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Robotic manipulators are widely used in industrial applications, and their rigidity and flexibility are very important factors during their deployment. However, their usage is not limited to repetitive point-to-point tasks and can be used for more real-time control of various processes. This paper uses a 7-degrees-of-freedom manipulator to control an unstable system (Ball and Plate) as a proof of concept. The Ball and Plate system is widely used for testing algorithms designed for unstable systems, and many recent works have dealt with robotic manipulators as a control motion system. Robots are not usually used to control unstable systems, but bipedal robots are an exception. This paper aims to design a controller capable of stabilizing an unstable system with solid robustness while keeping actuator action values as low as possible because these robots will be indented to work for a prolonged time. An algorithm for an LQ polynomial controller is described and designed, and the whole setup is tested for ball stabilization in the center. The results show that the designed controller stabilizes the ball even with large external and internal disturbances while keeping the controller effort as low as possible.

Continuous Stirred-Tank Reactors (CSTR) belong to basic technological equipment frequently used in the the production of various types of chemicals. These systems are quite complex with many nonlinearities. So, the conventional linear control with fixed parameters can be questionable or unacceptable. The solution should be found in so-called “non-traditional” control approaches like Adaptive, Robust, Fuzzy or Artificial Intelligent methods. One way is the utilization of selftuning adaptive schemes but computations are quite difficult, clumsy and time-consuming. This paper brings an alternative principle called robust approach. This approach considers a linear system with parametric uncertainty which covers a family of all feasible plants. Then a controller with fix parameters is designed so that for all possible plants the acceptable control behavior is obtained. The two degree of freedom (2DOF) structure for the control law was chosen. All calculation and simulations of mathematical models and control responses was performed in the Matlab and Simulink environment.

Unfortunately, the major group of the systems in industry has nonlinear behavior and control of such processes with conventional control approaches with fixed parameters causes problems and suboptimal or unstable control results. An adaptive control is one way to how we can cope with nonlinearity of the system. This contribution compares classic adaptive control and its modification with Wiener system. This configuration divides nonlinear controller into the dynamic linear part and the static nonlinear part. The dynamic linear part is constructed with the use of polynomial synthesis together with the pole-placement method and the spectral factorization. The static nonlinear part uses static analysis of the controlled plant for introducing the mathematical nonlinear description of the relation between the controlled output and the change of the control input. Proposed controller is tested by the simulations on the mathematical model of the continuous stirred-tank reactor with cooling in the jacket as a typical nonlinear system.