On the nonlinear dynamics and control of flexible orbiting manipulators

The paper studies nonlinear dynamics and control of a class of space station based mobile flexible two-link manipulators, normally referred to as the Mobile Servicing System (MSS).The governing nonlinear, nonautonomous and coupled equations of motion are described first followed by the modal discretizations procedure. A parametric response study suggests situations with unacceptable levels of deflections and accelerations for certain proposed missions, as well as station libration and payload positioning errors.An inverse control technique is proposed to achieve high tracking accuracy of the MSS in presence of maneuver induced disturbances. The control strategy is so designed as to regulate the libration of the Space Station as well as to insure joints tracking of prescribed trajectories, while limiting the effect of the structural vibration during large slewing maneuvres of the MSS. Two different control schemes, both based on the feedback linearization technique, are developed and their relative merit assessed.This investigation was supported by the Centers of Excellence Program, Grant No. IRIS/C-8, 5-55380, and Natural Sciences and Engineering Research Council of Canada, Grant No. A-2181.     

On the nonlinear slewing dynamics and control of the Space Station based Mobile Servicing System

A relatively general Lagrangian formulation for studying the nonlinear dynamics and control of space-craft with interconnected flexible members in a tree-type topology is developed. Versatility of the formulation is illustrated through a dynamical study of the Space Station based two-link Mobile Servicing System (MSS). The performance of the MSS undergoing inplane and out-of-plane slewing maneuvers is compared. Results indicate that, in absence of control, the maneuvers induce undesirable librational motion of the Space Station as well as vibration of the links. Nonlinear control, based on the Feedback Linearization Technique (FLT), appears promising. Quasi-Closed Loop Control (QCLC), a variation of the FLT, is applied to control the libration of the Space Station. Once the attitude of the Space Station is controlled, the performance of the MSS improves significantly. For a 5-minute maneuver of the MSS, the maximum control torque required is only 34.5 Nm.Nomenclature f _i ¹ , f _i,j ¹ fundamental frequency of bodies B _i and B _i,j, respectively - l _c, l _i, l _i,j length of bodies B _c, B _i, and B _i,j, respectively - m _c, m _i, m _i,j mass of bodies B _c, B _i, and B _i,j, respectively - % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaerbhv2BYDwAHbacfiGab8xCayaaraqefavySfgDP52BGWuAU9gD% 5bxzaGGbciaa+zgacaWFSaGaa8hiaiqa-fhagaqeaiaa-jhaaaa!4B1F!\[\bar qf, \bar qr\] vector representing flexible and rigid generalized coordinates - % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaerbhv2BYDwAHbacfiGaa8hkaiqa-fhagaqeaiaa-jhacaWFPaqe% favySfgDP52BGWuAU9gD5bxzaGGbciaa+rgaaaa!4A18!\[(\bar qr)d\] vector representing the desired rigid generalized coordinates - (I _xx)k, (I _yy)k, (I _zz)k principal inertia of body B _k about X _k, Y _k, and Z _k axes, respectively; ksc, i or i, j - K _p, K _v displacement and velocity gain matrices - N _q total number of generalized coordinates - % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaerbwvMCKfMBHbacfiGab8xuayaaraqefavySfgDP52BGWuAU9gD% 5bxzaGGbciaa+zgaieaacaqFSaGaa0hiaiqa-ffagaqeaGqaciaa8j% haaaa!4AEF!\[\bar Qf, \bar Qr\] control effort vectors for flexible and rigid coordinates, respectively - Q , Q , Q control effort for pitch, roll and yaw degree of freedom, respectively - _k ^y , _k ^z tip deflection of a beam type appendage (B _k) in the Y _k and Z _k directions, respectively.     

Periodicity of pricing and marketing efforts in a distribution channel

Most research about cooperative (coop) advertising programs in channels relies on the assumption that manufacturers and retailers decide of pricing and marketing efforts simultaneously. This paper evaluates this central assumption and investigates the optimal periodicity (sequence of move) of pricing and marketing efforts (ME) decisions for a distribution channel. We develop a game theoretic model that accounts for pricing at each level of the channel, for the manufacturer’s ME mix strategies (a direct ME to consumers and coop advertising program offered to the retailer) and the retailer’s ME as well. We obtain solutions for a bilateral channel under different vertical interaction scenarios; when the channel is led by the manufacturer, the retailer or when channel members decide simultaneously of each of their marketing mix decisions (vertical Nash). We compare the effect of pricing and ME decision periodicity on outputs for each channel member. The main findings suggest that simultaneous decision-making of pricing and ME is optimal only for high enough levels of the manufacturer’s ME effects. For very highly effective marketing efforts, sequential play of pricing and ME allows channel members to implement equilibrium strategies and achieve maximum profits that would not be achieved with simultaneous decision-making. This highlights the importance of relaxing the simultaneous play assumption of pricing and ME in a distribution channel.     

A dynamic model for advertising and pricing competition between national and store brands

We study the relationship between the pricing and advertising decisions in a channel where a national brand is competing with a private label. We consider a differential game that incorporates the carryover effects of brand advertising over time for both the manufacturer and the retailer and we account for the complementary and competitive roles of advertising. Analysis of the obtained equilibrium Markov strategies shows that the relationship between advertising and pricing decisions in the channel depends mainly on the nature of the advertising effects. In particular, the manufacturer reacts to higher competitive retailer’s advertising levels by offering price concessions and limiting his advertising expenditures. The retailer’s optimal reaction to competitive advertising effects in the channel depends on two factors: (1) the price competition level between the store and the national brands and (2) the strength of the competitive advertising effects. For example, in case of intense price competition between the two brands combined with a strong manufacturer’s competitive advertising effect, the retailer should lower both the store and the national brands’ prices as a reaction to higher manufacturer’s advertising levels. For the retailer, the main advantage from boosting his competitive advertising investments seems to be driven by increased revenues from the private label. The retailer should however limit his investments in advertising if the latter generates considerable competitive effects on the national brand’s sales.     

Vendor Management Inventory with consignment contracts and the benefits of cooperative advertising

Most of the cooperative advertising literature has focused on studying the effects of such programs considering marketing variables. This paper integrates production and inventory management with pricing and advertising considerations to assess the effects of cooperative advertising programs in bilateral monopolies. We consider a supply chain where a Vendor Managed Inventory (VMI) along with a consignment contract is implemented to coordinate the chain. We develop and solve a differential model for two games. The first one is a benchmark scenario where no cooperative advertising is offered, while the manufacturer offers the cooperative program in the second game. The main results show that cooperative advertising programs, usually considered as successful marketing initiatives, can be very difficult to implement in a supply chain undertaking a VMI policy with a consignment contract, in which operations and marketing interface is taken into account. A cooperative program mainly hurts the manufacturer’s profits, and can be profit-Pareto-improving only in a few cases. Although the retailer is generally willing to receive a support from the manufacturer, she can opt for a non-cooperative program when the largest part of the supply chain profits goes to the manufacturer. We developed several special cases to strengthen our findings.     

A Novel Thermostable and Alkaline Protease Produced from Bacillus stearothermophilus Isolated from Olive Oil Mill Sols Suitable to Industrial Biotechnology

This study was conducted to identify a new alkaline and thermophilic protease (Ba.St.Pr) produced from Bacillus stearothermophilus isolated from olive oil mill sols and to evaluate its culture conditions, including temperature, pH, carbon and nitrogen sources, and incubation time. The optimum culture conditions for cell growth (10 g/L) and protease production (5050 U/mL) were as follows: temperature 55 °C, pH 10, inoculation density 8 × 10⁸ CFU/mL, and incubation time 24 h. The use of 3% yeast extract as the nitrogen sources and galactose (7.5 g/L) as the carbon sources enhanced both cell growth and protease production. Using reversed-phase analytical HPLC on C-8 column, the new protease was purified with a molecular mass of approximately 28 kDa. The N-terminal sequence of Ba.St.Pr exhibited a high level of identity of approximately 95% with those of Bacillus strains. Characterization under extreme conditions revealed a novel thermostable and alkaline protease with a half-life time of 187 min when incubated with combined Ca²⁺/mannitol. Ba.St.Pr demonstrated a higher stability in the presence of surfactant, solvent, and Ca²⁺ ions. Consequently, all the evaluated activity parameters highlighted the promising properties of this bacterium for industrial and biotechnological applications.     

Kinetic properties of pancreatic and intestinal sPLA2 from chicken and mammals using the monomolecular film technique

The interfacial kinetic and binding data for the pancreatic and intestinal sPLA2 from bird and mammals show that these enzymes have dramatically different ability to bind and hydrolyse phospholipids. The main conclusions from our experimental data indicate that phosphatidylcholine monolayers (PC), in contrast to phosphatidylethanolamine (PE) and phosphatidylglycerol (PG), were resistant to the hydrolysis by human intestinal sPLA2. Conversely, chicken intestinal sPLA2 was found to be able to hydrolyse all the phospholipids tested, including PC. The experiments show also that the interfacial penetrating ability of chicken sPLA2 (from intestine and pancreas) was higher than their mammalian's orthologs. This observation is confirmed by the activity of pancreatic chicken PLA2 measured on PC film showing that the interfacial pressure window that permits sPLA2 activity was very large, between 5 and 20 dynes cm(-1), compared with the porcine pancreatic sPLA2-IB which was inactive at pressure above 15 dynes cm(-1). In trying to establish a structure-function relationship, we examined the surface electrostatic potentials of the various sPLA2 from chicken and mammals. We reported in this study that the binding, orientation and persistence of sPLA2 at the lipid-water interface is probably governed by the electrostatic and hydrophobic forces operative at this surface. These variations argue strongly that these enzymes are not isoforms and that they are expected to have functions other than the release of lipid mediators for the biosynthesis of the eicosanoids.