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A common practice in a system identification exercise is to perturb the system of interest and use the resulting data to build a model. The problem of interest in this contribution is to synthesize an input signal that is maximally informative for generating good quality models while being “plant friendly,” i.e., least hostile to plant operation. In this contribution, limits on input move sizes are the plant friendly specifications. The resulting optimization problem is nonlinear and nonconvex. Hence, the original plant friendly input design problem is relaxed which results in a convex optimization problem. We formulate a SemiDefinite Programme using the theory of generalized Tchebysheff inequalities to derive tight bounds on the quality of relaxation. Simulations show that the relaxation results in more plant friendly input signals.