ControlSoft Inc., USA.
ISA Trans. 2010 Oct;49(4):519-27. doi: 10.1016/j.isatra.2010.03.012. Epub 2010 May 14.
Internal model-based control (IMC) has been shown to possess many advantages over PID control, particularly in the presence of significant process deadtime. Implementation of IMC is simplified in a large class of industrial applications where the process dynamics can be adequately characterized by a simple first-order model requiring only estimates of process gain, lag time constant, and deadtime for implementing the controller design. Tuning of the controller is easily and intuitively done by adjusting the filter time constant; decreasing the time constant speeds up the closed-loop response, and increasing it yields generally a slower but more stable response. There are problems, however, in applying the IMC approach to an integrating process, i.e., a process with a pole at the origin. First, for a first-order lag filter, the steady-state error due to a process input disturbance is generally non-zero. This error can be reduced to zero with a higher-order lead lag filter with proper choice of filter parameters. This is at a cost, however, of increased design complexity, amplification of noise in the controller signals, and a potential numerical overflow issue due to an integrator within the IMC computation loop. To overcome these problems, an alternative IMC implementation is proposed where the integrator in the model is approximated by a first-order lag with a very large time constant. It is shown analytically and verified by computer simulation that this approach assures zero steady-state error for setpoint (SP) changes and process disturbance inputs. Computer simulation studies also show that the transient response can be satisfactorily tuned by proper choice of the filter time constant and that potential numerical instability issues are essentially eliminated. Further, since the choice of time constant in the lag used to approximate the integrator function in the modified IMC also affects the PV(t) response approach, another degree of freedom in the tuning process is introduced. This modified IMC approach has been used successfully in several real-world applications.
内模控制（IMC）相对于 PID 控制具有许多优势，尤其是在存在显著过程滞后时。在很大一类工业应用中，过程动态可以用一个简单的一阶模型来充分描述，该模型只需要估计过程增益、滞后时间常数和死区时间，就可以实现控制器设计。通过调整滤波器时间常数，可以轻松直观地对控制器进行调谐；减小时间常数会加快闭环响应速度，而增加时间常数则会导致响应速度变慢但更稳定。然而，将 IMC 方法应用于积分过程（即具有原点极点的过程）存在一些问题。首先，对于一阶滞后滤波器，由于过程输入干扰引起的稳态误差通常不为零。通过选择适当的滤波器参数，可以使用更高阶的超前滞后滤波器将误差降低到零。然而，这需要增加设计复杂性、放大控制器信号中的噪声，并且由于 IMC 计算循环中存在积分器，可能会出现数值溢出问题。为了克服这些问题，提出了一种替代的 IMC 实现方法，其中模型中的积分器用具有非常大时间常数的一阶滞后来近似。通过分析和计算机仿真验证，这种方法可以确保设定值（SP）变化和过程干扰输入的稳态误差为零。计算机仿真研究还表明，通过适当选择滤波器时间常数，可以对瞬态响应进行满意的调谐，并且基本上消除了潜在的数值不稳定性问题。此外，由于在修改后的 IMC 中用于近似积分器功能的滞后中选择的时间常数也会影响 PV(t)响应逼近，因此在调谐过程中引入了另一个自由度。这种改进的 IMC 方法已成功应用于多个实际应用中。
