Feasibility conditions on PID controller synthesis using dominant pole assignment

In this paper, an innovative design method of PID controller based on genetic algorithm tuning parameters, VHDL description and FPGA implementation is proposed. The parameters of the PID controller are optimized by using genetic algorithm. The intelligent PID controller based on genetic algorithm is realized by using FPGA. During the realization process, the functional modules of the system are divided based on top-down design method. Each module of the system is described with VHDL language. Finally, the closed loop tests of the intelligent PID controller based on FPGA and genetic algorithm are implemented by means of DSP Builder and Matlab/Simulink. Simulation results have shown that the design method of the intelligent PID controller based on FPGA and genetic algorithm is verified, and it has some advantages such as design flexible, self-tuning on line, high reliability, short cycle of technical development, high running speed and so on. This intelligent PID controller based on FPGA and genetic algorithm can be applied in high control precision digital control system with high speed responsibility and high stability.

It is important to know how far non-dominant poles can be located away from the dominant poles since the closed-loop system transient response may not be as expected, if the non-dominant poles are not placed far enough from the dominant pole pair. Even if the arbitrary pole assignment is possible with a full state feedback or an output feedback controller with the order of plant order minus one, low order controllers and especially PID controllers are used in most practical applications. Therefore, the farthest possible non-dominant pole locations with PID controllers are found for all pole systems in this study. Proposed calculation method is demonstrated on two different examples and the closed-loop system performance is investigated with the designed PID controllers.

A new design method for PID controller using user-specified gain margin and phase margin for delayed systems has been proposed. The proposed PID controller is particularly useful in auto-tuning. The controller parameters are calculated using several approximations and elimination processes. The robustness of the proposed controller is verified by different simulation examples.

Although the traditional PID controller is widely used in many fields, the system parameters varying and external disturbances existing in the DC servo system will cause large overshoot or poor stability. To improve the performance of the PID controller, a compound servo control system combining the conventional PID control and the fuzzy control is presented to meet the demand of a vehicular antenna servo system in this paper. Incorporating the fuzzy control and the conventional PID control, this paper presents a design method of the fuzzy PID controller that is based on the fuzzy tuning rules and formed by integrating two above control ideas. Simulation results are presented to show the efficiency of the proposed controller. The practical control effect shows that the control system that adopts the fuzzy PID controller has better performance than that of the traditional PID control system, and meets the performance requirements of the servo system.

In the process of frozen food production, its refrigeration system is a typical large inertia, nonlinear, strongly coupled system, which is prone to large overshooting during operation, resulting in cost increase and quality control problems. This paper solves the problem of large overshoot in the digital PID control process by designing a fuzzy control, and designs a practical fuzzy controller so that the design method of the fuzzy PID controller can be realized in the simulation and actual control of the freezing system. A genetic algorithm optimization scheme is also designed for the fuzzy PID control system to optimize the fuzzy controller’s affiliation function, control rules, as well as proportionality and quantization factors, to enhance the model’s dynamic characteristics and robustness. Design of food quick-freezing simulation experiments and use the model in the refrigeration system control in practice, compare the performance of this model with the PID, fuzzy PID model, and found that the temperature difference set value of 4 ℃ and 3 ℃, respectively, the parameters of the traditional PID controller in the commissioning stage of the system after the end of the rectification to remain fixed, which makes the actual quality of the cooling water temperature difference control degradation. And the fuzzy genetic PID controller still has good control quality. In this paper, the model curve converges rapidly, the overshoot is only 3.9%, and the regulation time is only 450M seconds. The designed method of the study is feasible and has high industrial application value.

When a controlled object has a nonlinear characteristic, a good control result is not always obtained with fixed PID gains. This paper proposes a design method of a nonlinear PID controller using a neural network to overcome the problem. In the proposed controller, PID gains are tuned online by a neural network and a controlled object is controlled by the PID controller with the tuned PID gains. The neural network learns by a learning algorithm based on the Extended-Fictitious Reference Iterative Tuning (E-FRIT) and the backpropagation. The FRIT is a method that tunes control parameters directly by using a set of operating data. The main advantage of the FRIT is that the parameters can be determined without any mathematical model. The FRIT evaluates only a control response, whereas the E-FRIT does it as well as the difference of manipulated variable. In this paper, the E-FRIT is utilized for a learning algorithm of a neural network. Simulation examples are provided to show an effectiveness of the proposed method by simulation examples.

Based on the ant colony system (ACS) algorithm and fuzzy logic control, a new design method for optimal fuzzy PID controller was proposed. In this method, the ACS algorithm was used to optimize the input/output scaling factors of fuzzy PID controller to generate the optimal fuzzy control rules and optimal real-time control action on a given controlled object. The designed controller, called the Fuzzy-ACS PID controller, was used to control the CIP-I intelligent leg. The simulation experiments demonstrate that this controller has good control performance. Compared with other three optimal PID controllers designed respectively by using the differential evolution algorithm, the real-coded genetic algorithm, and the simulated annealing, it was verified that the Fuzzy-ACS PID controller has better control performance. Furthermore, the simulation results also verify that the proposed ACS algorithm has quick convergence speed, small solution variation, good dynamic convergence behavior, and high computation efficiency in searching for the optimal input/output scaling factors.

Motivation: In designing linear feedback systems, tracking quality specifications are typically mapped into admissible domains in the complex plane and then the root locus technique is used to synthesize a controller that places closed loop poles in the desired locations. This methodology motivates the first goal of this chapter: to generalize the notion of admissible domains and the root locus technique to LPNI systems. Accomplishing this goal leads to a quasilinear method for PID controller design.

A PID controller design method through IMC scheme to work in Smith predictor configuration for processes having long dead time is presented in this paper. The Smith predictor controller is obtained via IMC scheme, and then the PID controller is derived by frequency response matching. As the approximation of the controller is involved in frequency domain, the method is applicable for both high-order and low-order processes. The efficacy of the method is illustrated through simulation of different examples and performance improvement is observed.

In this paper, a frequency response based design method of PID controller is proposed for higher order (HO)/-plus delay time (HOPDT) systems. The HO/-PDT models are converted into real and imaginary part at a frequency where a criteria similar to amplitude and phase margin is utilized to get the constraints on the parameters of the controllers. To reject noise and load disturbances, the constraints given by sensitivity and complementary sensitivity function are also considered. The proposed method has superior features for systems with high order, time delays and monotonic or oscillatory responses. Three simulation examples are included to show the effectiveness, simplicity and applicability of the proposed method.

This paper compares two approaches to tune PI controllers in a multivariable process. A modified Direct Synthesis method extends the technique to a multivariable system. Results show that the modified Direct Synthesis technique relies on model accuracy and suitability of the desired transfer function and process model. The effectiveness of this technique may break down when these conditions are not met. Genetic algorithms provide a method based on the evolution of species via natural selection. The GA method allows the use of a specific structure, such as PI controller, and then gets the best possible results for that structure. The concept has been adapted into an optimization technique that can be used to find the best controller parameters to meet user defined transient specifications for a complex process. Thus, the robustness of the method allows it to outperform the former technique. Simulation results are shown to illustrate the comparisons between these two methods and the effectiveness of Gas.

This paper proposes a small-sized two-wheeled Unmanned Aerial Vehicle(UAV) in order to get into and visually inspect a narrow part, for example, a bridge bearing. First, we present the two-wheeled multi-copter loading with a digital control device to downsize the wheel of the size of 66cm to size of 25cm. Second, for high accuracy positioning of inspection, a new design method of the optimal digital PID controller for the multicopter is proposed. The optimal controller minimizes a cost functional. The design method is reduced to the standard LQR method and is straightforward. The effectiveness is demonstrated by some flight experiments moving on a wall.

This paper proposes a fractional order PID analytical design framework for industrial robot based on digital twin. The effectiveness of the digital twin real-time optimization framework is verified by the simulation of PMSM motor speed control. The digital twin framework implemented in this paper consists of three following parts: multi-domain modeling, behavioral matching and control optimization. Firstly, the physical system is modeled to realize the omni-directional monitoring of robot and the kinematic simulation of single-axis motor. A model similar to the real physical system can be obtained in the step of behavioral matching, which is conducive to the next step of controller parameter optimization. The analytical design method of the five-parameter fractional order PID controller is then presented to optimize the parameters based on the accurate model after behavioral matching, so that the control system can meet the given frequency domain specifications and the required tracking performance. The simulation results show that the fractional order PID controller is robust to loop gain changes. In terms of time domain performance specifications like rise time, overshoot, and adjustment time, fractional order PID controller performs better than integer order PID controller.

The potential of symbolic algebra for the design of control systems is illustrated through several examples. It has been shown in particular, that (a) the exact calculations provided by symbolic algebra can be used to utilize some of the direct (but numerically error prone) methods efficiently in control system design, and (b) symbolic manipulations by a computer can help control engineers at several stages of the design. The block diagram reduction, calculation of all stabilizing controllers, dominant pole assignment and robust pole assignment are taken as case studies.

This paper presents a guide of design procedure for an Unmanned Areal Vehicle quadrotor construction based on PID controller. The procedure includes system modeling with Euler angles, components choice and identification and PID controller synthesis. Simulation results and experimental validation for free flight in outdoor are presented to show the effectiveness of the proposed procedure.