1546 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 55, NO. 5, OCTOBER 2006 A Modification to Realize Dead-Beat Performance of Control Systems—Signal Correction Technique Acintya Das, Rajib Bag, and N. G. Nath Abstract—A technique for realizing dead-beat performance of control systems is investigated. The technique involves an injection of an additional signal to the system input to act in addition to its normal actuating signal. The technique is named “Signal Correction Technique (SCT),” which is found useful in partic- ularly modifying a biological control system where the system parameters and the input command of the system to be controlled are kept undisturbed. Index Terms—Additional signal, biological system, dead-beat transient response, performance modification of control systems, signal correction technique. I. I NTRODUCTION V ARIOUS techniques have been adopted in the past [1]–[5] for compensating or realizing dead-beat transient performance of control systems. These compensations, in gen- eral, refer either to the removal of the instability of control systems [6] or the modification for realizing a dead-beat tran- sient response of the control systems. In compensating a control system, either a proper controller is incorporated within the system or a device to process the input commands of the system to be compensated [7], [8]. The incorporation of a controller within the system, however, introduces extra poles and zeros of the transfer function of the system, and processing of the input command too introduces some extra zeros [9] to the transfer function of the system. There exist some systems like a biological control system, where it may not be possible either to incorporate a controller within the system or to process the system input command. In such a case, it would be convenient to compensate the system if a suitable electrical signal could be applied to the system input to act in addition to the normal actuating signal (input command) of the system. Injection of an additional signal, which is, in general, a high-frequency (HF) signal to the system input, apart from the removal of system instability, is found to modify [10] the system nonlinearity, making the system linear and stable. This technique of injecting an additional signal to realize the dead- beat transient performance of a control system is called “Signal Correction Technique (SCT),” which would be very much useful in realizing the dead-beat transient performance of the Manuscript received July 20, 2004; revised March 3, 2006. A. Das is with the Kalyani Government Engineering College, Kalyani, Nadia, West Bengal, India. R. Bag is with the Center of Advanced Study in Radiophysics and Elec- tronics, University of Calcutta, Calcutta 700 009, India (e-mail: rajib_bag@ yahoo.com). N. G. Nath is with the Department of Applied Electronics and Instrumenta- tion Engineering, Haldia Institute of Technology, Haldia, Midnapore, India. Digital Object Identifier 10.1109/TIM.2006.881589 control systems where either incorporation of any compen- sating network within the system or processing of the input command is not permitted in the system. The proposed SCT is developed in this paper by considering the presence of the additional signal to the system input along with the determi- nation of the nature of the signal required to realize the dead- beat transient performance of the control systems. The form of the additional signal would, however, be different either for its application to any other point except the input point or for its application to a nonlinear system. The SCT is, however, verified in this paper by considering the realization of dead-beat transient performance of a lightly damped linear second-order control system. II. MATHEMATICAL BACKGROUND Consider an nth order unity feedback MISO control system where R is the command input, and R 1 is another input that may be present in the system at any nodal point of the signal flow graph of the system in Fig. 1. C(0),C ′ (0),...,C (n-1) (0) are the initial conditions of the system. With R 1 present at any node, the output response can be expressed as C(s)=[D 1 ,D 2 ,...,D n-2 ,D n-1 ]     C(0) C ′ (0) . . . C (n-1) (0)     +[D 1 ,D 2 ,...,D n-1 ]R 1 (s)+ D n R(s) (1) where D 1 = 1 Δa n s n  n  i=1 a i s (i-1)  D 2 = 1 Δa n s n  n  i=2 a i s (i-2)  . . . D n = K Δs n and Δ= K a n s n n  i=0 a i s i . Among the initial conditions, C ′ (0),...,C (n-1) (0) denote the derivatives of the initial condition C(0). With the presence of the input signal R only and with zero initial conditions, (1) is reduced to C(s)= D n R(s). 0018-9456/$20.00 © 2006 IEEE