Adaptronic system

An adaptronic system thus is characterized by adaptability and multifunctionality. The aim is to combine the greatest possible number of application-specific functions in one single element and, if appropriate, in one specific material (see Fig. 1.1). 

Fig. 1.1. Transition from a a conventional system to b an adaptronic system...

Examples for adaptronic systems with a more distinct visionary character are window panes whose transparency automatically regulates itself or can be adjusted within seconds by pressing a button and hydroplanes whose aerodjmamic profile adapts itself to the prevailing flight conditions. 

Functional materials constitute the essential basis of all adaptronic systems. The made-to-measure production of functional materials, wherein several functions are interlinked at a molecular level, is therefore of special importance. The more application-specific functions are combined in one single element, the bigger is the advantage in terms of an adaptronic system optimization. Multifunctionality can, however, not be a characteristic feature of an isolated element, but should always manifest itself by meeting user-specific requirements within a system interrelationships. Thus the same element can produce a decisive compression of functions in a given case (A), while it can be completely worthless in a given case (B). 

A general overview in Sect. 5.2 about the simulation of adaptronic (mechanical) systems is followed by a discussion of steps to be taken towards a mathematical model of an adaptronic structure in Sect. 5.3. Once a mathematical model of the adaptronic system has been derived and implemented numerically, analysis and simulations have to be carried out to characterise its dynamic behaviour. A survey of related methods and algorithms is given in Sect. 5.4. Simulation goals such as stability, performance and robustness are discussed, especially for the case of actively controlled structures. The modelling and simulation process is also demonstrated by a practical example in Sect. 5.5, while Sect. 5.6 gives an outlook on adaptronic system optimisation techniques. 

The system s dynamic response variables such as displacements and velocities are contained in the state vector x n x 1). Physical quantities that exert excitations on the system (e. g. external forces and actuator forces) are collected in an input vector u p x 1), and measured quantities (sensor signals) in an output vector y(g x 1). For actively controlled adaptronic systems, the task is to generate a suitable input u t) from a given output y t) such that the system exhibits desirable dynamic behaviour. 

The efficiency and proper positioning of actuators and sensors in adaptronic systems can be analysed using the concepts of controllabihty and observability. To make the basic ideas more clear, adaptronic structures are taken as an example. Loosely speaking, controllability and observabihty also mean that the actuator force and sensor vectors are not orthogonal and preferably parallel to the relevant vector (e. g. natural mode) or state to be controlled or observed. 

If an adaptronic system is modelled in a state-space description (5.3), (5.4), its observability and controllability can be determined numerically by various methods. A common way is to compute the eigenvalues of the controllability and observability Gramians... 

Controllers for adaptronic systems can be designed based on general proofs of stability, as in the case of collocated dissipative controllers, or based on a mathematical model of the system. In the latter case, it is often important to represent the d3mamics of a system very accurately because the stability and performance of the controller can only be checked with the mathematical model in the first place. Discrepancies between the dynamic behaviour of the mathematical model and the real adaptronic system may lead to loss of performance and even instability when the controller is finally implemented with the real system (see Sect. 5.4.2). This then would have to be corrected by sometimes time-consuming adjustment of the controller parameters to the actual plant properties and behaviour, if possible at aU. 

The stability of a controlled dynamic system is said to be robust if the controller designed using a mathematical model stabilizes the real system in spite of modelling errors and/or parameter changes in the adaptronic system. A similar definition holds for the robustness of performance. 

Numerical analysis and simulation of adaptronic systems can be performed in the time or in the frequency domain depending on the representation of the system in the state space or as a matrix of transfer functions. In addition to performance criteria, important goals are stability and robustness of an adaptronic system. In the case of adaptronic structures, performance criteria are often given in terms of allowable static and dynamic errors relating to structural shape if subjected to specified disturbances. Many applications also involve limits in energy consmnption and actuator stroke or force, which must be checked in time-history simulations. A comprehensive introduction on the different aspects and their interaction can be found in [14]. Current research in the field is for instance presented in [15] and [16]. 

Every dynamic adaptronic system must be checked for stability in the case of disturbances. For linear elastic adaptronic structures, asymptotic stability as defined in Sect. 5.2.4 is guaranteed if the poles (or eigenvalues) of the closed-loop active system lie in the left complex half-plane, i.e. if they have negative real parts. More stringent stability criteria, such as the generalized Nyquist criterion [7], also consider the zeros of the adaptronic system. 

A typical practical example for adaptronic systems or systems with adaptronic subsystems are large and high precision astronomical telescopes as shown in Fig. 5.2. This example is from [19]. 

A brief overview on different software tools related to the simulation of adaptronic systems is given. Since for the core tasks there are several tools which are continuously improved, actual comparisons are difficult and also depend on the specific criteria relevant for each of the application cases. So the overview should be considered as representative but not necessarily as complete. 

For all of the tools mentioned, proper application requires the knowledge of the physical and modelling background together with that on the steps mentioned in this chapter, and engineering insight into the adaptronic system to be developed. 

It is possible to achieve an even higher degree of multifunctionality when multifunctional materials are being used. This shall be illustrated with the following example actively controlling structural geometry is a typical task performed by adaptronic systems. Piezoelectric stacks, for instance, are used... 

As a final example of a MR fluid controlled adaptronic system, the smart prosthesis knee developed by Biedermann Motech GmbH [178-181] is presented. This system shown in Fig. 6.91 is a complete artificial knee that automatically adapts and responds in real-time to changing conditions to provide the most natural gait possible for above-knee amputees. The heart of this system is a small magnetorheological fluid damper that is used to semi-actively control the motion of the knee based on inputs from a group... 

---