OPTIMAL path planning with OPTIMAL journey time and the motor saturation limit are two main challenges in mobile industrial robot design. The motion speed and motor saturation limit are important factors determining the required torque. Calculating the OPTIMAL torque value reduces the construction and motor selection costs. This paper proposes the THEORY of OPTIMAL CONTROL open-loop base model for path planning by simultaneously minimizing the journey time, wheels’,torque for industrial robots. In this study, nonlinear equations of robot motion were considered as a constraint in OPTIMAL CONTROL problems. Next, the cost function was proposed, including the torque of the left and right wheels and time-related terminal conditions and disturbance, in which the nonlinear equations of the industrial robot motion are assumed as constraints. The final equations were numerically solved, and the effectiveness of the proposed method was demonstrated by simulating and path design for industrial robots' motions along with considering motor saturation limit.

A lot of researches have been focused on the CONTROL design of systems regarding to time OPTIMAL moving of end effectors between two points in Cartesian space. Also a number of researchers have tried to solve the time invariant problem of CONTROL systems. A few works were done for time varying systems. For 2D gantry crane systems, the equations of motion and state space equations were obtained. Switching times have been calculated for such crane by means of phase plane analysis and algorithm genetic. The best input for system is Bang-Bang input and phase plane analysis here uses an open loop method.If the length of cable does not vary during the motion, the switching times were obtained, by the results of Genetic Algorithm method and have been verified by the phase plane method. It is shown that the Algorithm Genetic method is a useful method for obtaining switching times. If the length of cable varies during the motion, the oscillation of a cable in the end of the motion were justified and CONTROLled by means of Fuzzy CONTROL method. The rule-based method has been used for adjusting the fuzzy CONTROLler.

Active magnetic bearings (AMBs) are relatively new members in bearings family. Against other bearings which support loads by forces produced by fluid film pressure or physical contact, AMBs support loads by magnetic fields without any contact with the shaft and make it to be levitated. Because of that feature, AMBs have lots of benefits in comparison with other bearings. This paper presents modelling of AMBs with one and two degrees of freedom and the necessary parameters and equations for CONTROL of them is driven. Then, a numerical method based on orthogonal functions called Direct Method for OPTIMAL CONTROL in AMBs is presented with or without inequality constraints. The approach consists of reducing the OPTIMAL CONTROL problem with a two-boundary-value differential equation to a set of algebraic equations by approximating the state and CONTROL variables. This approximation uses orthogonal functions with unknown coefficients. In addition, the inequality constraints are converted to equal constraints. The problems are solved using Legendre and Haar bases. Simulation results demonstrate the benefits of Legendre functions method in compared with those using Haar bases.

This paper presents robust OPTIMAL CONTROL of an uncertain nonlinear switched system with forced subsystems. The uncertainties include external disturbance and parametric uncertainties. Switching signal and CONTROL input are designed to minimize a given cost function. Approximate DYNAMIC programming (ADP) has been efficiently applied to certain switched systems as an OPTIMAL CONTROL strategy. Since approximate DYNAMIC programming method is model based, there would seem to be some difficulties to apply approximate DYNAMIC programming to uncertain switched system. To overcome these mentioned problems, this paper presents an appropriate model. In order to apply proposed CONTROL approach, robust time-delay CONTROLler is added with ADP CONTROL. At first uncertainties are compensated by robust time-delay CONTROLler. Then the switching signal and the CONTROL input are design by approximate DYNAMIC programming that provides a feedback solution for unspecified initial conditions. The discussing boundedness of states and simulation results verify the effectiveness of the proposed CONTROL approach.