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This paper is aimed at modelling a two-wheeled self-balancing robot driven by the geared DC motors. A mathematical model consists of two main parts, the model of robot's mechanical structure and the model of the actuator. Linearized equations of motion are derived and the overall model of the two-wheeled self-balancing robot is represented in state-space realization for the purpose of state feedback controller design.

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A general method for the synthesis of 1 alkyl(allyl)(benzyl) substituted (indol 3 yl) sulfanylalkanecarboxylic acids and hexane 1,6 diyl(1,4 phenylenemethylene)bisindol 3 yl sulfanylalkanecarboxylic acids from the corresponding N substituted indoles and bisindoles, thiourea, iodine, and halogencarboxylic acids was developed. The oxidation of substituted (indol 3 yl)sulfanylalkanecarboxylic acids for the first time afforded their analogs containing the sulfonyl group. New (2 hydroxyethyl)ammonium salts of 1 R indol 3 ylsulfanyl(sulfonyl) alkanecarboxylic acids, which are structural analogs of highly active immunomodulators of indacetamin and VILIM, were synthesized. Among the studied (2 hydroxyethyl)ammonium salts of 1 R indol 3 ylsulfanylacetic and sulfonylalkanecarboxylic acids, the compounds exhi biting high dose dependent antiproliferative activity by the ability to affect the spontaneous and mitogen stimulated splenocyte proliferation of mice in vitro were found.Tris(2 hydroxyethyl)ammonium salts of aroxyacetic acids, whose cation has the compact tricyclic atrane (2,8,9 trihydroprotatrane) structure favoring the penetra tion of a substance through cell membranes, are a new class of pharmacologically active substances. 1 They pos sess 2-12 anti aggregation, membrane stabilizing, antiox idant, antisclerotic, antiphlogistic, cardiotropic, analge sic, hypocholesterolemic, immunomodulating, and anti tumor activity considerably exceeding or different from the effect of the initial biologically active acids and trieth anolamine.Earlier synthesized analogs of these compounds, viz., alkanolammonium salts of (het)arylsulfanyl (sulfonyl)acetic acids (Het)ArS(SO 2 )CH 2 COO -• •N + R 1 R 2 (CH 2 CH 2 OH) n (R 1 , R 2 = H, Alk, CH 2 CH 2 OH; n = 1-3), 13-15 and their complexes with salts of biomicroelements 16,17 are lowly toxic (LD 50 = = 1300-6000 mg kg -1 ), also exhibit high and diverse bio logical activity, such as hemo and immunotropic, car diotropic, antiphlogistic, antithrombotic, antioxidant, adaptogenic, hypocholesterolemic, etc., and are highly ef ficient growth stimulating preparations for biotechnolog ical processes. 18,19 Biological activity of alkanolammonium salts of sulfur containing acids is not inferior and often exceeds the activity of related alkanolammonium salts of aroxyacetic acids. The activity is enhanced with an increase in the oxidation state of the sulfur atom and depends on the structure of the (2 hydroxyethyl)ammonium fragment. 14, 15 Indole derivatives, 20 in particular, (indol 3 yl)sulfanyl alkanecarboxylic acids and their salts, are worthy of spe cial attention as biologically active substances, 21 interme diates for the synthesis of medical preparations 22-24 and technically valuable products. 25 We have earlier found by screening efficient non toxic (LD 50 = 1300-3000 mg kg -1 ) immunoactive compounds, viz., tris(2 hydroxyethyl)ammonium indol 3 yl and 1 benzylindol 3 ylsulfanyl acetates (indacetamin and VILIM, respectively).Indacetamin has a wide range of biological activity and is an e...