Enhancing the performance of parallel cascade control using Smith predictor

Parallel cascade controllers are used in chemical processing industries to improve the dynamic performance of a control system in the presence of disturbances. In the present work, a delay compensator has been incorporated in the primary loop of the parallel cascade control system. The secondary controller is designed using the internal model control (IMC) method. The primary controller is designed based on a direct synthesis method for the delay-free system. Design of controllers for slow (when the secondary loop dynamics is slow i.e. process contains poles sufficiently slower than the desired closed loop response) as well as fast dynamics (when the inner loop dynamics is fast i.e. process contains poles sufficiently faster than the desired closed loop response) of the secondary process is considered. The method provides robust control performances. Significant improvement in the closed loop performances are obtained with the delay compensator over that of a conventional parallel cascade control system. Several case studies are considered to show the advantage of the proposed method when compared to other recently reported methods.     

A frequency response model matching method for PID controller design for processes with dead-time

In this paper, a PID controller design method for the integrating processes based on frequency response matching is presented. Two approaches are proposed for the controller design. In the first approach, a double feedback loop configuration is considered where the inner loop is designed with a stabilizing gain. In the outer loop, the parameters of the PID controller are obtained by frequency response matching between the closed-loop system with the PID controller and a reference model with desired specifications. In the second approach, the design is directly carried out considering a desired load-disturbance rejection model of the system. In both the approaches, two low frequency points are considered for matching the frequency response, which yield linear algebraic equations, solution of which gives the controller parameters. Several examples are taken from the literature to demonstrate the effectiveness and to compare with some well known design methods.     

Design of PID controllers in double feedback loops for SISO systems with set-point filters

A PID controller is widely used to control industrial processes that are mostly open loop stable or unstable. Selection of proper feedback structure and controller tuning helps to improve the performance of the loop. In this paper a double-feedback loop/method is used to achieve stability and better performance of the process. The internal feedback is used for stabilizing the process and the outer loop is used for good setpoint tracking. An internal model controller (IMC) based PID method is used for tuning the outer loop controller. Autotuning based on relay feedback or the Ziegler-Nichols method can be used for tuning an inner loop controller. A tuning parameter (λ) that is used to tune IMC-PID is used as a time constant of a setpoint filter that is used for reducing the peak overshoot. The method has been tested successfully on many low order processes.     

Stabilizing frequency weighted controller reduction approach

This note addresses the problem of instability in frequency weighted controller reduction methods based on similarity transformations. The aim is to reduce the complexity of the controllers derived by modern controller design packages for practical applications. For a given controller a framework is proposed that parameterizes a set of reduced controllers that preserve the stability of the closed loop system. Then based on this result a complementary algorithm to obtain a stabilizing stable reduced controller based on the two sided frequency weighted reduction method is presented. In addition, a sufficient condition for the existence of such a framework is derived.     

A new approach to design of a dynamic output feedback stabilizing control law for LTI systems

We present a new state-space approach to construct a dynamic output feedback controller which stabilizes a class of linear time invariant systems All the states of the given system are not measurable and only the output is used to design the stabilizing control law In the design scheme, however, we first assume that the given system can be stabilized by a feedback law composed of the output and its derivatives of a certain order Beginning with this assumption, we systematically construct a dynamic system which removes the need of the derivatives The mam advantage of the proposed controller is regarding the controller order, which may be smaller than that of conventional output feedback controller Using a simple numerical example, it is shown that the order of the proposed controller is indeed smaller than that of reduced-order observer based output feedback controller     

Analytical fractional PID controller design based on Bode’s ideal transfer function plus time delay

In this paper, a fractional order PID controller cascaded with a fractional filter is proposed for higher order processes. In this analytical design methodology, one or two reduced fractional orders plus time delay models are used to represent higher order system transfer functions. The controller parameters are determined so as to meet certain frequency domain specifications. A unity feedback reference model is employed where Bode’s ideal loop transfer function plus time delay of the fractional order model is placed in the forward path. The addition of this time delay provides the exact determination of frequency domain specifications if the system either intrinsically owns a time delay or a time delay is injected by its reduced order model. The proposed methodology is compared with two other related methodologies and it has been observed that the proposed controller performs much better than the others. Moreover, some empirical formulas for time domain characteristics of the reference model are numerically derived in terms of certain frequency domain specifications and time delay of the fractional reduced order model. The accuracy of these formulas is tested by simulations. The iso-damping, noise attenuation and load disturbance suppression performances of the proposed controller are also considered and compared with those of other related controllers.     

Robust MPC-based current controller against grid impedance variations for single-phase grid-connected inverters

Recently, LCL filters have been widely used in the output of single phase inverters. Since, the grid side inductor in these filters is in series with the grid impedance at the Point of Common Coupling (PCC), it may create new resonances. This phenomena may take the control loop toward instability. In this case, in order to have a reliable operation, the current controller should be insensitive to the grid impedance variation. In order to damp these resonances, researchers have presented some methods using active or passive damping. These methods added an extra loop to the control loop, an extra passive component in the filter or extra sensor in the control process. But in most of them, the complexity and the cost of controller have been increased. Therefore, presenting a simple control method without extra sensor, passive component or extra arrangement can be a promising approach. This paper presents an MPC-based current controller, which is simple and robust against the grid impedance variation and even the variation of the LCL filter parameters. In contrast to classical multi-loop controller like Proportional-Resonant (PR) controllers, the proposed control method does not need any parameter tuning. In the proposed controller, the switching plan and duty cycles are determined by a cost function and a switching table. Therefore, at the same time with any variation in grid impedance, the proposed controller changes the next switching state and duty cycle. Operating performance like look-up table, searching in all possible switching states to find the best state for the next switching period, makes the controller adaptive and robust against the variation of LCL filter parameters. In order to confirm the effectiveness of the proposed controller, simulations and experimental results of the proposed controller are compared with a classical PR controller.     

Computation of stabilizing PI and PID controllers for processes with time delay

In this paper, a new method for the computation of all stabilizing PI controllers for processes with time delay is given. The proposed method is based on plotting the stability boundary locus in the (kp, ki) plane and then computing the stabilizing values of the parameters of a PI controller for a given time delay system. The technique presented does not need to use Pade approximation and does not require sweeping over the parameters and also does not use linear programming to solve a set of inequalities. Thus it offers several important advantages over existing results obtained in this direction. Beyond stabilization, the method is used to compute stabilizing PI controllers which achieve user specified gain and phase margins. The proposed method is also used to design PID controllers for control systems with time delay. The limiting values of a PID controller which stabilize a given system with time delay are obtained in the (kp, ki) plane, (kp, kd) plane, and (ki, kd) plane. Examples are given to show the benefits of the method presented.     

Composite fuzzy sliding mode control of nonlinear singularly perturbed systems

This paper deals with the robust asymptotic stabilization for a class of nonlinear singularly perturbed systems using the fuzzy sliding mode control technique. In the proposed approach the original system is decomposed into two subsystems as slow and fast models by the singularly perturbed method. The composite fuzzy sliding mode controller is designed for stabilizing the full order system by combining separately designed slow and fast fuzzy sliding mode controllers. The two-time scale design approach minimizes the effect of boundary layer system on the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. The simulation results show improved system performance of the proposed controller as compared to existing methods. The experimentation results validate the effectiveness of the proposed controller.     

Robust stabilization of uncertain nonlinear slowly-varying systems: Application in a time-varying inertia pendulum

This paper considers the problem of robust stabilization of nonlinear slowly-varying systems, in the presence of model uncertainties and external disturbances. The main contribution of this paper is an extension of the Slowly-Varying Control Lyapunov Function (SVCLF) technique to design a robust stabilizing controller for nonlinear slowly-varying systems with matched uncertainties. In the proposed strategy, the Lyapunov redesign method is utilized to design a robust control law. This method, originally, leads to a discontinuous controller which suffers from chattering. In this paper, this problem is removed by using a saturation function with a high slope, as an approximation of the signum function. Since, using the saturation function leads to loss of asymptotic stability and, instead, guarantees only the boundedness of the system's states; therefore, some sufficient conditions are proposed to guarantee the asymptotic stability of the closed-loop uncertain nonlinear slowly-varying system (without chattering). Also, in order to show the applicability of the proposed method, it is applied to a time-varying inertia pendulum. The efficiency of the designed controller is demonstrated through analysis and simulations.     

Fractional order phase shaper design with Bode’s integral for iso-damped control system

The phase curve of an open loop system is flat in nature if the derivative of its phase with respect to frequency is zero. With a flat-phase curve, the corresponding closed loop system exhibits an iso-damped property i.e. maintains constant overshoot with the change of gain. This implies enhanced parametric robustness e.g. to variation in system gain. In the recent past, fractional order (FO) phase shapers have been proposed by contemporary researchers to achieve enhanced parametric robustness. In this paper, a simple methodology is proposed to design an appropriate FO phase shaper to achieve phase flattening in a control loop, comprising a plant controlled by a classical Proportional Integral Derivative (PID) controller. The methodology is demonstrated with MATLAB simulation of representative plants and accompanying PID controllers.     

Autotuning of a new PI-PD Smith predictor based on time domain specifications

The paper extends a recent work on a modified PI-PD Smith predictor, which leads to significant improvements in the control of processes with large time constants or an integrator or unstable plant transfer functions plus long dead time for reference inputs and disturbance rejections. Processes with high orders or long time delays are modeled with lower order plant transfer functions with longer time delays. The PI-PD controller is designed so that the delay-free part of the system output will follow the response of a first-order plant or second-order plant, where it is appropriate, assuming a perfect matching between the actual plant and model in both the dynamics and time delay. The provided simple tuning formulas have physically meaningful parameters. Plant model transfer functions and controller settings are identified based on exact analysis from a single relay feedback test using the peak amplitude and frequency of the process output. Examples are given to illustrate the simplicity and superiority of the proposed method compared with some existing ones.     

A hybrid intelligent controller for a twin rotor MIMO system and its hardware implementation

This paper presents a fuzzy PID control scheme with a real-valued genetic algorithm (RGA) to a setpoint control problem. The objective of this paper is to control a twin rotor MIMO system (TRMS) to move quickly and accurately to the desired attitudes, both the pitch angle and the azimuth angle in a cross-coupled condition. A fuzzy compensator is applied to the PID controller. The proposed control structure includes four PID controllers with independent inputs in 2-DOF. In order to reduce total error and control energy, all parameters of the controller are obtained by a RGA with the system performance index as a fitness function. The system performance index utilized the integral of time multiplied by the square error criterion (ITSE) to build a suitable fitness function in the RGA. A new method for RGA to solve more than 10 parameters in the control scheme is investigated. For real-time control, Xilinx Spartan II SP200 FPGA (Field Programmable Gate Array) is employed to construct a hardware-in-the-loop system through writing VHDL on this FPGA.     

Fuzzy control of multivariable process by modified error decoupling

In this paper, a control concept for the squared (equal number of inputs and outputs) multivariable process systems is given. The proposed control system consists of two parts, single loop fuzzy controllers in each loop and a centralized decoupling unit. The fuzzy control system uses feedback control to minimize the error in the loop and the decoupler uses an adaptive technique to mitigate loop interactions. The decoupler predicts the interacting loop changes and modifies the input (error) of the loop controller. The controller was tested on the simulation model of "single component vaporizer" process. The results indicate that the decoupling controller shows better performance for set point and load changes.     

Multi-loop control of UPS inverter with a plug-in odd-harmonic repetitive controller

This paper proposes an improved multi-loop control scheme for the single-phase uninterruptible power supply (UPS) inverter by using a plug-in odd-harmonic repetitive controller to regulate the output voltage. In the suggested control method, the output voltage and the filter capacitor current are used as the outer and inner loop feedback signals, respectively and the instantaneous value of the reference voltage feedforwarded to the output of the controller. Instead of conventional linear (proportional-integral/-resonant) and conventional repetitive controllers, a plug-in odd-harmonic repetitive controller is employed in the outer loop to regulate the output voltage, which occupies less memory space and offers faster tracking performance compared to the conventional one. Also, a simple proportional controller is used in the inner loop for active damping of possible resonances and improving the transient performance. The feedforward of the converter reference voltage enhances the robust performance of the system and simplifies the system modelling and the controller design. A step-by-step design procedure is presented for the proposed controller, which guarantees stability of the system under worst-case scenarios. Simulation and experimental results validate the excellent steady-state and transient performance of the proposed control scheme and provide the exact comparison of the proposed method with the conventional multi-loop control method.     

超精密微动台控制器带宽优化研究

为提高超精密微动台的控制带宽,改善控制性能,针对微动台模型包含机械谐振以及时滞的特性研究一种优化回路成形(Optimized loop shaping,OLS)控制器设计方法。通过回路成形方法分析得出PID控制器相位超前量不足是造成带宽受限的主要因素,并给出一种能实现高带宽的高阶控制器。利用回路成形(Loop shaping,LS)设计方法将控制器参数设计描述为优化问题,并利用遗传算法对其进行求解。将OLS控制器与试验整定的PID控制器进行试验对比,结果显示采用OLS控制器的系统的上升时间、调整时间、定位精度都有较大幅度地改善,最大超调量有所增加但仍在工程允许的范围内,表明所提出方法能够减小控制器设计对经验的依赖并有效提高地超精密微动台的控制性能。     

Set-point manipulation approach towards online performance improvement in existing process control loops

The majority of current industrial process control systems are based on PID control. However, in many of these systems, once the initial setup has been carried out, it is difficult to implement subsequent continuous improvements on the control performance without shutting down the production and disarming the overall system to retrofit alternative controllers. These measures to integrate additional instruments for allowing such flexibility incur heavy costs in terms of time and resources. In this paper, we propose an approach towards achieving the control adaptations which cannot be achieved easily with an existing closed-architectural system. The approach leverages on a set-point manipulation mechanism which allows a virtual modification of the closed-architectural system. In this way, process performance of existing plants can be continuously improved without the need to continuously alter the existing closed loop system. The implementation of the proposed configuration is illustrated with respect to a PID controller although the framework proposed is amenable to higher order controller as well. Simulation examples and experimental results are furnished to show the motivation for such an approach and the improved performance achievable with the proposed approach.     

Robust stabilizing first-order controllers for a class of time delay systems

In this paper, stabilizing regions of a first-order controller for an all poles system with time delay are computed via parametric methods. First, the admissible ranges of one of the controller’s parameters are obtained. Then, for a fixed value of this parameter, stabilizing regions in the remaining two parameters are determined using the D-decomposition method. Phase and gain margin specifications are then included in the design. Finally, robust stabilizing first-order controllers are determined for uncertain plants with an interval type uncertainty in the coefficients. Examples are given to illustrate the effectiveness of the proposed method.     

无辨识预估PSD控制

针对原无辨识PSD的不足，本文提出了PSD参数的同步自适应方法，计算量小，且对于均值为零的测量噪声具有更强的抗噪能力。为了更好地应用于时滞过程，利用无时滞PSD系统渐近稳定的特点，提出了无预估模型的PSD自适应预估控制算法。仿真和实验验证了算法的有效性。     

Relay-enhanced multi-loop PI controllers

In this paper, the development of relay-enhanced multi-loop PI controllers is described for multivariable processes. The control system employs a relay in series with the controller. The relay can ensure a satisfactory level of closed-loop performance and it also yields oscillations for tuning of the PI controller based on an equivalent process model for each loop. A simulation example [on a two-inputs-two-outputs (TITO) process] is provided to illustrate the effectiveness of the proposed method and to compare its performance to an existing method.