Performance analysis of robust stable PID controllers using dominant pole placement for SOPTD process models

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordThis paper derives new formulations for designing dominant pole placement based proportionalintegral-derivative (PID) controllers to handle second order processes with time delays (SOPTD). Previously, similar attempts have been made for pole placement in delay-free systems. The presence of the time delay term manifests itself as a higher order system with variable number of interlaced poles and zeros upon Pade approximation, which makes it difficult to achieve precise pole placement control. We here report the analytical expressions to constrain the closed loop dominant and nondominant poles at the desired locations in the complex s-plane, using a third order Pade approximation for the delay term. However, invariance of the closed loop performance with different time delay approximation has also been verified using increasing order of Pade, representing a closed to reality higher order delay dynamics. The choice of the nature of non-dominant poles e.g. all being complex, real or a combination of them modifies the characteristic equation and influences the achievable stability regions. The effect of different types of non-dominant poles and the corresponding stability regions are obtained for nine test-bench processes indicating different levels of open-loop damping and lag to delay ratio. Next, we investigate which expression yields a wider stability region in the design parameter space by using Monte Carlo simulations while uniformly sampling a chosen design parameter space. The accepted data-points from the stabilizing region in the design parameter space can then be mapped on to the PID controller parameter space, relating these two sets of parameters. The widest stability region is then used to find out the most robust solution which are investigated using an unsupervised data clustering algorithm yielding the optimal centroid location of the arbitrary shaped stability regions. Various time and frequency domain control performance parameters are investigated next, as well as their deviations with uncertain process parameters, using thousands of Monte Carlo simulations, around the robust stable solution for each of the nine test-bench processes. We also report, PID controller tuning rules for the robust stable solutions using the test-bench processes while also providing computational complexity analysis of the algorithm and carry out hypothesis testing for the distribution of sampled data-points for different classes of process dynamics and non-dominant pole types.KH acknowledges the support from the University Grants Commission (UGC), Govt. of India under its Basic Scientific Research (BSR) schem

Delay Handling Method in Dominant Pole Placement based PID Controller Design

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.Time delay handling is a major challenge in dominant pole placement design due to variable number of poles and zeros arising from the approximation of the delay term. We propose a new theory for continuous time PID controller design using dominant pole placement method mapped on to the discrete time domain with an appropriate choice of the sampling time to convert the delays in to finite number of poles. The method is developed to handle linear systems, represented by second order plus time delay (SOPTD) transfer function models. The proposed method does not contain finite term approximations like various orders of Pade, for handling the time delays which may affect the number and orientation of the resulting poles/zeros. Effectiveness of the proposed method have been shown using numerical simulations on nine SOPTD test-bench processes and another six challenging processes including single, double integrators and process with zero damping.European Regional Development Fund (ERDF

Quantum Algorithm of Imperfect KB Self-organization. Pt II: Robotic Control with Remote Knowledge Base Exchange

The technology of knowledge base remote design of the smart fuzzy controllers with the application of the "Soft / quantum computing optimizer" toolkit software developed. The possibility of the transmission and communication the knowledge base using remote connection to the control object considered. Transmission and communication of the fuzzy controller’s knowledge bases implemented through the remote connection with the control object in the online mode apply the Bluetooth or WiFi technologies. Remote transmission of knowledge bases allows designing many different built-in intelligent controllers to implement a variety of control strategies under conditions of uncertainty and risk. As examples, two different models of robots described (mobile manipulator and (“cart-pole” system) inverted pendulum). A comparison of the control quality between fuzzy controllers and quantum fuzzy controller in various control modes is presented. The ability to connect and work with a physical model of control object without using than mathematical model demonstrated. The implemented technology of knowledge base design sharing in a swarm of intelligent robots with quantum controllers. It allows to achieve the goal of control and to gain additional knowledge by creating a new quantum hidden information source based on the synergetic effect of combining knowledge. Development and implementation of intelligent robust controller’s prototype for the intelligent quantum control system of mega-science project NICA (at the first stage for the cooling system of superconducted magnets) is discussed. The results of the experiments demonstrate the possibility of the ensured achievement of the control goal of a group of robots using soft / quantum computing technologies in the design of knowledge bases of smart fuzzy controllers in quantum intelligent control systems. The developed software toolkit allows to design and setup complex ill-defined and weakly formalized technical systems on line

Time Delay Handling in Dominant Pole Placement with PID Controllers to Obtain Stability Regions using Random Sampling

This is the author accepted manuscript. The final version is available from Taylor & Francis via the DOI in this recordThis paper proposes a new formulation of proportional-integral-derivative (PID) controller design using the dominant pole placement method for handling second order plus time delay (SOPTD) systems. The proposed method does not contain any finite term approximation like different orders of Pade for handling the time-delay term, in the quasi-polynomial characteristic equation. Rather it transforms the transcendental exponential delay term of the plant into finite number of discrete-time poles by a suitable choice of the sampling time. The PID controller has been represented by Tustin’s discretization method and the PID controller gains are obtained using the dominant pole placement criterion where the plant is discretized using the pole-zero matching method. A random search and optimization method has been used to obtain the stability region in the desired closed loop parameters space by minimising the integral squared error (ISE) criterion by randomly sampling from the stabilizable region and then these closed loop parameters are mapped on to the PID controller gains. Effectiveness of the proposed methodology is shown for nine test-bench plants with different lag to delay ratios and open loop damping levels, and the effect of choosing different sampling times, using credible numerical simulations.ESIF ERDF Cornwall New Energy (CNE

Stabilizing region in dominant pole placement based discrete time PID control of delayed lead processes using random sampling

This is the final version. Available on open access from Elsevier via the DOI in this recordData availability: Data will be made available on request.Handling time delays in industrial process control is a major challenge in the dominant pole placement based design of proportional-integral-derivative (PID) controllers due to variable number of zeros and poles which may arise from the Pade approximation of the exponential delay terms in the characteristic polynomials used for stability analysis. This paper proposes a new concept for designing PID controllers with a derivative filter using dominant pole placement method mapped onto the discrete time domain with a suitable choice of the sampling time to convert the continuous time time-delays into finite number of discrete time poles. Here, the continuous-time plant and the filtered PID controller have been discretized using the pole-zero matching method for handling linear dynamical systems, represented by the first order plus time delay with zero (FOPTDZ) transfer function models of the open-loop system under control. We use a swarm intelligence based global optimization method as a sampler to discover the approximate the pattern of the stabilizable region in the controller parameter as well as the design specification space while also satisfying the analytical conditions for pole placement given as higher order polynomials. Simulations on test-bench plants with open-loop stable, unstable, integrating, low-pass, high-pass characteristics have been presented in order to demonstrate the validity and effectiveness of the proposed control design method.European Regional Development Fund (ERDF