Josef Böhm

State-space generalized predictive control for redundant parallel robots

Abstract The article deals with the design and properties of generalized predictive control (GPC) for path control of redundant parallel robots. Redundant parallel classification means redundant number of actuators, i.e., more actuators than degrees of freedom of the robot. Control of such structures suffers from several new control problems like potential inconsistency of steady state positions or nonuniqueness of control actions. The article explains classical direct derivation of GPC and its modification based on square root two-step design of control actions for solving the control problems. As an example for verification of algorithms, a prototype of a planar redundant parallel robot is used. Both design approaches are compared and several possibilities of extensions are presented for taking into consideration additional requirements, like smooth course of actuators or fulfillment of the anti-backlash condition.

PREDICTIVE CONTROL APPLIED TO PLANAR PARALLEL ROBOTS

Abstract The design of suitable control is essential part of application of parallel robots. Together with appropriate control, the parallel robots are promising way to significantly improve accuracy and speed of machine tools in industrial production. This paper deals with the design and results of one possible control approach represented by model-based predictive control in absolute formulation. It explains exact linearization of used, initially nonlinear models, which are sequentially transformed to discrete state-space form. Control algorithm is derived in square-root form. The results are substantiated by real laboratory experiments showed in several representative figures.

MULTIOBJECTIVE PROBABILISTIC MIXTURE CONTROL

Abstract Paper formulates the problem of multiobjective probabilistic mixture control design and proposes its general solution with both system model and target represented by finite probabilistic mixtures. A complete feasible algorithmic solution for mixtures with components formed by normal auto-regression models with external variable is provided.

MATLAB-Toolbox for CAD of Simple Self-Tuning Controllers

Abstract The contribution presents a MATLAB-Toolbox for design, simulation and verification of single input single output (SISO) discrete self-tuning controllers. The proposed adaptive controllers who are included into a Toolbox can be divided into two parts. The first part covers PID adaptive algorithms using traditional Ziegler-Nichols method for the setting of the controller parameters, the second part of described controllers is based on the pole placement design. The MATLAB-Toolbox is very successfully used in Adaptive Control Course in education practice for design, simulation and verification of self - tuning control systems in real - time conditions. It is suitable for design and verification of the industrial controllers, too.

Practical Aspects of Self-Tuning Controllers

Abstract The contribution presents a class of single input single output (SISO) discrete self-tuning controllers suitable for industrial applications. The proposed adaptive controllers can be divided into three parts. The first part covers РID adaptive algorithms with utilization of traditional methods. The second part is based on polynomial solutions of control problems and the third part is derived using of the minimization of linear quadratic criterion. All types of algorithms were unified and incorporated into a Matlab - like Toolbox for self-tuning control.

MATLAB-Toolbox for Design and Verification of Self-Tuning Controllers

Abstract The contribution presents a MATLAB-Toolbox for design, simulation and verification of single input single output (SISO) discrete self-tuning controllers. The proposed adaptive controllers who are included into a Toolbox can be divided into two parts. The first part covers PID adaptive algorithms using traditional methods and pole placement design, the second part is describes controllers based on the minimization of quadratic criterion. The MATLAB-Toolbox is very successfully used in Adaptive Control Course in education practice for design, simulation and verification of self - tuning control systems in real - time conditions.

Software Tools for Use of Prior Knowledge in Design of LQG Adaptive Controllers

Abstract A systematic probabilistic approach to off-line design of LQG adaptive controllers can be supported by use of prior information in each design step. The prior information processing and its use is a relative new topic. The article contributes to understanding of the prior knowledge importance by a simulation case study. A toolbox ABET for MATLAB (MathWorks) is presented that makes it possible to carry out each step of design of adaptive controller with use of prior knowledge.

Model Switching in Multiple-Model LQ Controller

Abstract Multiple model representation is used here to represent given system. The LQ controller is designed respecting the whole set of models. Such controller is conservative. Better control behaviour can be obtained when the probability of particular model is provided. Probabilities of models in the set are estimated on-line.The approach is demonstrated on the control of a nonlinear plant. As such example, the elevation dynamics of a helicopter model was used.

Robust Adaptive Controller with Fine Grain Parallelism

Abstract Two issues associated with an adaptive linear quadratic controller are addressed in the paper: numerical robustness of the adaptive estimator with respect to low excitation in the closed control loop and rather high computational complexity of the controller. The algorithm presented in the paper uses The estimator used in the paper is based on the inverse-updated square-root recursive least squares (SR-RLS) identification algorithm (Moonen and McWhirter 1993). To increase numerical robustness of the algorithm for weak excitation, the regularized exponential forgetting is used. The multi-step control design uses an autoregression system model with exogenous input (ARX model). Computational complexity of the resulting algorithm is reduced by using the systolic paradigm for its implementation.

Multivariable LQ Controller Optimization as an Event Driven Process

Abstract The classical approach to an LQ synthesis rely on state space models. Their structure is too rigid and the attempt to use them for the description of large systems with specific structure usually leads to inefficient model of high dimensionality with a lot of zero elements in the corresponding matrices. The proposed approach shows how to minimize quadratic criterion using dynamic programming without the need of the state space form of the linear model. The criterion is represented by a list of events each one described by a triple [time, channel, value]. The dynamic programming then consists of a sequence of actions defined by the time instant and a type of data. Models required for the expectation step have a form of a multi-input single-output linear regression models. The data vector of such model can contain data sampled with various rates, theoretically also quite irregularly.