The paper addresses the problem of constrained pole placement in discrete-time linear systems. The design conditions are outlined in terms of linear matrix inequalities for the Dstable ellipse region in the complex Z plain. In addition, it is demonstrated that the D-stable circle region formulation is the special case of by this way formulated and solved pole placement problem. The proposed principle is enhanced for discrete-lime linear systems with polytopic uncertainties.
Swing-up control of a single pendulum from the pendant to the upright position is ﬁrstly surveyed. The control laws are comparatively studied based on swing-up time from a given initial state to the upright position. The State Dependent Riccati Equation is found eﬀective for designing the swing-up control law under saturating control input. The control law is extended to a linear combination of sine function of the angle and the angular velocity, and a variable structure control with a sliding mode given by the linear combination. Making the swing-up time correspond to a colour, which is similar to the Fractal analysis, colour maps of the swing-up time for given control parameters and initial conditions yield interesting Fractal-like ﬁgures.
There exist numerous modelling techniques and representation methods for digital control algorithms, aimed to achieve required system or process parameters, e.g. precision of process modelling, control quality, fulfilling the time constrains, optimisation of consumption of system resources, or achieving a trade-off between number of parameters. This work illustrates usage of Finite State Machines (FSM) modelling technique to solve a control problem with parameterized external variables. The structure of this work comprises six elements. The FSM is presented in brief and discrete control algorithm modelling is discussed. The modelled object and control problem is described and variables are identified. The FSM model is presented and control algorithm is described. The parameterization problem is identified and addressed, and the implementation in PLC programming LAD language is presented. Finally, the conclusion is given and future work areas are identified.