| Abstract: | In this paper automatic error elimination between outputs of n identical double-integral plants (K/s2) with different output initial conditions will be studied with two distinct objectives: (1) making all the identical steady-state outputs to be the double integral of any common input x(t); (2) having all the identical steady-state outputs track perfectly a reference input r(t). Thus fulfilment of objective (1), which can be viewed as a synchronization problem, commands that the whole MIMO system work on a closed-loop principle during the transient time in order to eliminate the errors between the n outputs; and on an open-loop basis during the steady-state phase in order to preserve the operation of the plant transfer functions (i.e. double integration) upon their inputs x(t). We shall see that objective (1) can always be attained if, once and for all, the plants are interconnected through identical PD-controllers (1 + Ts), no matter what form the common inputs x(t) may have. This is a far cry from the orthodox feedback control systems in which the type of input always plays a decisive role in selecting the appropriate controller. Having arranged the system for achievement of objective (1), we will show, with a unique technique, that objective (2) can be achieved through use of only one replaceable controller H(s), which operates on the difference between the reference input r(t) and any one of the n outputs. That is, each time r(t) is changed with the possible necessary change of controller H(s), we can make any number of outputs follow the reference input. This second objective can be considered as both synchronization and tracking, which in the text we shall refer to as tracking. We shall also show, without any alteration in the arrangements of our MIMO system, that objective (1) can also be achieved for identical plants of transfer functions K/s2(Tfs + 1)]. Through two examples, various observations discussed in the text will be demonstrated. Finally, armed with our previous results for simple-integral plants (K/s) and the results obtained in this paper, we shall briefly discuss triple-integral plants (K/s3) and q-integral plants (K/s(q)). |
