks to the item "1" above.
I hope this answers your question.
Cheers!
@Burak Yueksel
thank you by your answer. that was really helpful !!!
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